The Editorial board wishes to thank the following institutions for help and sponsorship : UNESCO, IMU, Comité National Français des Mathématiciens, Collège de France, École Polytechnique, Institut des Hautes Études Scientifiques, Institut de Mathématiques (Jussieu), UFR 921 (Université Pierre et Marie Curie).

WMY2000 EDITORIAL BOARD

## EDITORIAL BOARD

Prof. A. A. Ashour

Prof. Mohammed H. A. Hassan

Prof.Mitsuo Morimoto

Prof. Mogens Niss

Prof. Rolando Rebolledo

Chairman CDE
SANTIAGO DE CHILE (Chile)
e-mail : This email address is being protected from spambots. You need JavaScript enabled to view it.

Prof. Anna Sierpinska

Prof. Mireille Chaleyat-Maurel

Prof. Gérard Tronel

Université Pierre et Marie Curie
Laboratoire d'Analyse Numérique, tour 55 5ème étage
4, Place Jussieu
F-75252 PARIS Cedex 05 (France)
e-mail : This email address is being protected from spambots. You need JavaScript enabled to view it.

## Fifth Forum of Young Women Mathematicians

The "Fifth Forum of Young Women Mathematicians" ("Cinquième Forum des Jeunes Mathématiciennes") was held at the Institut Henri Poincaré in Paris, France, on Friday and Saturday, January 21-22, 2000. This annual meeting is an excellent occasion for scientific exchange and gives young researchers the opportunity to present their work in a stimulating environment. This year, it was part of the French program for the WMY2000 Project (World Mathematical Year 2000), also sponsored by UNESCO. The forum always consists of a scientific part, which gives an overview of the current state of mathematical research, and a historical-sociological part, which is intended to stimulate debates on current issues of women in the scientific community. This year, the scientific talks were given by twelve young mathematicians and six established mathematicians from all over France and Europe. The first debate was introduced by historians Delphine Gardey and Michelle Perrot, and followed the talk "Historical approach to relations between women, science and technology" by Delphine Gardey. The second debate, "Parity in the scientific community", was introduced by Claudine Hermann (Professor at the Ecole Polytechnique and member of E.T.A.N.) who reported on the activity of the European community about the question of Women and Science.

The forum program is available at the web-site:

http://www.desargues.univ-lyon1.fr/home/fem/agjan00.html

This meeting was organized by the association "femmes et mathématiques"

http://www.desargues.univ-lyon1.fr/home/fem/fem.html

## Macau, 11-14 January 2000

Mathematics occupies a crucial and unique role in the human societies and represents a strategic key in the development of the whole mankind. The ability to compute, related to the power of technology and to the ability of social organisation, and the geometrical understanding of space-time, that is the physical world and its natural patterns, show the scientific and cultural role of Mathematics in the history of Civilisation and in the future development of the Information Society.

With the aim of celebrating this theme, the first international conference held in the World Mathematical Year 2000 was organised by a Portuguese-Chinese committee, chaired by Iu Vai Pan, Rector of the University of Macau that hosted the meeting. The international scientific committee, chaired by J.-L. Lions former IMU President, selected a number of invited speakers and three main topics for the round tables on Mathematics, History and Culture, Technology and Development and Computers and Information Society, respectively.

Some of the main aspects of the conference subject were illustrated, from an historical perspective, by Wu Wen-Tsun (Beijing) and Hsiang Wu-Yi (Hong-Kong) with tentative comparisons of the mathematical achievements in ancient Chinese and ancient Greece, by Luis Saraiva (Lisboa) with an overview of the growing use of mathematical techniques during the Age of Discoveries with a reference to the Portuguese seafarers and scientist of the 15th and 16th centuries and their contributions, and by Qi Minyou (Wuhan) that described the Chinese translation of the Euclid's "Elements" initiated in the beginning of the 17th century with the aid of M.Ricci. The choice of the city of Macau for this conference honours its significant historical role as a bridge of commercial and cultural exchanges between the East and Western civilisations, since the beginning of the Portuguese presence in 1557, and its future continuation after the return to China the 20 December 1999. Partial topics of contemporary mathematics were illustrated by Constantine Dafermos (Providence), that surveyed aspects of the theory of partial differential equations, over the past century, highlighting the close interaction with physics and technology, by Irene Fonseca (Pittsburgh) that referred new developments in the calculus of variations and current issues in phase transitions and image segmentation in computer vision, by Jean Mawin (Louvain) that treated spectral theory and its role in functional analysis and non-linear problems in theoretical physics, and by Alfio Quarteroni (Lausanne and Milano) that illustrated the increasing importance of mathematical models in life sciences with the example of analysis of cardiovascular diseases.

The development of research in mathematics in several countries and how socio-economic factors favour or hinder it, was examined by M.N. Narashimhan (Bombay and Trieste), the role of numerical and non-numerical tools in the modelling of technological processes was analysed by E.R. de Arantes e Oliveira (Lisboa) and several aspects of the cross-fertilisation between computer science and mathematics, including examples related to fundamental data structures and database algorithms, computational geometry and number theory, or communication protocols, were illustrated by Philippe Flajolet (Paris).

• The round table on Mathematics, History and Culture, organised by J.F. Queiro' (Coimbra), had its focus on important moments of the mathematical past and present on social, cultural and philosophical problems, included topics such as mathematical museology by E. Giusti (Firenze), mathematics and music by J.F.Rodrigues (Lisboa), history on Indian mathematics by Bhadra Man Tuladhar (Kathmandu) and aspects of the mathematical thinking, practices and categories by E. Knobloch (Berlin).
• The round table on Mathematics, Technology and Development, organised by A. Damlamian (Paris), illustrated the role of mathematics in the technological development of their country or region with the presentation of personal views of how future developments are envisaged in the beginning of the 21st century. The participants came from Australia, N. Barton (Sydney), from the USA, A. Friedman (Minneapolis), from China, Li Ta-tsien (Shanghai) and from Europe, R. Jeltsch (Zurich).
• Finally the round table on Mathematics, Computers and Information Society was organised by Zhou Chaochen (Macau), director of the International Institute for Software Technology of the United Nations University. In addition to C.Zhou, that presented some examples of the impact of mathematical logic in computer science, E. Neuwirth (Vienna) illustrated recent aspects of computer supported didactic of mathematics, P. Veiga (Lisboa) referred the new paradigms and new skills of life in the Information Society and G. Kahn (Paris) emphasised the role of mathematics and computer science in the Society of Knowledgement.

The overall outcome of this conference will appear in book form and has contributed not only to highlight significant aspects of the contents and meaning of Mathematics as a driving force in human progress, but also to show the role of the contribution that Mathematics had played and will continue to play in History as a major factor for the development of an increasingly global world and civilisation.

José Francisco Rodrigues (Director of the Centro de Matematica e Aplicacoes Fundamentais and Professor of Mathematics at the University of Lisbon)

## Final Report

The Conference on Mathematics and the Century was held in Cairo-Egypt during the period 15-20 January 2000. The Conference was an event of the WMY2000 initiative launched by the International Mathematical Union. The Conference was hosted in the Tiba Rose hotel in Cairo where most of the foreign participants were lodged.

I. Scientific activities:

The Conference was opened at 10AM on January 15, 2000. The opening ceremony was, attended by H.E. Prof. Dr. Mofeed Shehab, Egyptian minister of scientific research. In addition, Prof. M. Yosry president of the Egyptian Academy for Science and Technology (ASRT), Prof. Jacob Palis, President of the International Mathematical Union (IMU), and also representing the Third World Academy of Science (TWAS), Prof. M. El-Deek, Head of the UNESU Regional Office for Science and Technology for the Arab States (ROSTAS) addressed the conference. A message of good wishes from Prof. M. Verasoro Director of Abdus Salam International Centre for Theoretical Physics was delivered by Prof. A. Ashour chairman of the conference. The opening session was followed by the Millenium lecture, delivered by Sir Michael Atiyah. The title of the lecture was " A Thousand Years of Mathematics".

• The conference's sessions consisted of 11 plenary lectures and of 24 topical sessions. Some of the plenary lectures covered general fields are:    Rewriting the history of mathematics,  Education of mathematics,   Relation between Mathematics and  Sciences " Is  Interdisciplinary Research Possible? ",  Mathematical Aspects of Transportation.  General reviews of the recent researches and standing problems were also   delivered. In this aspect the following lectures are relevant:  A global view of dynamical systems;  Einstein's theory of space-time and gravitation;  A geometrical theory for the unification of all fundamental forces;  Transfer of energy from low frequency to high frequency modes;  Stratification of algebras;  Multivariate statistical distributions.
• Each topical session comprised an invited 40-minute talk and 3-4 contributed papers. The invited topical lectures covered:  Finite groups,  Radical theory;  Enumerative geometry; Moduli problems in geometry;  Asymptotic behaviour of solutions of evolution equations; Instability of nonlinear evolution equations;  Non-smooth dynamical systems;  On approximations of functions;  On a semi-analytic method for the solution of some elliptic B.V.P;  On robust layer resolving methods for computing numerical approximations; Eigen values for fractal drums;   Electrostatic models and orthogonal polynomials;  On the developments on theory of functions of several complex variables; Invertibility preserving linear maps; Entire functions sections;   Optical solitons; Non-classical properties of intermediate states;  On the relativistic 2-body problem; Singularities in general relativity; Linear geometry of light cone;  Advances and new results in prediction;  and Theory of accelerated experiments.
• The topical sessions were grouped in the following sections: Algebra (4), Applied mathematics (4),  Computer Science, and Operational research, Analysis (4),  Analysis and diff. eqn.  Quantum theory (2),  Statistics; Numerical analysis,  Relativity(2) and  geometry,  Optimization and control , Topology.  The plenary and invited topical lectures covered a broad spectrum of research in mathematics and its applications together with the history of Mathematics and Mathematics Education. Details of the program can be found in the web site http://wmy2000.math.jussieu.fr/Cairo/cairo2000.html

The Conference offered a unique opportunity for mathematicians from Egypt, and nearby countries to have an overview of the actual status of research in many areas of the mathematical sciences and to tighten connections with their colleagues in other countries. The Conference was attended by 132 participants, coming from 19 countries, including 11 invited plenary speakers and 24 invited topical speakers. For a complete list of participants and the distribution of participants by country see web site http://wmy2000.math.jussieu.fr/Cairo/cairo2000.html In the closing ceremony at 5.00 PM on Jan 20,2000, Prof. Narasimhan the Director of Mathematics in ICTP gave a short speech and Prof. Ali H. Nayfeh of Virginia Polytech. USA spoke for the invited speakers and Prof. Ashour chairman of the conference gave some concluding remarks.

## I RAISING PUBLIC AWARENESS OF MATHEMATICS

by Vagn Lundsgaard Hansen, chair of EMS--committee on WMY 2000

Raising Public Awareness of Mathematics (RPAMaths) is probably the most important goal originally set for the World Mathematical Year 2000. And there are good reasons for that. The role of mathematics in society is subtle and not generally recognized in the needs of people in everyday life and most often it remains totally hidden in scientific and technological advancements. The old saying The one who lives hidden lives best" is not true in present day society. If a subject becomes invisible, it may soon be forgotten and eventually it may even disappear.

Mathematics has a prominent place in school curricula all over the world and probably nobody can imagine such a fate for our subject. But if we do not constantly care about the image of mathematics, we will see continuing pressures to lower the amount of mathematics at primary schools, secondary schools and at the university level. Mathematics is exciting to many people but at the same time is considered difficult and somewhat inaccessible by more. Since mathematics is a fundamental cornerstone in several diverse areas of society, it is important for civilization as a whole that mathematicians do their utmost to help explaining and clarifying the role of mathematics.

In the back of their minds most people find that mathematics is important, but they may have forgotten why. We have to find ways of informing them. Displaying posters with mathematical messages at public places, making videos, producing booklets, arranging exhibitions and activities related to mathematics, in particular to the contents of the posters, can prove to be very effective in such an endeavour.

Indeed we hope so. On March 3--5, 2000 the European Mathematical Society organized a meeting in Paris between the partners in a contract with the European Commission under the program Raising Public Awareness of Science and Technology, where such things were on the agenda. There are two other partners in the contract, a team in Paris under direction of professor Mireille Chaleyat-Maurel and a team in Bangor, UK, under direction of professor Ronnie Brown. The main impact of the coordinated campaign resulting from the contract should be obtained during the European Science and Technology Week, November 6--12, 2000, but much of the material prepared for the campaign will undoubtedly be useful in many other contexts for years to come.

In the spring of 1999, the European Mathematical Society arranged a competition to encourage the idea of creating posters with a mathematical theme that would catch the eye and be representative of mathematics and its uses. The posters submitted for the competition are now included in a web-gallery: http://www.mat.dtu.dk/ems-gallery .

Several of the posters from the competition have already been used, or will be used, in various contexts. At the moment, I know of such uses of ideas in the posters from the competition in Canada, Germany, France, UK, Italy, Portugal, Spain and Denmark. The posters from the EMS-competition and several other posters were presented and discussed intensely during the meeting. By the end of the meeting a brainstorm was conducted to bring forward even more ideas.

The Paris team is responsible for the final selection and production of the posters to be used during the European Science and Technology Week. I am confident that the team shall produce some graphically attractive and mathematically interesting posters to the general public. Electronic files of the posters will be made available for use in appropriate contexts.

The production of CD-roms and Video clips was presented by Ronnie Brown from the Bangor team, which is responsible for this part of the contract on RPAMaths. He was assisted by Mike Yates, who is the owner of the company SUMit Software, which will be doing the detailed work on the CD-roms. The progress can be followed on the web site for the project: http://www.bangor.ac.uk/ma/CPM/rpamath . Feedback is encouraged to improve the final result.

The experiences of the Bangor team gained in connection with their 1989 Exhibition Mathematics and Knots' and the subsequent web site building on sculptures and on knots in 1996-7 (links from the above rpamath site) are most valuable and makes me confident that the part of the RPAMaths project on CD-rom and Video clips will be successful. Also these products will be made available for appropriate uses.

To explain the contents of the posters, CD-roms and Video clips, small booklets will be produced and made available at relevant places.

The EMS-committee of the WMY 2000 is also interested in collecting knowledge of articles about mathematics appearing in major national newspapers in different countries; hopefully such articles can be translated into several languages and be of use in other countries. Material can be sent to me on the address mentioned below.

The RPAMaths project as a whole relies on considerable efforts of individuals in several European countries taking time out of their usual positions to work for this project. The contract with the European Commission is very much appreaciated as a means to get all this working, but clearly it covers only a modest part of the campaign compared to the collected efforts made by individual members of the mathematical community. We are greatly indepted to everybody working on making the World Mathematical Year 2000 a successful year.

Professor Vagn Lundsgaard Hansen Department of Mathematics Technical University of Denmark Building 303 Dk-2800 Kongens Lyngby Denmark, This email address is being protected from spambots. You need JavaScript enabled to view it.

## II Report for RPMath meeting, Paris, March 3-5, 2000.

Ronnie Brown and Mike Yates attended from Bangor. We both found the meeting very stimulating in meeting people, and in seeing the current achievements and future plans of our partners.

Mike's company SUMit Software is subcontractor to the project at Bangor, and will be doing the detailed work on the CDRoms, for which there has been considerable discussion on planning. Mike is an Honorary Professor at Bangor, and also Professor Emeritus at Manchester University, where he was Professor of Mathematical Logic till 1980. He now has ten years experience in educational software, part of it working with a strong multimedia company in Liverpool.

Mike has already redeveloped the web site for the project (http://www.bangor.ac.uk/ma/CPM/rpamath). Contributions to this, and comments, are welcomed, especially those which show the broad nature of the collaborations on this project. The web site is important for showing what is being done. Suggestions, comments, files, links,... should be sent to This email address is being protected from spambots. You need JavaScript enabled to view it..

Ronnie Brown gave a computer presentation explaining the methodological principles underlying the construction of the 1989 Exhibition Mathematics and Knots' by the Bangor team R. Brown, N.D. Gilbert, T. Porter. These principles were in two parts: (i) structure, and (ii) content.

(i)Structure: The exhibition was designed to be reproducible, transportable, not requiring management and supervision. We were fortunate to have excellent graphic design advice over the design period of four years to attain these ends.

(ii)Content: This we feel was the most original part. The title should really be Mathematics through Knots', since the aim was to explain some basic methods of mathematics to the general public. Thus part of the intention was to show mathematics as valuable in itself, and to show how the pursuit of these methods and aims led to applications which could not be seen from the start.

We also came to realise that the exhibition format is one of the hardest. It is not enough to show things, or ideas; there has to be an overlying philosophy, an intention on the impression that is to be conveyed to the viewer, and each aspect of the exhibition has to fit with that intention. Each board has to tell a story in itself, as far as possible by graphical means, and yet each board has to be related to the others.

It should now be clear why the development and realisation of this structure took four years!

The methods which were displayed through knots were: representation; classification; invariants; breaking a complicated object or procedure into simple parts; laws; analogy; applications. Part of the overall aims were: advanced mathematics from an elementary viewpoint; making mathematics concrete.

Putting the exhibition on the web in 1997 allowed the description of these aims, and much other material, to be incorporated into various levels of the hypertext, keeping the original boards at the top level. Thus the web format turns out to be a wonderful and flexible tool. An unforeseen consequence of making the exhibition was the collaboration with the sculptor John Robinson, and the web sites of his sculptures and the knot exhibition are expected to form a core of the CDROm(s) in preparation for the RPAMath project.

Acknowledgements: The main support for the original exhibition came from COPUS (Committee for the Public Understanding of Science), and for the web presentation from the Philip Trust and the London Mathematical Society.

## Challenges, Opportunities and Strategies for South-South Co-operation in Science and Technology in the 21st Century

Mohamed H.A. Hassan

Executive Director, Third World Academy of Sciences (TWAS)

Secretary General, Third World Network of Scientific Organizations (TWNSO)

## Introduction

The South enters the third millennium facing monumental challenges when it comes to efforts for economic progress and sustainable and equitable development. At the core of these challenges is the ability of the South to participate in and benefit from the rapid advances in scientific research and technological innovations that now drive economic and social development. These powerful forces are largely controlled by industrialized countries in the North and are mostly directed to address the problems and needs of rich countries. The South, as a whole, contributes little to modern science and technology. Yet, if acquired and properly utilized, new trends in science and technology offer immense possibilities for solving many of the problems impeding economic and social progress in the South.

The South must therefore intensify co-operative efforts to enhance its indigenous capacity to generate, manage and utilize science and technology in ways that address its own basic needs. For this to take place, regional and inter-regional efforts must be vigorously pursued. The ultimate goal of these efforts should be to develop collaborative programmes in capacity building for scientific education and research, and to establish new regional alliances among academia, governments and industries to address real-life problems.

This background paper discusses the challenges and opportunities for South-South co-operation in science and technology and presents several strategies for strengthening collaboration among developing countries. Such strategies, which must be firmly anchored to the best available science and technology in the South, are most likely to succeed through networked centres of excellence focusing on problems of common concern.

## Challenges to South-South Co-operation in Science and Technology

The most critical challenge facing the developing world is how to bridge the huge gap between the North and the South in the production and utilization of scientific and technological knowledge. Measured in terms of publications, the science-rich North, representing 20% of humanity, contributes more than 90% of the world’s share of current scientific knowledge; meanwhile, the science-poor South, representing 80% of humanity, generates less than 10% of this knowledge. In terms of technological output, measured by patents, the inequality is much greater. The South's 1995 share of patents, held by the two largest and most international patent systems in the USA and Europe, amounted to less than 1% of the world's total.

What is more disturbing is that the North-South divide in scientific output and technological innovations is constantly widening. On the one hand, the North, with its huge investments in research and development (R and D), is rapidly advancing the frontier of scientific knowledge. On the other hand, developing countries are spending small proportions of their gross domestic product (GDP)— often less than 1 percent — on R and D. Put another way, the world's total R and D expenditure in 1994 was about US-Dollar 470 billion; only 10% of that amount was attributed to the South. This makes it very difficult for the South to develop their capacity to catch-up.

Huge investments in scientific research and knowledge in the past 30 years have been the driving force behind the considerable wealth and high living standards now being enjoyed by the North. In 1995, the income share of the richest 20% of humanity was 86% of the world's total. Other statistics tell the same story. For example, the richest 20% of humanity's ratio of income compared to that of the poorest 20% of humanity rose from 30:1 in 1960, to 61:1 in 1991, to 82:1 in 1995.

Reducing these disparities will be a major challenge facing South-South co-operation in the 21st century. Previous efforts by national governments and international development agencies to overcome poverty and stimulate growth in developing countries have not recorded much success. Rapid globalization, driven by revolutionary advances in technology and information and communication systems and characterized by economic liberalization, free trade, and increased competition have often widened the gap between poor and rich nations. The impact of globalization on the composition of financial flows, for instance, has been dramatic. Overseas development aid, a major source of external funding for development projects in poor countries, slid from US$56.4 billion in 1990 to US$44.2 billion in 1996. At the same time, foreign direct investment and private financial flows soared from US$41.9 billion to US$256 billion. Such trends have benefited only a few developing countries with large economies. The primary challenge, then, is how South-South co-operation can help the majority of developing countries close the knowledge gap and effectively respond to and benefit from rapid globalization by enhancing their capacities in science, technology and knowledge. Such efforts will serve as cornerstones for the transition of the South to sustainable economic growth and development.

The second important challenge relates to finding solutions to the critical real-life problems confronting most Third World countries. Such problems include poverty; tropical diseases; food, energy and water shortages; and their adverse impacts on biological resources, climate and water quality. Harvard University economist, Jeffrey Sachs, contends that since poor countries are mostly located in ecological zones different from those in the North, they face different health and agricultural problems and that those differences are often a fundamental cause of persisting poverty. The challenge for South-South co-operation, therefore, is how to mobilize the best science in the South and elsewhere and direct it towards development problems in the developing world.

## Opportunities for South-South Co-operation in Science and Technology

The revolution in information and communication technologies has created unprecedented opportunities to narrow the knowledge gap between the North and the South by providing equitable access to the world's stock of scientific knowledge to everyone, everywhere. Through electronic mail and the internet, data can now be instantly transferred across vast distances, providing science-poor countries with the possibility of access to the latest scientific and technological information for addressing local and global problems. In fact, scientists in the South with internet facilities can now communicate easily with each other and their colleagues in the North to form new virtual networks and global research teams.

But many members of the world community cannot fully participate in and benefit from this information revolution. Unfavourable economic conditions and the high cost of wire-line infrastructure have made it difficult to provide these facilities to people in poor Third World countries, particularly those living in remote areas. The total number of telephone lines in the 48 LDCs is 1% of the number of lines in the USA. Only 1% of the world's telephone lines are in Africa and about half of these are in South Africa alone.

On the other hand, rapid advances in wireless digital systems based on satellites or cellular transceivers can provide a much less expensive and permanent solution to communication problems in developing countries. Among the many advantages of wireless telecommunication systems over wire-based systems are that they can be developed quickly and are not affected by natural hazards. Several developing countries — Argentina, Brazil and China, for instance — are investing heavily in digital communication systems. Telephone networks in such small countries as Botswana, Djibouti, Ghana, Maldives, Mauritius and Qatar, are now completely digital, bypassing the older wire-based systems and leapfrogging to this new technology. This trend deserves to be emulated by other developing countries. The new information age will soon make it possible for any scholar, teacher or student to acquire a cheap small portable computer that will provide access to virtually any source of information anywhere, anytime.

Another important opportunity relates to the applications of innovative techniques in biotechnology and genetic engineering to improve food production, preserve the environment and natural resources, and combat tropical diseases. Although most of the current research in this rapidly advancing field is carried out in the laboratories of the North, several developing countries, including Argentina, Brazil, China, Cuba, India, Mexico and Singapore, have established research programmes in modern biology and biotechnologies of high standard. These countries are in a strong position to assist others in the South to develop their local capacities in this vitally important field.

Still another opportunity for developing countries is related to the distribution of the world's natural resources. The developing world is blessed with vast natural resources and possesses most of the world's biodiversity, as well as much of the deeply rooted traditional knowledge associated with these genetic assets. The South, however, has not yet gained much from its natural riches. Many developing lack the scientific and technical skills and financial resources to protect and sustainably exploit these irreplaceable biological resources. In a world economy driven by globalization and competitiveness, the South will likely find its natural resources to be one of its best comparative advantages. Meanwhile, big multinational pharmaceutical and biotechnology companies in the North have expanded their bioprospecting and gene-hunting in developing countries. In 1990, world sales of medicine derived from plants discovered by indigenous people totalled US$43 billion. Yet, people in the South received little financial benefit from these commercial efforts. Similarly, the 1998 World Development Report noted that a unique plant in Madagascar used by a global pharmaceutical company to develop two anti-cancer drugs generated more than US$100 million in sales with no financial returns to the country. Such large developing countries as India, Brazil and China have devised biodiversity laws to protect their genetic resources from biopiracy. However, the trade-off between stricter protection laws — as called for by India and China — and relatively liberal legislation — as advocated by Brazil — must be carefully assessed against the ultimate goal of protecting local interests and encouraging foreign investment. Developing countries must work together to build their capacities in genomics science and develop skills in international property right and patent issues, to be able to negotiate bioprospecting agreements with foreign companies that would maximize the benefits to their economy and local communities.

## Strategies for South-South Co-operation in Science and Technology

Any strategy to promote South-South collaboration must bear in mind the diversity of countries in the South. These countries vary enormously in size. China has a population of 1.2 billion, almost twice the population of the 48 Least Developed Countries (LDCs). Some large countries, such as Argentina, Brazil, China, India, Mexico, South Africa and South Korea, have enviable records of scientific achievement compared to the others. A few — for example, South Korea, Malaysia, Singapore and China (Taiwan) — have made considerable economic and technological progress in recent years. Yet, many LDCs have not experienced significant development for some time. Nevertheless, regardless of their size and stage of development, every country in the South lags behind every country in the North in terms of wealth, scientific and technical productivity, and military power.

The most productive and beneficial South-South co-operation strategies are those anchored to the best science in the South. Without the full engagement of the South's most outstanding institutions and most accomplished scientists, South-South co-operation will not make a real difference. For this reason, it is necessary to develop a comprehensive audit of institutions and individuals that have achieved excellence in scientific research and training in the South. The Third World Network of Scientific Organizations (TWNSO), in collaboration with the Third World Academy of Sciences (TWAS) and the South Centre, recently took a major step in this direction when, in 1998, the three organizations published a book profiling the capabilities of 430 scientific institutions of excellence in 52 developing countries. These institutions have expressed a readiness to participate in regional, inter-regional and international networks, and scientific exchanges and training programmes for young scientists from developing countries other than their own. Many of the institutions have achieved levels of competence comparable to institutions in industrialized countries.

Human resources development should be a top priority in South-South co-operation strategies. The dearth of highly qualified scientists and technologists in most Third World countries has hampered the development and application of science and technology to the socio-economic needs in the South and has been a key factor behind the large number of foreign consultants in the LDCs. As Thomas Odhiambo, former president of the African Academy of Sciences, recently observed, roughly 100,000 high-level experts, equivalent to the number of foreign experts working in Africa, were part of Africa's brain drain during the 1990s.

Major efforts, therefore, should be mounted to fully utilize institutions of excellence in the developing world to train young scientists from countries with inadequate research and training facilities. To facilitate this goal, governments in the South and international development agencies should co-sponsor a massive programme of scholarships to enable students to pursue graduate and postgraduate education in these institutions. South-South co-operation in postgraduate training at institutions of excellence in the South has several advantages. Apart from being much less expensive than training in the North, it promotes the indigenous generation and application of knowledge and could help slow the brain-drain. Furthermore, training a new generation of scientists in Southern institutions will encourage these scientists to build scientific collaboration with their peers in the South and to build permanent links with the institutions at which they obtained their training.

An important initiative in this direction has recently been taken by the Third World Organization for Women in Science (TWOWS) in collaboration with the Third World Academy of Sciences (TWAS). With financial support from the Swedish Agency for Research Co-operation with Developing Countries (Sida-SAREC), a postgraduate fellowship programme has been established to enable young female students from the LDCs to pursue their PhD studies at centres of excellence in the South. The large number of applications received from talented female students — more than 150 for 25 openings — demonstrates the demand for such South-South initiatives.

The South's efforts to achieve science-led sustainable development depends on fully engaging its most able and talented minds. Special programmes, like the Math and Physics Olympiads, aimed at identifying and encouraging youthful talent should be supported through South-South collaboration at the regional and inter-regional levels. Gifted children selected for these programmes should be nurtured in an environment conducive to the development of their talent. This can be achieved through the creation of a specialized system of schools and colleges for gifted children. The South Korean government pursued such a strategy when it established several highly competitive high schools for training talented children and the Korean Institute of Technology (KIT) to enable them to pursue their university undergraduate education. The system has been instrumental in the development of a critical mass of highly qualified and talented leaders in science and technology. The creation of such a pool, in turn, has been a key factor in South Korea's unprecedented pace of economic growth.

Therefore, the first element in any strategy for South-South co-operation is to utilize the best research and training centres in the South to train young and talented scientists from other countries, especially those from the LDCs, to create a critical mass of world-class leaders able to address the critical problems facing the countries of the South. This measure should be reinforced by efforts to stem the migration of the best scientists from the South to the North by providing them with incentives and adequate research facilities and by involving them in national development programmes. Many of the best scientists from developing countries continue to leave their homes for better economic and working conditions in the North. A recent IMF study "How big is the brain drain?" presents dramatic and disturbing statistics. In several Third World countries, the migration rate of highly educated individuals to developed countries exceeds 30% of the total at home. And in some countries, more individuals with college degrees live abroad than in their country of origin.

The second element in any strategy for South-South co-operation is to engage leading research institutions in the South in joint research projects aimed at finding solutions to critical real-life problems facing large regions of the South. Such problems include tropical diseases, food security, energy needs, soil and water management, deforestation and desertification. Regional and inter-regional co-operation in science and technology based on efforts to network centres of excellence to tackle specific development-oriented research problems carry substantial benefits for developing countries: Although at different stages of development, many developing countries share similar social, cultural and economic roots. As an example, the Third World Network of Scientific Organizations (TWNSO) — with financial assistance from the Global Environment Facility (GEF) — has recently formed a network of centres of excellence in dryland biodiversity in 16 developing countries and designed a project to facilitate the sharing of successful experiences in the conservation and sustainable use of genetic resources. Networks to address other problems of critical importance to sustainable development — for example, centres focusing on the study of medicinal plants, fresh water and renewable energy — are being developed. These networks should take advantage of recent advances in cross-cutting technologies, such as biotechnologies and information and communication technologies, to enhance their efforts to create the new knowledge needed to address the problems of the South. This knowledge must be generated locally because it is not readily available in the North.

The third element is to promote the sharing of innovative experiences in science and technology in developing countries that have been successfully implemented and have directly benefited the quality of life in the South. In co-operation with the United Nations Development Programme's Special Unit for Technical Co-operation among Developing Countries, TWNSO recently published a volume highlighting examples of successful initiatives in science and technology in the South. Titled Sharing Innovative Experiences, the volume, which contains 29 case studies from some 15 nations in the developing world, complements the Academy's efforts to create scientific centres of excellence. The centres have been designed to nurture home-grown brain power for progress; the case studies offer proof of how science has been put to work for the benefit of people — providing ground truth that science serves as an indispensable tool when tailored to meet the needs of the population. The next collection of case studies will focus on the use of medicinal and indigenous plants for sustainable development in the South. Work on this volume, which involves 15 centres of excellence, began this autumn. Centres participating in these projects are equipped with modern communication systems to facilitate the sharing of knowledge and best practices.

The fourth element in this strategy is to encourage scientific leaders in the South to offer independent, authoritative opinions to decision-makers on issues of critical importance — for example, the potential impacts of advances in electronic communications, biotechnology, alternative energies, resource conservation and new materials. This goal can be realized by assembling interdisciplinary panels of experts that include the South's most prominent researchers in the natural and social sciences. Such independent, scientifically based and timely advice coming from scientific leaders in the South should prove of great benefit to national governments, regional and inter-regional organizations and regional development banks. Indeed linking scientific expertise to the financial resources and know how found in the developing world's development banks might provide an enduring framework for sustainable development in the South.

The policy debate on the application of biotechnology to genetically modified (GM) plants, which is currently taking place both within the South and between the South and North, would be greatly enhanced by an in-depth authoritative study prepared by scientific experts in developing countries. Citizens and decision makers in the South need to know more about recent trends in research activities, field trials and the commercialization of GM crops to enable them to devise appropriate policies both for preserving their genetic resources and capitalizing on this new technology.

## Need for North-South Partnerships

As mentioned above, the capacity to generate new scientific and technological knowledge is concentrated in the science-rich countries of the North and is largely utilized to address the basic and material needs of these countries. The fact is that not much of this new knowledge has been used to address the critical problems of poor countries. As Sachs so aptly puts it: "All the rich-country research on rich-country ailments, such as cardiovascular diseases and cancer, will not solve the problems of malaria. Nor will the biotechnology advances for temperate-zone crops easily transfer to the conditions of tropical agriculture....rich and poor countries should direct their urgent attention to the mobilization of science and technology for poor country problems."

One of the most successful examples of North-South partnerships in science and technology involves the creation of a network of centres of excellence focusing on issues related to tropical agriculture. The system, sponsored by the Consultative Group of International Agricultural Research (CGIAR) since 1971, currently includes 16 international, independent and multidisciplinary institutions located in developing countries. By introducing new plant varieties and cultivation methods, the system sparked the "green revolution" in Asia and Latin America, which doubled global production of cereal crops between 1970 and 1990. The CGIAR system, which helped to combat hunger in large parts of the developing world, is now being challenged by the development and application of modern agricultural biotechnologies. These new tools complement traditional plant breeding programmes by extending GM technologies to such crops as bananas, sorghum, cassava and potatoes that are critical sources of food and income for many poor countries in Africa and Asia. CIGAR has begun to guide developing countries in the current global debate over GM crops. Last year, for instance, it called on developing countries to boycott the "terminator" gene technology introduced by Monsanto. The campaign succeeded in forcing Monsanto to abandon the programme.

Successful operation of the CGIAR system is based largely on the "centres of excellence" model framed by a clear mandate and a mission-oriented strategy. Because the centres are international in scope, local politics has not disrupted the system. Thus far, CGIAR has succeeded in generating stable funding from a large number of international aid agencies. This model needs to be replicated in other fields of critical importance to the developing world, including tropical diseases, information technology, biotechnology and renewable energies.

Another important model of North-South partnerships is based on the creation of networks to facilitate the mobilization of world-wide scientific expertise for addressing issues of global concern. The programme for Research and Training in Tropical Diseases (TOR), launched by the World Health Organization (WHO) in 1974, to deal with major diseases endemic to tropical countries, is an excellent example of this network approach. With support from several international funding agencies and pharmaceutical companies, WMO has also recently launched two major international programmes in tropical diseases designed to promote North-South collaboration in this field. The first is the Roll Back Malaria programme. Begun in 1998, this programme, which is supported by 12 Japanese pharmaceutical companies, has sought to devise a global strategy for controlling malaria. The second is the Global Alliance for Vaccines and Immunization (GAVI). Begun last year, this initiative, which is supported by the Gates Foundation, World Bank and UNICEF, is designed to reverse the upswing in preventable diseases by making vaccinations readily available for children living in poor countries. Other important networks that have been established under such international organizations as UNESCO, International Council for Science (ICSU) and WMO, include the World Climate Research Programme (WCRP), Man and Biosphere Programme (MAB), International Geosphere-Biosphere Programme (IGBP), and International Research Programme on the Structure and Function of Biological Diversity (DIVERSITAS). All of these efforts showcase the important role that UN-affiliated and other well-established international organizations play in global efforts to address critical public health and environmental issues. Such efforts have been handicapped in recent years by the chronic budget crises faced by the UN in particular and international organizations more generally.

North-South partnerships can be of great benefit to South-South co-operation strategies when such partnerships help build and maintain local capacities and excellence in science and technology. Development of Brazil's space programme and satellite technology offers an excellent example of this approach. In 1961, Brazil created a National Space Commission to develop satellite technology. Some 30 years later, in 1993, with assistance from a private US space firm, Brazil launched its first resource-data collecting satellite from Kennedy Space Center in Florida. Since then, Brazil has pursued two inter-related space initiatives: the Brazilian Space Mission (MECB) and the China-Brazil Earth Resources Satellites programme (CBERS). These initiatives, which now employ about 1000 scientists and engineers and 2000 technicians, use satellite technology to address down-to-Earth concerns: changes in temperature, humidity and carbon dioxide concentrations in the atmosphere and real-time data on alterations in soil and water quality. Equally important, the information gathered from these satellites has been shared with scientists in other developing countries through some 300 data-collecting platforms on Earth in Brazil and neighbouring countries. Brazil has also offered African nations access to the data through the United Nations Educational, Scientific and Cultural Organization (UNESCO).

Brazil's evolving space programme is a prime example of how North-South co-operation can be used to foster South-South co-operation. The effort began with the training of young Brazilian scientists and technicians largely in US universities and research laboratories. The programme's initial steps took place with the direct help of private firms and public institutions in the West: Brazil's first satellite was launched from the United States with a US rocket. The knowledge and know-how that Brazilian space scientists and technologists have acquired is now being put to use to help nations throughout the developing world examine critical environmental problems. At the same time, the initiative has raised Brazil's overall scientific skills and facilities. Today, a co-operative partnership with China has set the stage for even more rapid advances in satellite earth observing, data collection and communication in the future. All of this carries the promise of allowing researchers in the South to become true partners on projects devoted to global scientific issues. Such involvement could prove instrumental in 'southernizing' the North's scientific agenda. Research efforts could, as a result, be tied more closely to critical global issues as defined in part by input from scientists in the developing world. Ultimately, the entire global scientific community — both in the North and the South — would reap the benefits likely to accrue from using scientific data and knowledge to solve real problems faced by real people, especially the two-thirds of the world's population living in the developing world.

## Conclusions

The greatest challenge facing the developing world in this era of globalization is how to build and sustain its capacity in modern science and technology and how to jointly mobilize and direct its own capacity in science and technology to address the critical problems facing large parts of the South — for example, problems related to poverty, shortages of food, energy, and water, inadequate communication and transportation systems and persistent threats to public health posed by environmental degradation and the spread of tropical diseases. Systematically addressing such concerns will require co-ordinated and determined action by governments, private businesses and academia in the South defined by strategies for South-South co-operation.

The agenda for South-South co-operation outlined in this paper calls on the South’s best scientists and scientific institutions to join forces to direct their talent and expertise to address the South’s problems.

To facilitate the implementation of this agenda, a strong case for supporting the development of science and technology in the South should be made by: (1) providing concrete examples of successful experiences in the application of science and technology to basic human needs in the South and (2) by creating platforms both for research institutions and individual scientists and technologists in the South to interface directly with the ministries of planning and finance — the most powerful decision-making bodies when it comes to the allocation of financial resources.

Strong political will backed by firm financial commitments are essential ingredients for successful implementation of the strategies outlined above. The key financial institutions that should support such South-South institutions are the three regional development banks in Africa, Asia and South and Central America. In collaboration with the World Bank and UNDP, these three institutions may propose the establishment of a special fund to support these strategies and other initiatives aimed at lifting the status of science and technology in the developing world to a level that will enable it to address the critical developmental challenges facing the South and indeed the entire world.

All of this means that South-South co-operation holds the key to science-based sustainable development in the developing world. This co-operation, however, must be directed towards two critical goals: (1) enhancing the capacity of development countries, particularly the least developed counties, to fully embrace science and technology and (2) devising science and technology initiatives that seek to address — indeed solve — everyday problems.

The level of investment that the developed world, particularly the United States, has made in science and technology over the past decade — for example, in information technologies, biotechnology and material science — poses a daunting challenge to the countries of the South. The bountiful fruits of these investments, which have been harvested largely in the North — suggest that developing countries, with their meager budgets and resources, may never be able to match the scientific and technological prowess of developed countries. The increasing privatization of scientific research only compounds the problem.

But it is also important to emphasize that recent developments in science and technology present opportunities as well as challenges — in fact, the stage may now be set for unprecedented opportunities for the rapid advance of scientific know how and technological applications. That is because the same forces that are responsible for the increasing gap between the North and South may also serve as the building blocks for a more harmonious and equitable future. If the South can learn to take advantage of the new information technologies; if the potential benefits of biotechnology are applied to the developing world's indigenous resources for the benefit of its indigenous populations; if advances in resource conservation and energy production are integrated into national development programmes; if discoveries in material science find their way into domestic production processes, then the future of the South is likely to be marked by economic progress.

All of these are huge "ifs" and success is by no means certain. But the South has now reached a stage of scientific and technical development where it is possible — indeed imperative — for developing nations to learn from one another.

Successful steps in South-South co-operation, in short, provide useful markers for additional success in the future. And that may be best news of all. The more deeply entrenched South-South co-operation becomes, the more likely developing countries will be able to chart their own destinies.

Presented to the High-level Forum on South-South Co-operation in Science and Technology (Seoul, Korea — 14-17 February 2000

# EDITORIAL

This issue, number 8, of the latest news concerning 'World Mathematical Year 2000' is the last one before the year 2000 itself, and so maybe it is time for a first assessment of WMY2000. Remember that the Newsletter for WMY 2000 was launched by J.-L. Lions when he was the IMU President. It first appeared in 1993, with H. Gispert and M. Theis publishing the first two issues. Then in 1994, during the International Congress of Mathematicians in Zurich, J.-L. Lions decided to constitute an international editorial board for the Newsletter and to arrange a much wider dissemination of information concerning the World Mathematical Year, in particular concerning meetings organized specially in the year 2000. WMY2000 received formal sponsorship from UNESCO at that body's meeting in Rio de Janeiro in 1992.

The Agenda gives an idea of the timing of events for WMY2000 in different countries. The details of programmes are not given, but we can say that the three aims of the Rio's Declaration will be fulfilled. There exist many possibilities within the framework of these aims, which were:

• The big challenges in Mathematics for the next century;
• Mathematics and Development;
• mages of Mathematics.

Reading the Agenda we can see that the borders between the three aims are not watertight. For instance the Los Angeles Meeting organised by the American Mathematical Society will be devoted to the first aim, but it will include talks on the second aim; and the 9th International Congress on Mathematical Education will be focused on the second aim, but will deal with the first and third aims also. It appears that the "images of mathematics" aim of WMY2000 is the most difficult one to tackle, but various approaches to it have been adopted; for instance, the European Mathematical Society has launched a very interesting initiative to organize a poster campaign in subways of different cities about Mathematics - on the model of a previous world-wide campaign concerning Poetry. In particular, London, Paris, Buenos Aires, Brussels, Montreal, etc. have worked on the organization of this campaign; we hope that many other cities and towns will join this project. More precise information of this campaign will be given in future issues of the Newsletter in 2000.

What are our future projects? We hope to publish in 2000 four issues of the Newsletter 'WMY 2000', with the support of the mathematical department of UNESCO; we thank Professor S. Raither for his help and advice in this. We want to support all mathematical societies, national or local committees working on preparations for the World Mathematical Year. We think that all mathematicians will be aware of the fundamental place of mathematics in the cultural, economic and social life of each country, and they will promote their own speciality in some appropriate way. We also hope that the events in the year 2000 itself will not be the end of an era but the beginning of a new age for mathematics!

We thank all organizations who are supporting the Newsletter 'WMY 2000'. We hope that the 7000 copies of this issue will be distributed right throughout the World, and that the Newsletter 'WMY 2000' will carry on after the year 2000 to continue to promote mathematics!

# ICME 9 in Japan in the year 2000

(English translation from the Japanese, Japanese text available)

The 9th International Congress on Mathematical Education (ICME 9) will be held from July 31 to August 6, 2000 in Tokyo/Makuhari. To make this occasion of international encounter successful the International Program Committee (IPC) and the National Organizating Committee (NOC) are doing the preparation jointly.

The year 2000 coincides with the turn of millennium and symbolizes the turn of culture and civilization. In fact, the development and the popularization of computer have made our society more information-oriented and are going to change the paradigm of intellectual activities, while advancements in the international telecommunication have compactified the realm of intellectual exchanges. At this moment it is natural to re-assess the value and the mission of mathematics and mathematical education. This is not only the very target of the Mathematical Year 2000 but also the central subject of the ICME 9 of the year 2000, because it concerns directly the fostering and training of young students and pupils who must create and shoulder the culture in the coming century.

The ICME 9 is the first ICME to be held in Asia; this is another characteristic of this congress. The mathematic education is the world-wide activity with the commonly shared goal and method but it is also individualistic because it reflects and depends on the cultural tradition. Thus the international cooperation is indispensable to seek the right way for the mathematical education in the new century. Let us try to unite the synthetic wisdom of the East and the analytical spirit of the West at the ICME 9.

The program of the ICME 9 follows the pattern of its recent predecessors; for example, there are, among others, four Plenary Lectures (PL), about forty Regular Lectures (RL), thirteen Working Groups for Action (WGA), and twenty three Topics Study Groups (TSG).

The International Round Table (IRT) on the first day will be organized in the spirit of the WMY 2000. Panelists at the hall will discuss on the expected image of mathematical education in the twenty first century. A few celebrities around the world will also participate in the discussion through media of the international telecommunication.

We are now selecting the RL lecturers, while the names of the PL lectures and the themes of WGA and TSG can be found in the First Announcement, which is already distributed. Furthermore the latest information including the names and e-mail addresses of chief organizers of WGA and TSG can be seen on our official home page

http://www.ma.kagu.sut.ac.jp/~icme9/

We shall distribute the Second Announcement in this summer to every corner of the world inviting earnestly every interested people to the ICME 9.

Chair of IPC, President of NOC, ICME 9 Hiroshi FUJITA

# Buenos Aires - Argentina

The Centre of Mathematics and Design MAyDI from the University of Buenos Aires, has organized a national call to all Architecture and Design students of the whole country to participate on the bid for exhibition of posters in the Buenos Aires subway. The selection will be made by highly qualified members such as the Director of the School of Graphic Design at the University of Buenos Aires and the Director of the Research Centre MAyDI. Metrovias, a private enterprise, has offered us free space to expose the posters for a month in the 2000, at all stations of the net.

The Centre MAyDI has also organized another national contest to select an issue of commemorative stamps celebrating WMY-2000. Correos Argentinos is managing freely the reception of the presentations and will edit the winner stamp next year.

For both contests, we have performed a funding campaign with some industrial firms, newspapers, phone companies, scientific journals, domestic flight companies, editorials, professional associations, etc. The purpose of this campaign is to get contributions (money, supplies like books, journal subscriptions, printers, software, etc.) to cover first, second and third prizes as well as 10 special mentions. The prizes will be given at a public ceremony (13-14 December 1999) and winners from the provinces will get free tickets and 2 nights in a central hotel to receive them personally.

Director of the Centre of Mathematics and Design MAyDI
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Web page: http://members.xoom.com/maydi

# WMY 2000 IN BEJAIA (ALGERIA)

The Bejaia University organizes many events during the World mathematical Year;

1. An approach of the great mathematical challenges for the next century - Special session of mathematical seminar.
2. Industrial Mathematics and Computer Science Bejaia University and Sonacotrach,Edfmia,Sonelgaz,etc...
3. Image of Mathematics :
• A. Ribaucour in Algeria Mathematical contribution in Geometry, construction of Bejaia's Harbour.
• Play for children - 01 June 2000 during the "World Child Day " ."Leonardo Fibonacci in Bejaia" about the long stay of Fibonacci in Bejaia;
• Internet and Mathematics in Bejaia Internet and Teaching.
• Exhibitions and Conferences for general public. Mathematics and development between the IX and XIX centuries interconnexion between Algebra,
• Computation, Geometry, Astrology, Social Sciences, etc...
• Mathematical contribution of Maghrebian Mathematicians,before and now.

In the Spring of 1997, the Canadian Mathematical Society (CMS) created a Committee for WMY 2000, with a mandate to develop proposals for events during the year 2000 to make mathematics more visible in Canada. It was suggested that these events should be noticeably different from standard CMS activities, should recognize the diversity of mathematics and mathematical interests in Canada and should be imaginative, while recognizing the three aims of the IMU in its Declaration of Rio de Janeiro. Chaired by Bernard R. Hodgson, Université', Laval (current Secretary of ICMI), this Committee met at several physical locations as well as electronically, gathered suggestions from across Canada, and submitted its report in September 1998. The CMS has now committed $50,000 to these WMY 2000 proposals. In addition to the CMS initiative, other Canadian mathematical societies and institutes have proposed activities to celebrate WMY 2000. This report presents highlights of these exciting events now being planned in Canada for WMY 2000. In celebration of the World Mathematical Year, the CMS and CAIMS (Canadian Applied and Industrial Mathematics Society) have agreed to meet together for the first time, in a joint annual meeting, June 10-14, 2000 in Hamilton, Ontario. These two societies will be joined by the Canadian Operations Research Society, the Canadian Society for the History and Philosophy of Mathematics, the Canadian Symposium on Fluid Dynamics and the Canadian Undergraduate Mathematics Conference. This Year 2000 joint societies meeting is expected to bring together the largest number of Canadian mathematical scientists, from across Canada, ever assembled in one place. It is itself an historic event for Canada. Mathematicians from around the world are welcome to join this celebration; program information will be available soon at the web-site http://www.math.ca/. Closely coordinated with this joint societies meeting in June 2000, the Fields Institute will host a Symposium on the Legacy of John Charles Fields, at the Royal Ontario Museum in Toronto, June 7-9, 2000. This Symposium is supported also by the CMS, CAIMS, Centre de recherches mathématiques and the Pacific Institute for Mathematical Sciences. It will help to inform all Canadians of our unsung hero in the mathematical sciences, the visionary John Charles Fields and his exceptional legacy to the world of mathematics. He established the world's highest award for achievement in mathematics, now known internationally as the Fields Medal (and often referred to as the "Nobel Prize of Mathematics"). It is struck by the Canadian Mint, of Canadian gold, and shows the head of the ancient Greek mathematician Archimedes on the face. A scientific highlight of the Symposium will be presentations by Fields Medal winners of their medal- winning work and its impact on modern mathematics. Sir Michael Atiyah will deliver the Banquet Address on Friday evening. Professor Tom Archibald of Acadia University will give a plenary lecture on the life and times of John Charles Fields. As well as raising awareness of mathematics in Canada, this Symposium will be a significant retrospective contribution to World Mathematical Year 2000. Negotiations are underway to produce a documentary video and book, as a lasting record of this unique event. In Montreal, Operation Métro-2000 is being organized under the leadership of Christiane Rousseau, with support from CRM and CMS and other sources. This initiative will place posters in the Montreal subway system, designed to raise the awareness of the general public and particularly students of the importance and omnipresence of mathematics in the sciences and technology. It is part of a world-wide strategy of WMY-2000 to bring mathematics to the people, through posters in public places, such as subways. The Montreal posters will be strategically located in subway cars and those stations most frequented by students. The possibility is being explored of extending this effort to Toronto and other cities. In Western Canada, the WMY-2000 Museum of Mathematics Project will bring the highly acclaimed travelling public exhibition of mathematics, or Mathematiksmuseum to visit the Winnipeg Children's Museum, May 1 to 13, 2000, and the Saskatchewan Science Centre in Regina, May 15 to 27, 2000. The Mathematiksmuseum was developed in Germany by Professor Albrecht Beutelspacher of Justus-Liebig Universität, Giessen, and was shown during the International Congress of Mathematics in Berlin in 1998. The Pacific Institute for the Mathematical Sciences (PIMS) will substantially increase its activities to promote mathematics awareness, by holding public lectures, presentations, and hands-on workshops. A number of different events to be held in British Columbia and Alberta elementary schools focussing on presenting "fun" methods for doing math and computer science with children and their parents. Activity examples include soap bubbles, geometry and paper, probability experiments using pennies, and building geometric models from straw and paper. A Conference on Changing the Culture for the Next Millennium is designed to forge closer ties between the mathematics community, mathematics teachers, and industry. Featured talks and small group discussions focus on erasing barriers between these various communities. In a Mathematics is Everywhere campaign, like the Operation Métro-2000 in Montreal, PIMS will place posters on all components of public transportation systems in BC and Alberta, designed to raise the awareness of the general public and particularly students of the importance and omnipresence of mathematics in the sciences and technology. In response to the Video Lottery Terminal debate in the Province of Alberta, PIMS representatives met with officials from the Edmonton Science Center to set up an interactive exhibit on chance and probability. The inauguration will happen in year 2000. The activities described here are only a part of the local, national and international activities planned in celebration of World Mathematical Year 2000. The Canadian Mathematical Society for example will sponsor, in addition to the activities described in this proposal, Math Camps, a Virtual Canadian Math Trail, a Women in Math Poster and Mathematics Museum Exhibits. Across Canada, there will be additional public exhibitions and celebrations of mathematics, complementary to those described here, under the auspices of the CMS, CRM, l'Association mathématique du Québec (AMQ), the Ontario Association for Mathematics Education (OAME) and other sponsors. # WMY 2000 in Germany ## Activities of the German Society for Mathematics Education In early 1998 some members of the German Society for Mathematics Education (Gesellschaft für Didaktik der Mathematik, GDM) called into being an informal group caring about WMY 2000. This group consists by now of some 15 members. Contacts to all of them and the coordinator of the group can be made via the Internet: http://www.uni-giessen.de/gdm/wmy2000/ Regarding the three aims which were set by the declaration of Rio, the German GDM-group decided to focus ist activities on the third aim - the Image of Mathematics. All activities, including the preparatory ones in 1999, are aiming at the popularization and the improvement of the acceptance of mathematics especially in schools. In order to attract the attention of pupils and students at German schools to the event WMY 2000 and to raise their sensitivity for our aims, still this year a poster action will be started. We call upon pupils and students (from first-graders through college students) to create a poster concerning WMY 2000, which carries or depicts one of the following mottos (or a self chosen motto): • Mathematics for all • Together Mathematics • Hands on Mathematics • Mathematics - a rewarding thing • Mathematics - an exciting region • Mathematics - a concern of yours • Mathematics is fun • Mathematics - older than 2000 years • Future needs Mathematics • With Mathematics to new views • Fascination Mathematics • Mathematics may please you as well • Living Mathematics - more than only numbers. At the same time we encourage the pupils and students to put up their posters in their classrooms or in the hallways of their schools during the year 2000 or to make up a personal calendar of their posters for the year 2000. Posters, which turned out very well, can be sent to us by the pupils and students in order to take part in a calendar competition. A publishing house will print and publish a calendar showing the best 12 posters. This calendar will also show data of national and international events and projects in connection with WMY 2000. In the year 2000 the pupils and students will find many suggestions and ideas for mathematical activities not only on our web-site in the internet, but also through other conventional channels. All these activities are aiming at improving the image of Mathematics in schools and thereby in a much wider public. Please note that this article only represents activities of people in Germany, who deal with mathematics education. We do not and cannot speak for all people in Germany involved in mathematics. All communication with this group regarding WMY 2000 activities in Germany should be addressed to: Prof. Hans-Joachim Sander PH Mathematik Oberbettringer Str. 200 D-73525 Schwaebisch Gmuend Germany or via E-Mail to one of the group members (E-Mail addresses see our Homepage) or to This email address is being protected from spambots. You need JavaScript enabled to view it. # Editorial Board Berlin August 1998 From the left to the right : M.Morimoto, M.Niss, M.Chaleyat-Maurel, G.Tronel, A.Ashour, R.Rebolledo. # EDITORIAL Mathematics, a key for development Rolando Rebolledo, Chairman of the Commission on Development and Exchange of the IMU. A common idea in developing countries is that scientific research is a sort of a luxury which a poor nation cannot afford. Most citizens think that science, which needs enough funds and human resources, is only a challenge for developed countries, where a tradition of scientific research already exists. This prejudice is particularly striking among some entrepreneurs or private investors, for whom scientific research in developing countries is nothing but a fiction which could at most provide a suitable pretext for obtaining some tax reductions after some donations. On the other hand, the governments of developing countries, facing dramatically urgent basic needs of the population, tend to postpone scientific research and training for more prosperous days. Following the standards of neoliberal economic policies, a number of them have been implementing a diminution in the influence of the State, giving more opportunities to private investors and opening their countries to transnational commerce and economical activity. This gives raise to a huge import of sophisticated technology. As a result, small countries begin to be invaded by imported science and technology, without any real possibility of fully understanding the essential theory underlying each new device. The relationship between economic and scientific development becomes nowadays a highly complex and subtle subject. On one hand, an increase in economic development could bring additional funds and facilities for education and research. No scientific research could start in a given country without a minimal infrastructure and well trained human resources. On the other hand, an increase in industrial activity creates a need for more sophisticated technology which should demand a better scientific education. To advocate for science as a key feature of development could seem useless in developed countries. On the contrary, this is far from being well accepted in developing countries. One objective for the World Mathematical Year 2000 campaign could be the worldwide understanding that: Mathematics is a strategic keystone for the economic and cultural development of a nation. We, mathematicians, do have numerous arguments to support this thesis. Let me analyse some of them, hoping that many other colleagues will provide a long additional list in the near future. Non mathematicians in developing countries used to think that there is nothing new to discover in Mathematics. However, they are ready to accept that perhaps some technological advances have been in applications of our science. So that, a first point to make them understand is that Mathematics, as any other science, is making new discoveries every day. And, secondly, Mathematics is a part of any new technological invention. For this, one can provide numerous illustrations like the applications to computer sciences, communication theory, physics, finance, biology. To summarize, a first and most evident incidence in economic development of scientific research, and Mathematics in particular, is provided through technological innovation. However, the most important argument which supports our thesis, is connected with the development of human mind. Indeed, Mathematics is important for logical thinking. Our science provides the first contact with rationality and criticism at childhood level. When it is well taught, Mathematics gives the child the opportunity of learning about the scientific method in practice and having fun with their own scientific discoveries. Undoubtedly, the increasing worldwide use of computers in every day life, is giving rise to a new organization of knowledge as a whole. Scientists working in different and distant countries may collaborate almost instantaneously through the Internet. On the other hand, at a neurophysiological level, the relationship to knowledge is being deeply modified. This is particularly obvious when one observes the way in which children develop sophisticated skills while handling computer games, for instance. They tend to develop the ability of reproducing a whole process, or asequence of commands (leading to the next stage of the game), instead of memorizing an isolated fact. From this point of view, the way in which children are building up their memories comes closer to that of the mathematician who, if required, would be perhaps unable to write down by memory the hypotheses of a given theorem, but could perfectly recall its proof. In both cases, it is the motion of ideas, a subtle process of neuronal associations, which is revealed. So that, by its method, Mathematics is deeply connected with the acquisition of knowledge and the general development of the mind as a whole. Of course this is not a role of Mathematics alone, I defend the unity of all sciences, they are all related and interdependent in their development. However, no scientific development could start without first improving mathematics skills. It is almost a tautology to say that the mind structure of future women and men who will rule the developing countries during the next century is being decided today. And it is not an exaggeration to claim that Mathematics is the spinal chord of such a construction. As a conclusion, Mathematics is deeply involved in the development of the whole human mankind, so that, in particular is a strategic keystone for the economic and cultural development of any nation. Therefore it is an urgent need for both, scientists and governments of developing countries, to think and implement new strategies for improving mathematical training and research at all possible levels. Scientific societies have a great responsibility in this historic task. The IMU, through the Commission on Development and Exchange (CDE) and the International Committee for Mathematical Instruction (ICMI) is supporting mathematical activities in developing countries. However, a more clear involvement of official organizations in those countries is needed. Some national societies too, are trying to obtain from their governments a general policy on the development of sciences. This is being successful, for instance, in Chile, where the Mathematical Society is being officially asked to provide technical support in designing the new teaching programmes the school level. Moreover, the Chilean Mathematical Society is currently working on a proposal for the Law on the Development of Sciences in collaboration with all other scientific societies of the country and the Commission on Science and Technology of the Parliament. Finally, I want to stress that a successful World Mathematical Year 2000 should be a major breakthrough to convince any government of the importance of supporting Mathematics as a keystone for the economic and cultural development of a nation. To this end, the collaboration of all mathematicians over the World is needed. # AGENDA OF CONFERENCES IN MATHEMATICS http://acm.emath.fr/ The Agenda of Conferences (ACM) in Mathematics is a searchable database of mathematical talks, seminars and colloquia. ACM collects its information on mathematical talks directly from the Web pages of participating seminars. ACM has been used in France since February 1998 and it indexes about 100 outgoing seminars. ACM will soon be available to other countries. This site helps the mathematical community to find mathematical talks of interest and it also helps to promote mathematics, which is one of the goals of the World Mathematical Year 2000, by providing a real-time global view of the research activities in mathematics. National correspondents are needed! ACM needs national correspondents. Their role is to manage the intial translation of ACM, and then, the entries of the database for their country. The national correspondents will inform their colleagues about ACM by the way of their national mathematical society. Here is the list of the current national correspondents: • S. Cordier for Belgium and France • A. Jungel for Austria and Germany • S. Mancini for Italy • E. Pearl for Canada Contact: Stéphane Cordier, This email address is being protected from spambots. You need JavaScript enabled to view it.This email address is being protected from spambots. You need JavaScript enabled to view it. # Development of Mathematics 1950 - 2000 In view of World Mathematical Year 2000 it should be exciting and useful to take a serious look at the evolution of mathematics during the second half of the present century. The steering group of that challenging adventure is facing dilemmas about choices of ways and means, subjects and contributors. Several active mathematicians accepted to produce a comprehensive presentation of their own field for the collective volume ; so nonspecialists should be able to grasp the fundamental motivations, main problems and principal achievements during the late period. Hopefully, interactions with related scientific activities, such as physics, biology, etc., will appear at several occasions. As any classification inside mathematics has alway been a hazardous task, the various articles may appear to a certain extent as a heterogeneous accumulation. Moreover, the difficulty of the task should justify nonexhaustiveness. In order to facilitate the understanding of links between various contributions and to suggest the overall unity of mathematics, the editors intend to add logical diagrams and comment some scenic drives along several proposed routes through the volume. Supplementary references will be added to the papers. Also a large bibliographical and chronological documentation will be included. Some representative mathematicians have been willing to explain their personal views ; their possibly somehow unorthodox appreciations could stimulate further reflections. A description of specific geographic centers should serve as specimens for a historical study of outstanding local mathematical activities. The book is due to be published by Birkhäuser, Basle, at the beginning of 1999 at the latest. Jean-Paul Pier, Seminaire de mathématique, Centre universitaire de Luxembourg, 162A, avenue de la Faiencerie, L-1511 Luxembourg # National Year for Mathematics 2000 and Mathematics educational Ventures (MeV) National Year for Mathematics 2000 (NYMaths2000) is the current working title for a host of events, projects and initiatives aimed at raising the profile of mathematics within the UK. NYMaths2000 is intended to run in parallel with the National Numeracy Strategy and is expected to take place within the period January to December 2000. It will also support the wider objectives of increasing the mathematical skills base of the nation through a number of attractive and imaginative projects. We are currently working closely with the DFEE on this consultative stage with a view to setting up formal structures in the very near future. We feel that the vital role of mathematics has for too long been hidden from the public. This unseen engine which powers much of our modern world needs to be brought to the foreground and celebrated as one of this country's key creative industries. We thereby hope to encourage both students and adults to see mathematics as a key part of their educational and personal development. To those youngtalented mathematicians we want to show that a career as a mathematician can be highly stimulating and richly rewarding. We very much hope that the National Year for Mathematics 2000 will be the springboard for a real change in the way mathematics and science are seen in our culture. The projects we ourselves are initiating will aim to foster a greater appreciation, wider access, and a sense of participation between the public and the mathematical sciences. There has been the support of the Joint Mathematical Council and the National Education Business Partnership Network for our first project, the Mathemagical Mystery Tour travelling exhibition. This is now a Millennium Award Scheme holder (administered by the Royal Society and the British Association and funded by the Millennium Commission). After pilot events next Spring, the Mathemagical Mystery Tour will travel around the country from September 1999 to December 2000. This has also been a first step in international collaboration, with partners including Techniquest (Cardiff), NRICH (Cambridge) and WQED (Pittsburgh, USA). We have also initiated the first steps in compiling a list of all events, projects and initiatives currently being considered by organisations and individuals around the country. These are at various stages of development, from an idea for discussion to a fully funded national project. These can include in-school educational initiatives as well as after-school projects and also events aimed at a general audience. Please request the Events, Projects and Initiatives document for the latest information. One of our key tasks is to bring together in partnership people with similar aims, and to ensure that the funding and resources available will make a real impact at a local level and national level. To take part in NYMaths2000 please request the Call for Participation document which includes a form to fill in with details of your project. To give a flavour of some of the further projects being put forward we would like to highlight the Mathemagical Network, the expansion of Mathematics Masterclasses and Mathematical Challenges, the creation of Maths Clubs, Maths Resource Centres, Mathematics on the Tube poster campaign, Mathematics on postage stamps, Mathematical Art exhibitions, Mathematics in the Media and Mathematics in Museums. It is envisaged that the MeV will manage the Mathemagical Mystery Tour and will also coordinate further events for NYMaths2000. The MeV is in the process of incorporation as a non-profit organisation. The structure of the MeV will consist of Patrons, an Executive Board, an NYMaths2000 Committee, Corporate Patrons, Corporate Associates and Partnership Organisations. More details are available in the NYMaths2000 Sponsorship document. Our aim is that the MeV will continue initiating projects in the public understanding of mathematics beyond the year 2000 and we look forward to developing long-term relationships with individuals and organisations dedicated to the same goals. I would be happy to discuss any of these issues further and during this consultative period all comments, suggestions and advice will be gratefully received. Richard Mankiewicz, Chief Executive, MeVContact Middlesex University, Quensway, Enfield Middx EN3 4SF (UK) # WMY 2000 in Iran In early 1997 a National Commission for the World Mathematical Year 2000 was officially established in Iran. The Commission, headed by the Minister of Culture and Higher Education (MCHE), includes several other cabinet ministers, various dignitaries and a number of mathematical scientists. To underscore the importance the country attaches to the event, President Mohammad Khatami of I.R. Iran has agreed to be named the Honorary Chairman of the Commission. The day-to-day operation of the Commission is carried out by an Executive Comittee composed mostly of the mathematical scientists on the Commission and is headed by the Deputy Minister for Research of MCHE. The Executive Committee has set up a number of subcommittees to guide and coordinate WMY activities in such areas as popularizing mathematics, the role of mathematics in development, mathematics education and research in the coming century, publications and the documentation of the history of mathematics in the country. There was considerable debate from the beginning on whether the Executive Committee should take on an active role of top-to-bottom leadership or adopt a supportive role in assisting grass-roots initiatives formulated by relevant institutes, professional societies and other groups. In order to encourage broad involvement with WMY events, it was decided that a general call should go out to all concerned to define projects and proposals that fit certain broad criteria. The subcommittees then pursue the goal of coordination, guidance and the funding of acceptable incoming initiatives. However, the Executive Committee will be closely watchful to provide balance and, where necessary, inject the necessary leadership to ensure that all the major projected areas of activity receive proper over-all emphasis. Among the plans under way to bring mathematics to the public are the establishment of Mathematics Clubs, expansion of mathematical exhibitions in science parks and museums, publication of popular books on mathematics, mathematics and computer-science contests for various age groups, and the airing of a several series of radio and television programs that emphasize the relevance of mathematics and its role as the cornerstone of modern science and technology. The celebration of WMY 2000 provides a very opportune focus for mathematics related activities in Iran which have experienced remarkable growth in the last dozen years. Despite the existence of a well-entrenched historical tradition in mathematics, modern mathematics was implanted in the country only in the late 1930’s and its development was slow and uneven for most of the half-century following its introduction. Although the school system in Iran has generally performed a creditable job in preparing students mathematically for higher education, Iran has shared with other developing countries the difficulty of attracting top-notch talent to the fields of basic sciences in general and to mathematics in particular. There has been a significant reversal of this trend in the last decade fueled in part by well-publicized inception of national olympiads in mathematics and sciences and subsequent very successful participation of Iranian national teams in various international student olympiads. Iran’s entry into the International Mathematics Olympiad has finished in the top ten in six of the last seven years. Significantly, most of the alumni of these mathematics olympiads are choosing mathematics as their field of study at the university level. Another important development has been the belated introduction of doctorate programs in mathematical sciences. This has served to institutionalize mathematics research and has contributed greatly to the development of home-grown talent. WMY 2000 furnishes a timely framework in which to review and assess these and other developments and to provide a perspective and a blue-print for the future in a way that would meet the challenges of the new century. All communication regarding WMY 2000 activities in Iran should be addressed to: WMY 2000 / Office of Deputy Minister for Research, MCHE, P.O. Box 13145-554 / Tehran, Iran. A Web site covering Iranian activities in WMY 2000 is under construction and will be available in September 1998 : http://ipm.ac.ir/WMY2000 Contact: A.Rejali This email address is being protected from spambots. You need JavaScript enabled to view it. # EDITORIAL ## WMY 2000 - Some Themes for Discussion A. SIERPINSKA One of the goals for the WMY 2000, as stated in the Rio de Janeiro declaration, is that efforts should be made to improve the image and presence of mathematics in today’s " information society ". This goal is sometimes understood as follows : Mathematics has a poor image in the society because most people see it only as a boring school subject which they either failed or barely passed. So, at the occasion of the WMY 2000, mathematicians should undertake actions to show how exciting mathematics can be, and how widely applicable and actually applied it is in the modern "information society". Mathematical competitions, exhibitions, popular lectures should be organized to serve this purpose. This line of thinking seems to be based on the assumptions that (a) people’s apprehensions vis à vis mathematics are ill-founded, and (b) that mathematicians know what mathematics is and what has been or should be its role in society and the only thing that remains to do is to convey this clear understanding to " the general public ". I think that, instead of taking these assumptions for granted, the WMY 2000 could be an occasion to discuss them within the mathematical community itself. It may well be that our own " image of mathematics " does not always agree with reality. I am thinking here, in particular, about the forever repeated clichés that " the language and values of mathematics are universal ", and that the learning of mathematics plays " a key role for the development of rational thought ", which found their way to the " draft resolution " about the WMY 2000 presented to the UNESCO Conference in Paris in November 1997 (see WMY 2000 Newsletter, no. 5). In the following, I shall look at each of these statements in turn. Cultural roots and universality of the language and values of mathematics. The above mentioned " draft resolution " contained also a claim about the " cultural roots of mathematics ". I certainly agree with this, but I think that, if one takes a cultural view of mathematics, then one has to be cautious in the interpretation of the claim about the " universality of the language and values of mathematics ". If we see mathematics as a specifically human way dealing with change and complexity of the natural and social world then we can make some claims about its universality : Mathematics is a universal cultural phenomenon, in the sense that every culture creates a mathematics. For imagine a world, in which change and complexity have not been mentally organized into relationships, dependencies, patterns, order and tools for the comparisons of magnitude, all of which transcend the immediate historicity of the human life. Such a world would be unbearable and terrifying : it would be a Chaos, an antithesis of Cosmos. Because the mental " organizing systems " have to do with abstractions such as pattern, order, relationship, measure, they can be seen as prototypes of " roots " of mathematical ideas. As the mental "organizing systems " are a life’s necessity for humans living in social groups, they do appear in all cultures. But this is where universality ends, because the ways in which these " organizing systems " developed differ widely from culture to culture. The most differences are between oral cultures and cultures in which the written language plays an important role. But there are differences within cultures with written language as well. This is true in the historical sense, as when we compare ancient Western and Eastern mathematics (see, e.g. Joseph, G., 1991, Crest of the Peacock : Non-European Roots of Mathematics; Tauris, London). But it is also true when we look at the different cultural and institutional " niches " in which mathematics is practiced and developed in today’s world. Research mathematicians, architects, construction engineers, brokers, financial advisors, stock market employees, actuaries, are speaking different languages and what they value in the mathematics they are practicing is not the same. Mathematics, rationality and power It is said that the learning of mathematics is useful because it promotes the development of " rational thinking ". Two assumptions could be underlying this belief. One is that rationality should be modeled on mathematical thinking ; another is that a widespread rationality creates a society of intellectuals or a " government of reason ", free from criminal violence and wars. These assumptions were quite strong some thirty years ago, in the international New Math curricular movement. Teaching mathematics to all children, not as a set of computational and algebraic rules but as a theory-in-the-making, was supposed to turn these children into " little mathematicians ", focused on beautiful ideas and not on bodily matters. This was assumed to be and easy task, because, according to Piaget’s psychology (a major reference at that time), the child’s " natural rationality " is mathematical (roughly speaking, in the sense that human thinking is based in structures of mental operations analogous to groups of transformations in mathematics). With all due respect for the ideals and hopes of these people, we see today that they were wrong on several counts. It is very difficult to speak about something like " human natural rationality ". People normally develop a range of " rationalities ", situated in a variety of contexts of practice with which they engage. There is the " pragmatic logic " of everyday conversations at home, which is different from the logic of professional argumentation and instruments of persuasion in the workplace, which is yet different from the logic of mathematical proofs. One obvious difference is that the ordinary language does not satisfy the law of tertium non datur, and, for example, two negations do not cancel each other out. There are many negations, not just one negation in the ordinary language (e.g. " unhappy " and " not happy " do not mean the same thing). But even " the logic of mathematical proofs " is not ahistorical or acultural, nor is it independent from the socially constructed standards and styles. In the XIXth century, it was still all rigtht to say, for Abel, that Cauchy’s theorem about the sum of a series of continuous functions " souffre des exceptions ". So even " mathematical rationality " is historically and culturally situated, and is not, in some sense, " absolute ". It can be a dangerous thing to postulate a hierarchy of these different " rationalities ", and tell the child who comes to school, that the way he or she thinks in everyday situations is all wrong or inferior and that the school, and especially learning of mathematics, is going to straighten it up. This, however, happens at school all the time, and is the cause of many school failures. It is also one of the reasons why so many people grow with a deep dislike of mathematics. The hope that a " democratic government of reason " is going to prevent wars is also bound to failure. Wars are caused not by the paucity of rationality but by an excess of greed for money and power. While academic mathematics may have little to do with the rationality situated in people’s family of professional lives, it seems to have a lot to do with power. According to some researchers on situated cognition (e.g. V. Walkerdine, 1988, The Mastery of Reason, Cognitive Development and the Production of Rationality, London and New York : Routledge), the very " joy of doing mathematics ", so often evoked by those trying to motivate students to learn mathematics consists in the pleasure of control : " the learner of mathematics is not caught in the play of desire in the Imaginary, but believes himself to have control of it. ... It is extremely powerful and it involves the manipulation of a universally applicable symbolic system - a fantasy of playing God, " the Divine mathematician ", the fantasy inscribed in the Cogito, the Ratio " (ibid.). - The US based National Council of Teachers of mathematics overtly state in their " Standards " that the aim of mathematics education should be the achievement of " mathematical power " by all children. For them, the " mathematical power " is the key liberating factor in today’s technological world, opening the gate to a better life and a better society. But " mathematical power " is seen by some people in a negative way. If success in mathematics is perceived as " empowering " the individual, the failure is associated with an overwhelming feeling of powerlessness, lack of control (strangely absent when one fails, for example, in geography or philosophy!). Mathematics is seen as the " gatekeeper " (rather than as a " gateway ") to many professions and well paid jobs. It is hard to dispel this apprehension because the entry into many academic programs is based on a selection through mathematics examinations or courses with material and approach to its teaching that have little to do with the target profession. This apprehension is expressed in no uncertain terms by words such as " mathematical imperialism " or " colonialism ". On a more global plane, " mathematical power " is seen by some as destructive, when the involvement of mathematicians in war industry is evoked : mathematicians are sometimes thought responsible for much of what is called the " destructive power " of the Western culture. And this responsibility will have the tendency to grow in the future " information societies " with their menace of " wars in the cyberspace ". All in all, mathematics seems to be a mixed blessing, implicated in many cultural and political issues which it would be useful to discuss at the occasion of the WMY 2000. " The WMY 2000 Newsletter could become a forum for this discussion, but interested Readers are invited to propose other forms and modes of exchange of thoughts on the themes raised in this editorial (for example, a special conference in the year 2000, informal meetings of mathematicians working in industry, business, inner city schools, mathematics departments at universities, etc.)". # Mathematics and its Role in Civilization ## MACAU 2000. January, 11-14. In the framework of the WMY 2000, an International Conference on the general subject of the scientific and cultural role of the Mathematical Sciences in the History of Civilization and in the Future Development of Humanity will take place in Macau, China the 11-14 january 2000. As a joint initiative Portugal - China, it is being organized under the advice of an international scientific committee composed by J.L. Lions (Chairman, Paris), Gu Chaohao (Shangai), Li Ta-tsien (Shangai), E.R. Arantes e Oliveira (Lisboa), J.F. Rodrigues (Lisboa), J. Palis (Rio de Janeiro), D.G. Crighton (Cambridge), C. Dafermos (Providence, RI), and G. Kahn (Paris). Aiming a world-wide participation, the scope of this conference includes the following topics : • Comparison of the role of Mathematics in different civilizations, as well as exchanges and interactions in the past, with particular emphasis on the Orient/Occident encounter of Mathematical Cultures ; • The role of Mathematics in Calendars, Astronomy and Cartography and other aspects of Mathematics as a driving force in Human Progress ; • Current co-operation between industrialized and developing countries in the Mathematical Sciences and contributions of Mathematics for the Sustainable Development in Economy, Society and Industry ; • Mathematical research and education for Science and Technology and the popularization and understanding of Mathematics in diverse Cultures ; • Perspectives of Mathematics in the future of civilization and its role in the Society of Information. The city of Macau, in the south of China, having University, large Hotel facilities and an international airport, in addition to being close to Hong Kong, is an ideal location for such a meeting. In particular, Macau has a strong historical meaning as a bridge of commercial and cultural exchanges between East and West. After a long period of European presence, under Portuguese government since 1557, is will return to China administration in December 1999. Contacts : Prof. Jose’ Francisco Rodrigues This email address is being protected from spambots. You need JavaScript enabled to view it. Prof. Li Ta-tsien This email address is being protected from spambots. You need JavaScript enabled to view it. # Questions au Professeur Jean Pierre Bourguignon Q. : What would you like to see in the Newsletter WMY 2000? 1. Quelle importance revêt pour vous la déclaration de Rio qui proclame l’An 2000, année mondiale des mathématiques ? La déclaration de Rio est une tentative originale qui a, pour moi, trois vertus essentielles: affirmer l’ambition des mathématiciens de s’adresser au grand public ; faire ressortir leur capacité à coordonner au niveau mondial une action d’envergure ; faire apparaître leur unité disciplinaire en même temps que leur ouverture aux autres disiplines. On pourrait croire que les points de la déclaration vont d’eux-mêmes puisque, par exemple, les mathématiques sont une des sciences les plus internationales. Cependant les mathématiciens ont mis plus de temps que d’autres scientifiques à comprendre l’importance que revêt dans la société actuelle la communication en direction du grand public pour expliquer les enjeux de la discipline, son fonctionnement, ses ambitions et ses limites. Il y a aussi un caractère symbolique à ce que cette déclaration ait été faite à Rio de Janeiro (indépendamment de la tenue dans cette ville d’un sommet mondial sur l’environnement) : alors que le Brésil est un pays en plein développement, il a déjà une place importante dans la vie mondiale des mathématiques car, avec l’IMPA, il a su se doter très tôt (1957 je crois) d’une structure mobilisatrice pour la recherche à l’échelle du sous-continent sud-américain, sous l’impulsion de collègues ambitieux et capables. 2. Que pensez-vous des trois axes de l’opération (" Les défis du 21ème siècle ", " Les mathématiques : une clé pour le développement ", " Image des mathématiques ") ? Les trois axes de l’opération me semblent bien choisis car il permettent de mettre le doigt sur trois des vérités les plus méconnues concernant les mathématiques. On peut les paraphraser ainsi :les mathématiques sont vivantes et ont encore beaucoup de questions à résoudre, de concepts nouveaux à développer, de frontières à explorer ; le rôle des mathématiques dans le développement des sociétés modernes est fondamental car elles sont cachées dans beaucoup d’objets d’utilisation quotidienne ; la compréhension du rôle des mathématiques dans la société n’est pas seulement l’affaire de spécialistes ; elles doivent impérativement être rendues abordables à tous les citoyens qui doivent donc changer l’image qu’ils s’en font : de lointaines et ésotériques, elles doivent devenir familières et rassurantes. 3. Quelles manifestations souhaiteriez-vour voir organisées dans le cadre de l’année mondiale ? Je me réjouis que beaucoup d’initiatives se prennent de par le monde à l’occasion de l’année mondiale, et j’espère que toutes seront réussies. Je souhaite que l’on fasse un effort particulier pour organiser des actions qui pourront avoir un effet de longue durée. Il faut penser dès maintenant à 2001 et la suite. Réussir une mobilisation de cette ampleur juste pour une fête d’une année ne me semble pas à la hauteur des enjeux. En disant cela, j’ai conscience de ne pas répondre exactement à votre question. Il ne faut pas oublier que toute action d’envergure a des effets sur plusieurs groupes de gens : sur les personnes auxquels elles sont destinées et sur ceux qui les conduisent. Pour moi, l’effet sur les mathématiciens n’est pas le moins important. Il est devenu indispensable que les mathématiciens acceptent de regarder le monde qui les entoure, l’image qu’ils y projettent et les attentes qu’il déçoivent. C’est vital pour la bonne santé de notre communauté mais aussi pour celle de notre discipline. Les mathématiciens doivent inlassablement expliquer pourquoi la méthode abstraite dont ils sont des pratiquants quotidiens fonctionne, dans un va-et-vient non contraint entre une situation particulière et une situation générale. 4. L’établissement dont vous avez la charge ainsi que la SME prévoient-ils des manifestations pour l’An 2000 ? Avez-vous personnellement des projets ? Si oui, pourriez-vous les évoquer ? Pour le moment l’IHES a les yeux rivés sur la célébration de son 40ème anniversaire en octobre 1998, et, en tant que directeur de cette petite structure, je sais que nos faibles moyens ne nous permettent pas de courir trop de lièvres à la fois. Cependant des contacts ont déjà été noués avec la municipalité de Bures-sur-Yvette pour des actions à orientation locale, mais aussi internationale (parce que c’est la vocation de l’IHES) : sont envisagées l’édification d’une sculpture à vocation symbolique à l’entrée de la ville et de l’Institut, mais aussi des actions de jumelage Nord-Sud. La SME a mis sur pied, depuis plusieurs années, un comité pour l’année mondiale 2000 dont le responsable est Vagn Lundsgaard Hansen. Plusieurs projets vont être coordonnés à l’échelle européenne avec, divine surprise, l’intérêt affirmé de la Commission Européenne. Il y a des projets de colloques (Hanovre, ile de Samos, Grenade) visant souvent à renouer le fil de l’Histoire dans un contexte multi-culturel (notamment autour du bassin de la Méditerranée) mais aussi une ambitieuse opération visant à faire fleurir dans les métros de grandes villes européennes des affiches racontant des mathématiques pour le grand public pressé, mais bien entendu cela est élargissable à des métropoles du monde entier. 5. Quel est à votre avis l’avenir des mathématiques et des mathématiciens pour le prochain millénaire ? Je crois, en effet, qu’il est indispensable de faire une distinction entre l’avenir des mathématiques et celui de ceux qui se revendiquent comme mathématiciens. Les mathématiques sont une science dont le champ d’action n’a pas de limite, et l’avènement d’une société dominée par la communication et la gestion des grands systèmes leur donne une place encore plus centrale dans le développement. Cet avenir-là me paraît assurément plein de défis et très prometteur. Je crains, par contre, que les mathématiciens ne sabotent leur avenir à cause de leur capacité extraordinaire à exclure (je devrais dire " excommunier " car on touche là presque à une dimension religieuse) du champ de vision de la communauté mathématique des pans entiers de la connaissance par manque d’ouverture et finalement d’audace. Les mathématiciens ne doivent pas avoir peur de l’air frais du large. Récemment, pour évoquer ce problème, j’ai donné pour titre à une libre opinion dans la Gazette des Mathématiciens " S’ouvrir sans frilosité ". Cela me semble un enjeu capital. Si après l’année mondiale 2000, les mathématiciens pouvaient passer moins de temps à restreindre le champ des mathématiques, un grand pas aurait été accompli. Je suis sûr que la relation que nous avons avec des étudiants potentiels, et plus généralement avec nos concitoyens, en serait changée. # WMY. 2000 IN BURES SUR YVETTE D. JANIN, Mayor of Bures sur Yvette (FRANCE) When Professor Chaleyat-Maurel presented the World Mathematical Year project to me, my adhesion was immediate. The town Council even decided to make Mathematics the theme of communal activities in the Year 2000. The town of Bures-sur-Yvette lies in the heart of a valley where advanced scientific research has made its home. There is the IHES, and there are other structures too, all of whose teachers and researchers are made welcome. These institutions are an integral part of the Bures setting. Bures and its people very much want to bring Mathematics within the reach of the wider public and in particular of the very young. It was with this in mind that in 1996 we organized a week of Mathematics with two aims : to make people more aware of Mathematics and to make it more accessible. Primary schoolchildren were very much involved and solicited. The success of the talks and of the exhibition brought home to me the sometimes unexpected extent to which Mathematics are part and parcel of our everyday life. One outcome was the mathematical sculpture donated to the town by an artist taking part in the competition we organized. That is why we support and will actively participate in the celebration of the World Mathematical Year. Various projects are under study, another mathematical sculpture competition, for example, and the hosting of a mathematical Olympiad. # Editorial - Southeast Asia and Mathematics ## Mitsuo Morimoto In January 1997 a Workshop on Analysis was held in Suranaree University of Technology, Thailand. Professor Huzihiro Araki was the Japanese organizer and chose eight fields of analysis: operator algebras, function algebras, harmonic analysis, wavelets, hyperfunctions, Wiener functional integrals, solvable lattice models, and non-commutative differential geometry. I was invited to give an introductory lecture on hyperfunctions. As newspapers have reported, the spectacular success of Thai economy can be felt during a short drive between the airport and the city center of Bangkok. Applied Science has been developing satisfactorily in Thailand. However, the growth of theoretical science has lagged behind and Thailand is not doing much in mainstream theoretical sciences, especially in mathematics. At this stage in the progress of the country, Thailand felt a need to promote pure mathematics. With this in mind, Professor Sidney Mitchel, an American professor working at Chulalokorn University, organized the workshop. In the late nineteen seventies, the number of people with Ph. D.'s in mathematics in the Philippines could be counted on the fingers of one hand. There was, however, an active mathematical society, the Mathematical Society of the Philippines (MSP), whose membership consisted mostly of teachers of college-level mathematics. The leadership of MSP had a vision of creating a critical mass of researchers in mathematics in the country. They saw this as the first step towards establishing a stable and vital mathematics community. At the time, quite a number of Filipinos were enrolled in Ph. D. programs in mathematics abroad, particularly in the U.S.A., but the rate of return to the Philippines of these scholars was minimal. They were easily absorbed by educational and research institutions there, so it was not feasible just to wait for returning Ph. D.'s to form the critical mass. There was need for an intervention that would keep mathematicians working in the country. The resources of the three leading universities in the country, namely, Ateneo de Manila University, De La Salle University and the University of the Philippines could be tapped to form a Consortium in the Mathematical Sciences able to offer a local Ph. D. program in mathematics. The dearth of Ph. D.'s posed a problem when it came to thesis advising. The theses were, of course, to be of international standard. The solution to the problem was the creation of the sandwich program. The sandwich program concept, as implemented in the Consortium, consists of three stages : • Ph. D. students take the academic courses in any of the three universities. • Students go to a university abroad to start thesis research with a foreign adviser. • Students return home to complete the thesis with a local adviser. The study done abroad is sandwiched between studies done at home, whence the name. Initially, the links with the Southeast Asian Mathematical Society (SEAMS) and the grants from the German government (DAAD), the Australian government (IDP) ant the Japan Society for the Promotion of Science (JSPS) enabled scholars to spend time abroad with foreign thesis advisers, and, at times, allowed advisers to make a reciprocal visit to the scholars. Subsequently the growing exchanges between local universities and universities in the region provided similar opportunities. In its twenty-year existence the program has produced 45 scholars. Of these 31 were in the sandwich program. One of the successes of the program is the global perspective gained by its graduates from their exposure to a foreign work environment and culture. Graduates have become part of a global (or at least regional) network of researchers in their research area and their interaction with members of these networks has led to research that is published in international journals. Among Southeast Asian countries Vietnam has a relatively strong mathematical community. The Hanoi Institute of Mathematics is a center of excellence for mathematical research, although facilities like the mathematical library are in poor condition because of economic difficulties. Vietnam has been a target country for the Commission on Development and Exchange (CDE) of IMU. The CDE supported the research team of Le Van Thanh (Hanoi) for 1992 - 1995 and a project closely related to this research group in 1996. In March 1997, the CDE supported the "Colloque Franco-Vietnamien" held in Ho Chi Minh City, in cooperation with CIMPA/ICPAM. Several young mathematicians from the Philippines and China were invited to this colloquium in a spirit of regional cooperation. Historically and geographically Japan is closely related to Southeast Asia. Japan is a relatively advanced country in mathematics education and research. Although she already had her own indigenous mathematics, modern mathematics was introduced to Japan from western countries and has been one of the most important disciplines in the creation and development of her industry and economy. Japan has been trying hard to design a good national curriculum of mathematics for elementary and secondary schools. As a basis of industry, it is still vital for Japan, as it is for any other country, to improve the quality of mathematics education and to promote mathematics research nationwide. In World Mathematical Year 2000 Japan will host the Ninth International Congress on Mathematical Education (ICME - 9), the first ICME to be held in East Asia. There have been many international meetings on mathematics education and mathematics research, which have been useful for regional cooperation among mathematicians. ICME - 9 will be a much more meaningful occasion to advance international understanding and mutual assistance in the world, especially in East and Southeast Asia. In writing this article, I owe much to Southeast Asian mathematicians, especially to Professor Mari-Jo Ruiz of Ateneo de Manila University. I would like to thank them. # Expert Meeting "UNESCO and Mathematics" ## UNESCO Venice Office ## November 22-24, 1996 RECOMMENDATIONS From 22 to 24 November 1996 an Expert Meeting on "UNESCO and Mathematics" was held at the UNESCO Venice Office. Outstanding mathematicians from various parts of the world, as well as representatives of several important international organizations, like AMU, IMU, ICMS, ICPAM, ICTP and UNESCO, participated in this meeting. The meeting dealt with the important role of Mathematics in modern society, through its relationship with the other scientific disciplines. Emphasis was laid on UNESCO's role in the development of Mathematics, in particular in developing countries, through fruitful collaboration with the other organizations mentioned above. Past and present mathematical activities, including the prospects of further development within UNESCO's "Basic Sciences" Program, were also evaluated. At the conclusion of the Expert Meeting the following recommendations were made for future action : • General recommendations and the role of UNESCO • It is proposed that UNESCO strongly support the establishment and consolidation of regional networks in Mathematics . • The relationship between UNESCO and International Centres dealing with Mathematics should be reinforced, including financially. • Efforts should be made by UNESCO to ensure that mathematicians from developing countries have access to electronic data bases and the other modern means of communication that are so important in industrial and technological development. • UNESCO should support the establishment of a Clearing House to compile, test, analyse, evaluate, promote and disseminate newly developed educational and informative technologies in Mathematics education. • A special fund should be set up to foster specific activities geared towards fulfilling the objectives of World Mathematical Year 2000. • The usefulness of mathematical models for the solution of problems of social relevance must be made known to the widest general audience and UNESCO also has a role to play here. • UNESCO should encourage funding agencies in Member States to support Mathematics and study the possibility of launching a Foundation for Mathematics and Development . • Finally it was strongly recommended that a UNESCO Advisory Committee for Mathematics and Computer Sciences modelled on already existing ones should be set up. • Specific recommendations proposed by the participants in the meeting • to encourage the participation of expatriates in the development of Mathematics in their mother countries ; • to strengthen links and cooperation between UNESCO and existing industrialized centres dealing with Mathematics ; • to strengthen the collaboration between UNESCO and Venetian scientific institutions in carrying out projects. ## RESOLUTION The following draft resolution has been submitted to UNESCO's General Conference (November, 4-7, 1997) submitted by Luxembourg, Ivory Coast, France and Netherlands supported by Russian Federation, Brazil, Benin, Spain, Belgium, Uzbekistan, Philippines, Thailand, Denmark, Ireland, Colombia...... The General Conference. Considering the central importance of mathematics and its applications in today's world with regard to science, technology, communications, economics and numerous other fields, Aware that mathematics has deep roots in many cultures and that the most outstanding thinkers over several thousand years contributed significantly to their development, Aware that the language and the values of mathematics are universal, thus encouraging and making it ideally suited for international cooperation, Stressing the key role of mathematics education, in particular at primary and secondary school level, both for the understanding of basic mathematical concepts and for the development of rational thinking, Welcomes the initiative of the International Mathematical Union (IMU) to declare the year 2000 the World Mathematical Year and carry out, within this framework, activities to promote mathematics at all levels world-wide, Decides to support the World Mathematical Year 2000 initiative, Requests the Director General to collaborate with the international mathematics community in planning the World Mathematical Year 2000 and to contribute during 1998-1999 funds of$250.000 from the Regular Programme and Budget in support of preparatory activities.

PERSON IN CHARGE OF MATHEMATICS AT UNESCO

## Siegbert Raither

Division of Basic Sciences
UNESCO
1, rue Miollis
75015 PARIS (France)
">This email address is being protected from spambots. You need JavaScript enabled to view it.

# Letter to the Editor

regarding the Editorial by Attia A. Ashour on "International Organizations and Mathematics in the Developing Countries", this Newsletter 4, Autumn 1996

The Editorial starts out by complaining that only "certain aspects of mathematics or related to it, such as Computer Science, Information Theory, Statistics & Probability, Modelling, etc., have been established as worthy of support" by the governments of developing countries or the international organizations whose aim it is to help these countries, whereas mathematics as such has not. It then mentions some organizations which nevertheless do help mathematics there and claims that UNESCO is the main, if not the only, sponsor of the international organizations involved in this.

I disagree. The first statement seems to reflect a resentment felt by mathematicians working in some areas of mathematics against those concerned with other aspects, not unlike the grudge found frequently among pure mathematicians against applied ones (the author of the Editorial is himself an applied mathematician). It is not borne out by a broader, deeper and more differentiated analysis. A sample study of curricula and research programmes in developing countries reveals all too often a tendency towards building up in the first place fairly abstract mathematics and neglecting applied areas including some of those from the author's list above, e.g. statistics. This field finds indeed little support in spite of its profound mathematical content and the fact that it is one of the most needed mathematical domains. It is, by the way, precisely not pursued in the Department of Mathematics of the International Centre of Theoretical Physics mentioned by Ashour. Also, when I listened last year in Trieste to the lecture of the Deputy Director-General of UNESCO at the General Meeting of the Third World Academy of Sciences, it dawned on me that UNESCO could profit a lot from acquiring some more statistical methodology.

I do certainly not advocate reducing the support of pure mathematics, quite on the contrary (my own background stems from there), but instead of playing off some parts of mathematics against others we should try to further a harmonious and coordinated growth of all of them in developing countries. The problem is by no means restricted to mathematics : it is just one aspect of the strong dissociation of theory from practice observed on the scientific scene in many of these countries.

Regarding the international organizations mentioned in the Editorial, they are the larger ones with a strong "official" background. Their work has been extremely useful, UNESCO has invested its funds wisely by supporting them, and I hope that these activities will even grow in the future. I maintain, however, that, taken together, the work of smaller organizations of all kinds which had no support from United Nations bodies, and of dedicated individuals, has been more influential. Here we find governmental or semi-governmental institutions like Academic Exchange Offices and private foundations which then become de facto international organizations ; international learned societies like, in my field, the Biometric Society or the Bernoulli Society ; Third World minded groups in university departments of mathematics and governmental ministries of education, research or cooperation ; and individual mathematicians in developed countries who work with those of developing ones in their own institution or in those of their opposite numbers. Their funding comes from many sources and, added up, it is certainly far higher than what UNESCO can provide.

Krickeberg

A. ASHOUR's Response

"My editorial, as its title indicates, is meant for, and only for, information (much needed) about the international agencies which provide funds and help for mathematics and mathematicians in the developing countries. I confined the article to facts and expressed no opinions of my own. I am therefore rather surprised by the reactions of Prof Krickeberg, who obviously misunderstood the editorial and its purpose.

Attia Ashour

N.B. There is a typing mistake in the first line of the editorial. The word 'enjoys' should read 'does not enjoy'."

# ANNOUNCEMENTS: MATHEMATICAL INSTITUTIONS' PARTICIPATION IN WMY2000

"The ICMI WMY 2000 committee"

The Executive Committee of the International Commission on Mathematical Instruction (ICMI) has appointed an ad hoc committee to take the lead, on behalf of the Executive Committee, in planning and preparing ICMI's contributions to WMY 2000. The ICMI WMY 2000 Committee is meant to be both a 'think tank', to generate and propose ideas for WMY 2000 activities prior to and in 2000, and a 'task force' in charge of planning, and partly carrying out, the ICMI WMY 2000 programme. The Committee is chaired by ICMI's President, Professor Miguel de Guzman, Madrid (Spain). The Committee has the following members :

Professor Miguel de Guzman, Chair
SPAIN
fax : +34 1 6301699
e-mail : This email address is being protected from spambots. You need JavaScript enabled to view it.

Professor Bernard Hodgson
Universite Laval, Quebec, QC

Professor Hikosaboru Komatsu
Tokyo Science University, Tokyo,
JAPAN

Professor Lee, Peng Yee
National Institute of Education,
SINGAPORE

Professor Eduard Luna,
Barry University, Miami Shores, Florida
USA

Professor Michael Neubrand
Flensburg Pedagogical University, Flensburg
GERMANY

Professor Kaye Stacey
University of Melbourne, Parkville, VIC
AUSTRALIA

## French Committee for Mathematical year 2000

A French Committee for Mathematical Year 2000 (CFAM 2000) has been created. Its purpose is to coordinate and help initiate activities connected to WMY 2000 in France and to participate in international projects. The committee plans to work in an informal way. A number of projects are already planned or under consideration.

The CFAM 2000 includes representatives of both French mathematical societies (SMF and SMAI), of "Femmes et Mathématiques" and mathematics teachers' organizations (APMEP and UPS), as well as individuals.

The present members of the committee are : Martin Andler (chair), André Bellaïche, Jean Brette, Mireille Chaleyat-Maurel, Michel Enock, Catherine Goldstein, Jean-Pierre Kahane, Jean-Michel Kantor, Jean-Marie Schwartz, Gérard Tronel, Liliane Zweig.

c/o Martin Andler,
SMF, Institut Henri-Poincaré,
11 rue Pierre-et-Marie-Curie, 75231 Paris Cedex 05.
Fax : 33 01 40 46 90 96. E-mail : This email address is being protected from spambots. You need JavaScript enabled to view it..

## Mission pour la célébration de l'an 2000

(Mision for the celebration of year 2000)

The "Year 2000" appeals strongly to the imagination : to celebrate its advent the French government has launched a program

### "Célébration pour l'an 2000".

This program is in two parts :

1. April 6, 1997 to December 31, 1999. During this period of 1000 days meetings will be organized around the country in preparation of the Year 2000.

2. September 1999 - April 2001 - La France, l'Europe, le Monde. Meetings and exhibitions will take place on these general thema in different towns.

Information can be obtained from : Project@celebration 2000. gouv.fr

## (Conseil Québécois de l'Enseignement des Mathématiques)

The following events are planned in Quebec for the year 2000 :

• A unified Congress of all mathematical groups and associations of Quebec (Spring 2000). An exhibition of mathematical projects made by pupils of all levels will be organized for the general public.

• A mathematical exhibition will be held in Montreal.

• The French exhibitions "Horizons mathématiques" and "L'esprit informatique" will circulate in the large towns of Quebec.

The Canadian Mathematical Society has established a WMY 2000 Committee chaired by Bernard Hodgson to identify some ways of participating in the Mathematical Year 2000.

Contact : Bernard Hodgson
This email address is being protected from spambots. You need JavaScript enabled to view it.

The latest information on what AMS is doing for year 2000 is carried on the web page

http://ams.org/amsmtgs/wmy 2000.html

This Committee has been set up to coordinate plans for WMY 2000 with UNESCO. The following have agreed to serve on the committee : A. Ashour (Egypt), M. Chaleyat-Maurel , chair (France), M.S. Narashincan (India), M. Niss (Denmark), R. Rebolledo (Chile), A. Sierpinska (Canada) and G. Tronel (France).

# Editorial

## International Organizations and Mathematics in the developing countries

Attia A. Ashour

Mathematics enjoys the same popularity as other disciplines, (Biology, Chemistry, Physics, Earth Sciences, etc.) with neither the governments of the developing countries nor the International Organizations whose aim is to help these countries. However, certain aspects of mathematics or related to it, such as Computer Science, Information Theory, Statistics & Probability, Modelling, etc., have been established as worthy of support. It is not my intention here to enlarge on this or to give reasons for it. What I want to emphasize is that there is a need to recognize the importance of mathematics at large in its own right and to provide institutes of mathematics and mathematicians in the developing countries with the help needed to continue and improve their work and in particular to develop the "critical mass" which does not yet exist in some of these countries.

Fortunately, there are some International Organizations whose structure allows for this final aim. First and foremost comes the International Centre of Theoretical Physics (ICTP) in Trieste, Italy, which is sponsored by UNESCO, the International Atomic Energy Agency and the Italian Government. Although the primary concern of ICTP is Theoretical Physics, it has a strong Department of Mathematics. The Centre provides federation agreements with Mathematical Institutes and Departments in the developing countries. Each of such agreements allows 2 or 3 persons to visit the Centre every year and spend between 1 and 2 months there. The Centre also offers "Associateships" to senior mathematicians from the developing countries which allow them to visit the Centre for a period of eight weeks each year for five consecutive years. In addition, there is always the possibility to attend schools and seminars held at the Centre or in some developing country and sponsored by ICTP. The office of External Activities of ICTP provides several facilities for mathematicians in the developing countries. For example, it partially funds conferences held there, it initiates and supports subcentres or centres of excellence, it finances the visits of senior mathematicians, (sometimes regular yearly visits for periods up to five years). Help is offered in several other ways,such as the providing of books, journals, and computers.

Another institution whose activity is totally consecrated to mathematics and mathematicians in the developing countries is the International Centre of Pure and Applied Mathematics, (ICPAM or CIMPA as it is usually known) situated in Nice, France. The Centre is sponsored by both the French Government and UNESCO. The town of Nice and the University of Nice - Sophia Antipolis, especially its mathematical community, render invaluable services to the Centre. The activities of CIMPA since its creation in 1980 are mainly the holding of research schools in different branches of Pure and Applied Mathematics. Some of these schools are held in France but the majority now take place in the developing countries themselves. Training courses in Information Theory and Computer Science are also sponsored by the Centre. These activities are usually regional, thus allowing mathematicians from neighboring countries to participate in them. About 6-8 schools are held every year. Due to the growing of the activities of CIMPA, Regional Centres or "Antennas" have been established in Chili (for Latin America) and in China (for South East Asia) to further the aims of CIMPA and enhance its activities in these regions. Other regional centres are planned.

The International Mathematical Union (IMU) is helping mathematicians in the developing countries in several ways. It has established a solidarity fund to help young mathematicians from these countries to attend the International Congress of Mathematics (ICM) which is held every four years and is the most important gathering of mathematicians from all over the world. At the last congress which was held in Zurich, 1994, 120 young mathematicians attended the Congress at no cost to themselves or their institutions, thanks to the fund which paid for their travel and to the host country, Switzerland, which provided housing and subsistence. It is hoped to increase the number at the next Congress which will be held in Berlin in 1998 to at least 200. The IMU Commission for "Development and Exchange" (CDE) has the task of helping to fund the visits of senior mathematicians from developing countries to institutions in the developed world. It also partially funds International and Regional meetings held in the developing countries to allow high level mathematicians to contribute to these meetings. These activities of IMU are funded either directly or indirectly by UNESCO.

Regional Unions and Societies of Mathematics also exist. Examples of these are the African Mathematical Union, the Latin American Mathematical Society and the South East Asian Mathematical Society. These organizations help mathematicians in the respective regions to hold meetings and to publish regional journals. Again, UNESCO plays an important role in funding the activities of these organizations.

It is obvious from the above that UNESCO is the main, if not the only, Sponsor of the International and Regional Organizations which are helping to develop the mathematical sciences in the Third World. For that reason, it was thought that the time is now ripe to evaluate this help up to the present and to look into its future. There is also a need to coordinate between the recipients and to avoid overlaps. Thus, UNESCO decided to hold a Seminar "UNESCO & Mathematics" which will be jointly organized by CIMPA and ROSTE (UNESCO Regional Office of Science and Technology for Europe). It will take place in Venice, Italy, 22-24 November, 1996, and will be attended by representatives of the above mentioned organizations in addition to other distinguished mathematicians. The deliberations will no doubt also include "Mathematics in the 21st Century" and the International Mathematical Year 2000, with special emphasis on developing countries. It might be appropriate therefore to publish the recommendations of the seminar in a future issue of this Newsletter.

# Experiences with popularizing Mathematics

by Vagn Lundsgaard HANSEN, chair of EMS-Committee on WMY 2000

In a society with an increasing number of superficial distractions and governmental pressure for immediate economical results, it is no longer enough that we mathematicians keep the eternal values of our subject to ourselves.

There are some inherent difficulties. Mathematics contains serious, logical reasoning and cannot be dealt with in 20 seconds ; it needs concentration. Furthermore, although we all have been exposed to mathematics for many years in school, the layman only reluctantly allows the use of the language of mathematics ; it is considered boring. I have been told that the first mathematical equation used in a text reduces the potential number of readers by 50% and that the second one kills it. In general, I oppose this kind of straitjacket put on mathematical writings but you do have to go some way to avoid technical language if you want to present mathematics to a broader audience.

There are many mathematicians who have done much more than I have to popularize mathematics, but given the opportunity, I shall reveal some of my experiences.

In 1982, I was asked to design a shopping bag with a mathematical theme for a major food store chain in the Copenhagen area. (You can read more about this in a forthcoming article in The Mathematical Intelligencer). It gave me a lot to think about. I wanted to show that mathematics is not only theoretical but that it has something to do with grasping the world in which we live, and that the development of a theory is the result of the combined efforts of mathematicians in many countries over a comparatively long period. I also wanted to show that mathematics interacts with other sciences, and that it has applications. I ended up choosing Dirac's String Problem. The bag was produced in 200,000 copies. I received 25 'reprints'. Surely, I must be the mathematician whose work has been placed in the most wastebaskets in the world. Nevertheless, it was quite entertaining to do the work, and it did generate some interest at the time and also very recently.

The next experience I shall mention came in connection with the publication of the collected mathematical papers of the Danish mathematician Jakob Nielsen. We received a donation from the Carlsberg Foundation to make the publication viable, and I was asked to write an article for their annual report 1983. Since the article was to deal with Jakob Nielsen, and the reason for the donation was his mathematical contributions, I decided to include two short sections on his work in group theory and topology. It was a thoroughly refereed article - every member of the board reading it. They liked it, but as the secretary wrote me : "We do agree with you that there should be some mentioning of the mathematical world of Nielsen, but could we typeset the most "hefty mathematical parts with a small font since when it comes to mathematics, there are an awful lot of laymen." In 1989 I published a book in Danish on the role of geometry in our perception of the world. In 1993 it was translated into English and published by A.K. Peeters Ltd. under the title Geometry in Nature. The book is intended for the educated layman and in the preface to the English edition I say : "In fact, I planned the book so that our Danish Minister of Education would be able to read it (if he so wished)." From time to time, people have asked me whether I have tested it out on the Danish Minister of Education. My answer is that I did give him the book, and I can tell you that he remembers me. In a friendly review of the book in the Mathematical Reviews, the reviewer builds up a joke saying : "The reviewer would not be very optimistic on this score in the case of his British counterpart." I have had many delightful experiences in connection with the book including several favourable reviews.

In connection with the publication of the Danish book, I was asked to write an article for a weekly magazine published by the Danish Engineering Society. I put quite a lot of work into preparing an article for them. After submitting the article, I heard nothing from the magazine for a long time. Then one day, a young journalist, with a degree in engineering, wrote to me saying that the "article was too mathematical and dull." I was annoyed but decided to overcome it by writing a new article. And this time I made sure that it was not "dull." It was written in a relaxed style and within a few days I got a letter saying : "Yes, this is much better." The new article was published and, with hindsight, I think the journalist might have been somewhat right about the first version. But not quite!

In the above, it has been my intention to indicate that when you try to present mathematics to a broader audience including nonspecialists you are up against strong prejudices. This includes even many mathematicians who think that one should definitely not try to communicate mathematics to the public. I think this attitude is very wrong. We should in fact encourage people to do it. Mathematics is part of our culture - the most refined product of mankind. And it has important applications as well. We must learn to communicate mathematics and not to be so snobbish that we think it is impossible to tell other people what we are doing.

The public image of mathematics is first of all formed in connection with the teaching of mathematics at all levels. Journalists, politicians and other persons of importance for public opinion all have their own personal experiences with mathematics. And for some reason they most often believe that their own experiences are the general experiences. We must learn to communicate mathematics as a subject very much alive.

My conclusion is that the challenges are so great that for the WMY 2000 project to be successful, all mathematicians must work towards creating awareness about the importance and the great cultural values of our subject. Hence committees should be set up in all countries to work on the project. The EMS Committee on WMY 2000 accordingly sees as one of its important tasks to establish a catalogue of viable ideas on what to do. For that we need the input from local committees and individuals. Everyone is cordially invited to submit proposals to the EMS committee.

Professor, dr. Vagn Lundsgaard HANSEN
Department of Mathematics
Technical University of Denmark
Building 303
DK-2800 Lyngby
Denmark
e-mail : V.L. This email address is being protected from spambots. You need JavaScript enabled to view it.

# Mathematics and Arts

Thérèse CHOTTEAU's Exhibition

From June to July 12, the Institut Henri Poincaré in Paris opened the doors of its library to the joint exhibition of its collection of mathematical models and the sculptures of Belgian artist Thérèse Chotteau.

Out of 400 geometrical, topological and algebraic models, over a hundred recently restored were selected by Jean Brette, Head of the Mathematics Department of the Palais de la Découverte in Paris.

Most of them were manufactured out of wood, plaster, cardboard and wire at the beginning of this century. Their undecipherable plasticity already caught the eye of the surrealist artists, Man Ray and André Breton. Having seen three of them in the retrospective André Breton exhibition in the Centre Georges Pompidou in 1991, Thérèse Chotteau was led to discover the whole collection then stored in dark corridors of the Institut Henri Poincaré.

Searching for the reason of her fascination, she photographed and drew sketches of the models in the Institut Henri Poincaré and worked in her studio in Brussels on the relationship between geometrical form and human figure.

The idea of bringing together those intriguing forms and her sculptures seemed a necessity for her work as a sculptor. It is the result of all those connections apparent in this exhibition.

The subset of the exhibition presents two capitals, made of white precast concrete, for a house built for a mathematician. Their motive is geometry, through the eyes of child and adult. The house itself was designed on the theme of fractals by architect Thierry Gonze and some drawings are displayed here.

The exhibition has been an intriguing approach for the artist as for all visitors.

# Mathematics in Museums

The First Science Centre World Congress held in Vantaa, near Helsinki, from June 14 to June 18 was the occasion for an interesting gathering of many people from all around the world interested in mathematical exhibits and, more generally, for showing mathematics to general audiences.

One main point of note is the strong interest in mathematical exhibits - in particular in those which are cheap yet "with content"- coming from museum activities in Asian countries : Singapore, Philippines, Indonesia,...

Another interesting discussion centered around the very ambitious project of the Museum of Science in Barcelona : Mathematics in daily life. This project is carried at a European level. The author is C.ALSINA. J.WAGENSBERG and M.DEMAZURE asked for collaboration.

Even though mathematics are not a material, tangible, thing, interest in mathematics can be stimulated by exhibits that are beautiful or mind-teasing, or both!

There was a general agreement among the participants in this round table, that it is a non-trivial but useful task to pursue, through the year 2000 and thereafter.

Jean Michel KANTOR
Universite PARIS 7

# Mathematical Instituion's Participation in WMY 2000

The French association femmes et mathématiques ( women and mathematics) whose members are mathematicians working at universities or research institutes, or mathematics teachers in high schools or undergraduate colleges, will take an active part in the preparation of WMY 2000. The purposes of the association are to promote women in the scientific community, especially in mathematics, to encourage girls to study mathematics, and more generally the technical and scientific areas, and to be a meeting place for women mathematicians and women mathematics teachers.

Our project for WMY 2000 is to publish a book with texts written by women about mathematics: mathematics for themselves, mathematics in society and in relation with other disciplines, such as physics, computer science, biology, philosophy, sociology,... We also plan to include pictures of women mathematicians from around the world.

Femmes et mathématiques
I.H.P.
11, rue Pierre et Marie Curie
75005 PARIS - FRANCE

# Developement of Mathematics 1950-2000

In view of WMY 2000 and after the publication of DEVELOPMENT OF MATHEMATICS 1900 - 1950 (Birkhäuser, 1994) a group of mathematicians plan to produce a book outlining the evolution of mathematics during the second half of the present century.

We expect some forty articles, of about twenty pages each, to be written by outstanding mathemacians and to cover a wide range of mathematical areas. The editors will ultimately establish bridges between the various contributions in order to elucidate connections or provide supplementary bibliographical sources. We will also include some interviews of prominent mathematicians explaining their views on our science at the turn of the century. We intend to add data giving evidence of the changing aspects of mathematical activities. We will not avoid some remarks about the relations between mathematicians and the society they live in.

The book should allow the reader to become aware of striking and influential top results and to be informed about the state of affairs. It should stress the changes of ideas, viewpoints and motivations during the period 1950 - 2000.

The volume, due to be available already in 1998, will not reveal (as a kind of scoop two years ahead of the year 2000) the totality of mathematical achievements during the second half of the 20th century, but should serve as a basic and reliable reference for World Mathematical Year 2000.

e-mail : pier @ crpcu.lu

# Letters to the editors

I have just seen the Newsletter 3 for WMY2000. I would like to suggest that it would be worthwhile planning some major events around the theme of mathematics and visualisation & mental Imagery. Computer Scientists have largely usurped the term "visualisation', which used to refer to mental imagery and now refers to what is displayed on electronic screens. There is a growing awareness that throwing things on screens and sitting people in front of them is pedagogy. What rarely seems to be emphasized is the role of mental imagery in doing, teaching, and learning mathematics.

I suggest that mental imagery is a major under-exploited domain in mathematics education, and possibly in the teaching of mathematics itself. It would make a splendid topic for explicit work in the year 2000. I imagine it as the basis for work on popularising mathematical thinking, on mathematics education in schools and universities, and intersecting with computer science and other disciplines which use mathematics and mathematical displays. It is easy however to be swept away by screen images, and to forget the role of individual and collective mental imagery.

As you may imagine from my suggestion, I have thought a lot about this topic, written a few things, and helped chair a NATO conference on aspects connected with electronic screens. I am not interested in organizing events, but would like to be of assistance in planning events which focus on ways of working with mental imagery in and with mathematics.

Professor J. MASON
Centre for Mathematics Education
Mathematics and Computing Faculty
Open University
MILTON KEYNES MK7 6AA.
U.K.

# ICME-8, the 8th International Congress in Mathematics Education

July 14-21, SEVILLE, Spain

There are many deep epistemological differences between the domains of research in mathematics and in mathematics education. But there are also striking differences on the level of social behaviour of researchers in the two domains. These reveal themselves especially in the way the two groups hold their congresses. A typical participant of an ICME congress is most of the time engaged in discussion or conversation with n fellow participants, where n>1. Typical participants of an ICM congress rarely form groups with more than two elements. No time is allotted for discussions after lectures in an ICM. In an ICME congress the only lectures after which there is no time for discussion are the four plenary lectures. All the 45-minute lectures (there were around 60 such talks in Seville) are followed by 15-minute discussions. A major part of the programme is occupied by panel discussions, international round tables, working groups and topic groups, presentations of study groups, etc. Mathematics education is still a domain where it is not possible to remain a specialist in a narrow field of research: a broad view of the many aspects of the teaching and learning processes of mathematics, psychological, social, political, institutional, epistemological, cognitive, is necessary. This makes the discussions possible and fruitful.

Another important feature of the group of ICME participants is its enormous heterogeneity with regard to professional occupations and interests : primary school teachers, secondary school teachers, teacher trainers, university mathematics professors, researchers with a background in general education, researchers with a background in mathematics, representing a large variety of research programs and paradigms, ministry officers, national curriculum developers, etc. While this heterogeneity is beneficial for the domain as a whole and helps to keep the researchers’ feet on the ground, it also accounts for what participants experience as "problems of communication". It may moreover have a role in the creation of an atmosphère of "carnival" or "marketplace", since when people's backgrounds and interests diverge too much they can only communicate on a very superficial, ludic or commercial level (e.g. advertising the software they are using or the texts they are producing).

There is, however, one concern that is shared by everybody in mathematics education, and this is : how to make as much mathematics as possible accessible to as many as possible. Related to this question is the theme : 'Making mathematics in the world visible to the world' which ICMI (the International Commission on Mathematical Instruction) has chosen as its way of involvement in the activities related to the celebration of the WMY 2000. In Seville, the EC of ICMI decided to appoint an ad hoc Committee with the task of preparing the ICMI's contribution to the WMY 2000 and which will be in charge of planning related activities especially on the occasion of the 9th ICME which will be held in Japan, Tokyo/Makuhari, in precisely the year 2000.

Anna SIERPINSKA

# IMU Committee on Electronic Publishing

The timely distribution of mathematical work (articles, preprints, books, scripts etc.) is indispensable for mathematical research. It is of equal importance to guarantee quality, authenticity, longevity and retrievability. It is apparent that, at present, there is a transition from paper publication to publication in electronic form. New electronic journals appear and more and more preprint servers are set up. This development is not without problems.

How can papers be found efficiently in electronic archives ? What is the actual state of an E-script (which may change throughout its life) ? Who guarantees for its quality and authenticity ? Has an electronic article been published in traditional form and where ? Is the electronic version one has identical with the one somebody else references ? Will the paper be archived and where ? What happens with an electronic article if its "digital home" ceases to exist ?

To address these and related issues, the Executive Committee of the International Mathematical Union sets up a Publishing Committee. Its task is to write a report to the Executive Committee making suggestions how IMU could help in solving the issues mentioned above. The report is expected by April 1997.

IMU suggests addressing questions that can be answered in the very near future by the collaborative effort of mathematical societies, leading mathematical institutes, publishers and libraries with as little bureaucracy as possible. Among such questions are :

- Is it feasible to introduce an identification number for electronic mathematical articles (such as an ISBN number for a book) ?

- Can a international automatic registration system for new articles (preprints and papers published in journals) be set up ?

- Could there be a central or distributed archive (or a world wide directory system) for electronic preprints in mathematics ?

- What are the chances of defining and agreeing on a standard "first page", more precisely, on some kind of meta information, for every electronic article ? This should be structured in such a way that information about the paper and its location can be retrieved easily.

- If this is possible, how can links to the reviewing journals and from the reviewing journals to the articles be made ?

- How can the way of a paper from its preprint to its final journal publication form be tracked ?

- Which versions of an article should libraries archive and which not ?

IMU would not only like to see suggestions of possible solutions, IMU expects proposals for the implementation of solutions. IMU also asks the committee to consider the costs involved.

IMU is aware of the fact that, in several countries of the world, digital library projects are set up or in progress and that more and more publishers are entering the electronic publishing arena. The Committee is asked to investigate these plans and use the findings for its proposal. The suggestions for electronic publishing in mathematics should also take the developments in other scientific fields into account.

# Announcement African Mathematical Union

The African Mathematical Community will fully participate in the international effort. A Pan-African Committee for WMY 2000 was founded to initiate, promote and coordinate the African contribution to this World Project.

Two major scientific events are planned to be held in Africa in liaison with this program.

Major Project 1 : Organization of the "First Pan-African Congress on Industrial and Applied Mathematics" under the Theme: "Mathematical modelling and the development of Africa : Science, Agriculture, Industry and Management advance with Mathematics"

Major Project 2 : Publication of a scientific book on the theme : "African mathematical achievements in the 20th century"

Secretariat : The Pan-African Committee for WMY 2000 c/o The Cameroon National Committee for Mathematics,
B.P. 12041, Yaoundé, Cameroon.
Fax (237)22-38-00.

# Call for Logo - A Logo for WMY 2000

All ideas and propositions are welcome. We suggest the following basic principles :

• all symbols of the abreviation  WMY 2000 must be used
• the pictures must represent the notions of  WORLD and  MATHEMATICS.

# Acknowledgements

The Editorial board wishes to thank the following institutions for help and sponsorship : UNESCO, IMU, Comité National Français des Mathématiciens, Collège de France, Ecole Polytechnique, Institut des Hautes Études Scientifiques, Institut de Mathématiques (Jussieu), UFR 921 (Jussieu).

On May, 6th, 1992, in Rio de Janeiro (Brazil), the International Mathematical Union declared that the Year 2000 will be the World mathematical Year.
The Declaration of Rio sets three aims :

• The great challenges of 21st Century.
• Mathematics, a key for Development.
• The image of mathematics

In its November 11, 1997 plenary meeting, the UNESCO General Conference followed the recommendations of Commission III and approved draft resolution 29 C/DR126 related to the World Mathematical Year 2000, allocating US $20,000 to this series of events. The following 15 countries co-sponsored the draft resolution: Belgium, Benin, Brazil, Colombia, Cote d'Ivoire, Denmark, France, Ireland, Luxembourg, Philippines, Netherlands, Russian Federation, Spain, Thailand, Uzbekistan. The UNESCO resolution The General Conference Considering the central importance of mathematics and its applications in today's world with regard to science, technology, communications, economics and numerous other fields, Aware that mathematics has deep roots in many cultures and that the most outstanding thinkers over several thousand years contributed significantly to their development, and numerous other fields, Aware that the language and the values of mathematics are universal, thus encouraging and making it ideally suited for international cooperation, Stressing the key role of mathematics education, in particular at primary and secondary school level, both for the understanding of basic mathematical concepts and for the development of rational thinking, Welcomes the initiative of the International Mathematical Union (IMU) to declare the year 2000 the World Mathematical Year and carry out, within this framework, activities to promote Mathematics at all levels world-wide, Decides to support the World Mathematical Year 2000 initiative, Requests the Director General to collaborate with the international mathematics community in planning the World Mathematical Year 2000 and to contribute during 1998-1999 funds of$ 20.000 from the Regular Programme and Budget in support of preparatory activities.

In Memoriam  Jacques-Louis Lions

It is with deep regret that we announce the passing away of Professor Jacques-Louis Lions on May 17 2001.
He was the first to have the idea in 1992 of the World Mathematic Year 2000 when he was the president of the IMU. After that his contribution to its success was considerable.

# Editorial

The Twelfth General Assembly of the International Mathematical Union (IMU) was held in Lucerne (Switzerland) on July 31st and August 1st, 1994, just before the International Congress of Mathematicians, ICM'94, in Zurich.

It was on the occasion of the previous General Assembly in Kobe (Japan), August 18-19, 1990, that the following Resolution was voted:

"Since the IMU wishes to mark the turn of the century in a manner appropriate to the standards set up by David Hilbert in 1900, the General Assembly directs the Executive Committee (EC) to set up a committee to report to the adhering bodies by September 1991 on how to accomplish this, so that in 1994 the Assembly can discuss it and decide how to proceed".

Following this Resolution, the EC of IMU created a Turn of the Century Committee", chaired by Professor Jacob Palis Jr, Secretary of IMU, and having as members Professors V. Arnold, F. Hirzebruch, L. Lovasz, B. Mazur, S. Mizohata, W. Thurston, J. Tits, and S. Varadhan.

The IMU launched in May 1992 the World Mathematical Year (WMY 2000) with the sponsorship of UNESCO (Professor Federico Mayor), of the Third World Academy of Sciences (Professors Abdus Salam and Carlos Chagas), of the French Minister of Research and Space (Professor Hubert Curien), of the Brazilian Secretary of State for Science and Technology (Professor Helio Jaguaribe), of the Brazilian Academy of Sciences (Professor Israel Vargas) and, ICM'94 being organized in Switzerland, of the Swiss Federal Counsellor (Dr. Flavio Cotti). The document issued after this meeting was named "Declaration of Rio de Janeiro for Mathematics".

At the Lucerne General Assembly, a report was presented on the work of the Turn of the Century Committee and on the plans for WMY 2000.

The corresponding proposals were unanimously endorsed by the General Assembly:

## Resolution 2

"The General Assembly thanks the Turn of the Century Committee for its report. It asks the new Executive Committee to proceed with the planning of World Mathematical Year 2000, and to organize and coordinate activities such as:

1. inviting a select group of outstanding mathematicians to present their views on topics they expect to be central to mathematical activity in the next century.
2. selecting a number of symposia, some possibly organized together with other scientific bodies, dedicated to mathematics, its applications and its role in society.
3. events to be held under the auspices of the International Commission for Mathematical Instruction (ICMI), the Commission for Development and Exchange (CDE) and the International Commission for History of Mathematics (ICHM).

The Executive Committee is asked to explore the possibilities provided by communications technology for uniting activities the world over".

It is to be noted that, in her address at the Opening Ceremony of ICM'94, the Federal Counsellor, Mrs Ruth Dreifuss, endorsed WMY 2000.

Following these important decisions, there was considerable exchange of views on the subject during ICM'94, where many ideas and proposals were discussed.

A world-wide coverage for the Newsletter should therefore be systematically organized.

The Editors of the Newsletter, starting 1995, are :
Professor Mireille CHALEYAT-MAUREL (FRANCE)
Professor Gérard TRONEL (FRANCE)

World Correspondents for the Newsletter are :
Professor A. A. ASHOUR (ARAB REPUBLIC OF EGYPT)
Professor Mohammed H. A. HASSAN, Third World Academy of Sciences (ITALY)
Professor Angelo MARZOLLO , UNESCO (ITALY)
Professor Mitsuo MORIMOTO (JAPAN)
Professor Mogens NISS, Secretary of ICMI (DENMARK)
Professor Rolando REBOLLEDO, Chairperson of CDE (CHILE)
Professor Anna SIERPINSKA, Vice President of ICMI (CANADA)

All ideas and proposals connected with WMY 2000 should be sent to the Editors and to the World Correspondents.

It may be useful here to comment on part c) of the Resolution voted at the General Assembly of Lucerne. We recall, among the goals of WMY 2000:

• help for less developed countries. It is essential that the countries that are members of UNESCO be gradually able to reach a level justifying their admission to IMU by the turn of the century. This implies considerable additional efforts in the field of education, training and access to scientific information (Aim No. 2 of the Declaration of Rio de Janeiro).
• promotion of the image of Mathematics. Mathematics should be systematically present in the world of Information Sciences, thanks to examples and applications which will be scientifically exact and open to the largest number of people (Aim No. 3 of the Declaration of Rio de Janeiro).

Here it is important to note the complete agreement of these goals with those of the American Mathematical Society (AMS). They are all related, in one way or another, to the task of teaching mathematics, hence to the key role played in this respect by ICMI, CDE and ICHM.

We also want to stress the part to be played by the various electronic communication technologies. Witness the growing importance of e-mail and the ever-rising number of electronic journals.

Note that WMY 2000 Newsletter is now available on the IMU's WWW server and on the server of European Mathematical Society.

Electronic libraries and tele-conferences should be a set of fundamental tools for the end of this century and for the century to come. These tools should be made available to all mathematical centres in the world as soon as possible.

After our international discussions in Zurich, let us now all work together to achieve these goals.

Jacques Louis LIONS

# ICMI's INVOLVEMENT IN WMY 2000

## GENERAL PERSPECTIVES

The International Commission on Mathematical Instruction (ICMI) is very enthusiastic about WMY 2000 and is eager to contribute to activities up to and in that year as best it can. This article offers a brief outline of ICMI's ideas and measures so far. ICMI believes that it is important to establish rather clear overall purposes and general goals for the WMY 2000. The very idea of a World Mathematical Year is an extrovert one, attentive to the relations between mathematics, in all its manifestations, and the world in which it evolves. It seems that the key "problematics" is that in spite of the social and cultural significance of mathematics, its nature, roles, and functions are, to a considerable extent, invisible to the world outside the mathematical community. We therefore propose that the main task of the WMY 2000 be to "make mathematics and its role in the world visible to society in general, and to the general public in particular". The primary aim should not be to advertise and propagate the marvels of mathematics - lobbying and propaganda will hardly convince the kind of audience we would want to reach; on the contrary, they are more likely to be counter-productive. Instead, the task should be to reveal the five-fold nature of mathematics, as a pure science, an applied science, a system of instruments for decisions and actions, a field of aesthetics and, last but not the least, one of the major teaching/learning subjects in modern times. We should strive to present and demonstrate, and not just claim, these properties of mathematics. In so doing it should be emphasised that the creation and use of mathematics as we know it rely on human activity; that mathematics have a social and cultural history, and that mathematics has intimate relations with philosophical, scientific and practical issues.

## A GLOBAL CONGRESS OF MATHEMATICAL EDUCATION

It is a matter of course for ICMI, as IMU's commission on mathematical education, to place particular emphasis on educational activities in the WMY 2000. A key event of the year will be the Ninth International Congress on Mathematical Education, ICME-9. The congress will take place in a city, yet to be chosen by the ICMI Executive, by and large in accordance with the "classical format" of such congresses. However, in addition to the congress proper, ICMI intends to explore ways to expand and enhance ICME-9 into an event of even greater global significance by means of international communication networks. Thus, it might be possible to organize a number of simultaneous satellite conferences in strategically located places around the world, and provide interactive communication links between them and the main Congress. Such an arrangement would make it possible for huge numbers of people to participate actively in one global Congress and so place mathematics education on the agenda in all parts of the world. Should technological or financial constraints turn out to make this project unrealistic, a more modest scheme could be adopted in its place. A sequence of regional ICMI conferences could be organized, each devoted to a crucial issue or theme of mathematical education in that region, preparing to culminate in ICME-9.

## THE ROLE OF MATHEMATICS IN CULTURE AND SOCIETY

A great variety of public media should be activated to present, as concretely as possible, the ways in which mathematics continues to play an important part in modern society and culture, as it has done in the past. One idea could be to involve in this task the greatest communicators among mathematicians, mathematics educators, scientific writers, producers of scientific films and TV programmes, designers of exhibitions, etc.. If measures are taken in due course, it might be possible for IMU, ICMI and its affiliated study groups, to commission books and articles, public lectures, films, videos, TV programmes, computer-based information technology materials (including CD-roms), museum design, travelling exhibitions, and so forth, all touching on various aspects of the role of mathematics in the world of today and yesterday. As a very concrete example of what could be done, WMY 2000 organizers could invite a number of internationally well-known and influential politicians, composers, industrialists, journalists, film or theater directors, writers, scientists, and many more, all outside what could be labelled as the mathematical community, each to write a chapter of a book telling about his personal encounters and relationships (whether positive or negative) with mathematics. Again, the intention should not be just to produce rosy stories and propaganda lauding the marvels of mathematics but to give honest and authentic accounts of serious people's mathematical experiences. Another concrete idea is to establish a prize for the best talk given in public, and for the best book appealing to the general public, on the role of mathematics in the world.

## ICMI's PARTICIPATION IN WMY 2000

ICMI looks forward to contributing to the setting up of WMY 2000 in various ways, some of which are sketched above, while others are yet to be identified. The Executive Committee has decided to establish an Ad Hoc Committee to make specific plans for ICMI's involvement in the WMY 2000. The EC is in the process of appointing the members of this Ad Hoc Committee. Readers of this Newsletter will be informed of the composition of the Committee when it is complete.

Mogens Niss, Professor, Secretary of ICMI

# MATHEMATICAL INSTITUTIONS' PARTICIPATION IN WMY 2000

## EUROPEAN MATHEMATICAL SOCIETY (EMS)

The European Mathematical Society wishes to take a very active part in the preparation of WMY 2000. The third EMS Congress will be held in 2000 and should be included in the activities of WMY 2000. A special Committee with correspondents in each European country will shortly be appointed by the Executive Committee.

## BERNOULLI SOCIETY

The Bernoulli Society for Mathematical Statistics and Probability is in the process of establishing a committee to enable the Society to participate in the activities of WMY 2000. The committee will be chaired by past president O.E. Barndorff-Nielsen and its scientific secretary will be Professor Rolando Rebolledo. The scientific secretary of the Bernoulli Society, presently Professor Richard Gill, will be an ex officio member of the committee. Once the committee is in place, the names of all its members will be given in the next issue of the Newsletter. The 5th World Congress of the Bernoulli Society will be held in 2000, and it should be included as part of the WMY 2000 activities.

# INTERVIEW OF DAVID MUMFORD, PRESIDENT OF IMU

This interview took place in May, 1995, during the IMU Executive Committee meeting in Paris.

Q : How does IMU feel, and more precisely, what do you think about the WMY 2000 initiative?

D.M. : I think it is an excellent initiative and I think it offers a great opportunity to try and improve the image of mathematics and to try and give some inspiration to the mathematical community. This should be done in terms of several factors like Hilbert looking ahead to where we stand in mathematics and what the major challenges are and, at the same time, looking at our relations with the applications of mathematics, looking at the issues in mathematical instruction and looking at the hopes of involving the Third World more intensely in mathematical activities.

Q : Specifically on these three topics which have been defined for the WMY, have you a personal view on what the challenging problems in mathematics will be in the 21st century ?

D.M. : Ah! That is really a great question ; one would want to sit down and think about it much longer! I personally feel that a very important issue is to restore the free interchange of ideas between pure mathematicians and applied mathematicians. During the 19th century, you see that most mathematicians were both. Fourier series, for instance, were inspired by applications. But there has been a divergence, especially in the US, although I think to some extent in other countries too. I hope that the present emphasis on the usefulness of science in general (if the public is going to put money into scientific research, then it will be useful), will not lead simply to pushing applied subjects at the expense of work on pure subjects, but rather to a sense of common purpose where pure researchers can find inspiration in applications and use their theoretical ideas to grapple more effectively with applied problems. I think there has always been an interchange, but that will really be a major challenge.

Q. : What is your involvement in mathematical education ?

D.M. : It is a vast question. I'm involved in a particular project in the US, called "The Calculus Reform movement", where the goals have been to make instruction in Calculus more relevant to people who are specialized in all kinds of science and engineering and financial professions. Specifically, there is a group lead by Deborah Hughes-Hallet and Andrew Gleason which has written a series of texts now. They have what they call rule three : instead of simply teaching formulas and algebraic manipulations which are often the hardest things for people to apply, to understand their relevance, they are putting equal stress on numerical work and stating every general concept in terms of "How actually do you compute it on a calculator, how can you approximate when you have the data in front of you ?". That's one thing. Secondly, there is the visualisation approach that seeks to make effective use of graphical techniques to see the geometrical side of concepts. Finally, one must not forget algebraic manipulation. I should add that with these three technical methods of tackling the subjects, they also combine the idea of always including meaning for applications at every stage, so drawing applications from physics and chemistry, from economics. For instance, teaching multivariable calculus, when they start with integration. They start off with a graph representing the fox population in South West England which comes from this bible book of mathematical biology by Murray. And the question is : "How do we estimate from this graph giving the density of fox presence, the entire fox population?". So, this, of course, leads to and motivates integral calculus. I strongly believe that mathematical instruction should make a very serious effort to try to have real applications in mind. If you go back to the 19th century, you will find that almost all elementary school teachers often used examples with money : lending money and borrowing money, and so on, and every child understands money. This is concrete. I think statistics is a very important subject to bring into the school curriculum, because the kind of errors that schoolchildren are apt to make are very often errors in numerical judgement ; if you introduce the subject in schools, they will be better prepared.

Q. : What would you like to see in the Newsletter WMY 2000?

D.M. : What I hope will happen is that more concrete activities will gradually be formulated, with concrete plans for involving different groups, and so I think the Newsletter will evolve around these initiatives. We talked in the Executive Committee of IMU about the issue of the image of mathematics and tried to identify methods for explaining what mathematics is to the general public. I think there is no simple answer to this question. I think it is a very difficult challenge, I believe the most important thing is to find some individuals who are highly motivated and have the ability to put themselves in the place of the scientific public. Some people have this skill, and some don't. I think we have to resist a strong tendency to give lectures that are always more and more specialized.

Q. : Have you projects to change a bit the way IMU is organized?

D.M. : I have had two projects that I felt to be very important since people asked me to be President, that we are moving ahead on. One of these concerns the perception from the point of view of the US that the Union is some mysterious rather secret organization that is never clearly understood. Maybe one goal is to publicize what the Union is and what it does: we hope to have next April in New York City a meeting in connection with the meeting of the Executive Committee, to have a public forum, a round table discussion on Union activities, so the general public will see the valuable things it does. The other issue that I have been involved with is trying to increase the participation of applied mathematicians in the congresses and the method for doing this that we want to explore is to have joint activities with applied mathematical organizations. So we are not just talking about a subcommittee of the Union itself, but about involving groups like ICIAM, computer scientists, statisticians, mathematical physicists.

# LETTERS TO THE EDITORS

## In spite of the scientific value and the historical interest of Hilbert's famous Twenty-Three Problems enounced in 1900, one must agree that mathematics have developed in unforeseen directions throughout the XXth century.

In 1992, a symposium held in Luxembourg addressed the comprehension of that evolution during the first half of the present century. One issue was the publication of the volume "Development of Mathematics 1900-1950" (Birkhäuser, Basel, 1994, 3-7643-2821-5, 0-8176- 2821-5)" with articles by J. Dieudonné, J.L. Doob, G. Fichera, M. Guillaume, W. Hayman, C. Houzel, J.-P. Kahane, A. Lichnerowicz, J. Mawhin, L. Nirenberg, J.-P. Pier, W. Schwarz. The book presents a chronological list of major results obtained during the period under study (P. Dugac, B. Eckmann, J. Mawhin, J.-P. Pier); it also contains a list, drawn up by P. Dugac, of original and reference sources.

Whereas it is already hazardous to undertake this investigation of evolution up to 1950, a still more ambitious task would consist in tracing these movements during the later period, as former classifications and structures do not seem to apply any more. A group of persons has started on this historical and thematic study in view of World Mathematical Year 2000. They should appeal to specialists for contributions covering a wide spectrum of themes which would ultimately be linked by logical connections.

Jean-Paul Pier, Mathématiques
Centre universitaire de Luxembourg
162 A, Avenue de la Faïencerie, L-1511 Luxembourg (Luxembourg)
Fax : (352) 46.66.44.237.
e-mail : This email address is being protected from spambots. You need JavaScript enabled to view it.

## MUSIC AND MATHEMATICS : DREAM OR REALITY ?

Some years ago, I used to be irritated by the commonplace saying that mathematicians had a privileged relationship with music. However, for some time now, a number of contacts with people whose intellectual life was devoted to these two poles, and my own experience as musician and mathematician, have led me to rethink this view. In the Middle Ages, the Quadrivium included the four basic sciences which were arithmetic, geometry, astronomy and music. And Leibniz still spoke about the "secret calculation". Could this close tie between the two subjects over many years account for the symbiosis which we seem to note today? This question leads to another : although the medieval learning mentioned earlier derived from the Greek system, it was widely dominated by the Western European schools. Did this give rise to a qualitative or a quantitative difference in the relatedness of the two subjects in Western Europe and in countries with a completely different culture like China or India for instance? These are questions we would like to attempt to answer in the context of a study for the World Mathematical Year 2000. A questionnaire was proposed to the members of the Société Mathématique de France (SMF) with a view to collecting statistical data that will allow us to confirm or to infirm this music-mathematics relationship. We are planning to carry out a counter-test in another scientific area (possibly chemistry) to see if differences emerge.

This operation has already been successful among members of the SMF. We would now very much like to submit it to a wider sample. The questionnaire is now available in English on the web : Questionnaire Mathematics and Music . In advance we wish to thank all those who agree to spare a little of their time (not more than fifteen minutes) to fill in the questionnaire. Also, as I am new in the field, I am slowly discovering that many people have already delved into this issue from a historical, psychological or philosophical point of view. So I do hope that the people I have not yet had a chance to get in touch with will kindly let me have their opinion (and a bibliography, if they wish) in order to give more weight to the project.

Laurent Mazliak
Laboratoire de Probabilités
Université Pierre et Marie Curie
Tour 56 3ème étage
4, Place Jussieu
F-75252 Paris Cedex 05
France

# ANNOUNCEMENTS, NEWS FROM SCIENCE MUSEUMS

The Editorial board would like to open a column for information on the two last aims of the "Rio de Janeiro Declaration". It would be very interesting to collect more for the next issues.

ICME8
The Eighth Congress on Mathematical Education (ICME8) will be held in the city of Seville (Spain), from July 14 to 21, 1996. Electronic information is available on Mosaic. The URL is :http://icme8.us.es/ICME8.html

## FIRST SCIENCE CENTRE WORLD CONGRESS

Vantaa (Finland), June 14-18, 1996.
The Association of Science-Technology (ASTC) and the European Collaborative for Science, Industry and Technology Exhibitions (ECSITE) invite Science Centre professionals to the First Science Centre World Congress on the general theme Learning for tomorrow ".
Informations can be obtained from :

Ms. H. Von Troil,
HEUREKA po Box166,
FIN-013001 Vantaa (Finland).

## CITÉ DES SCIENCES ET DE L'INDUSTRIE, PARIS (France)

In the Science Museum of Cité des Sciences et de l'Industrie (Paris, La Villette) was opened a new presentation of the permanent exhibition in the mathematical department. The originality and the aims of this presentation are to offer a more attractive and better image of mathematics to the general public visiting the museum. Starting with models from daily life or Pythagoras' Theorem, the visitor can go on to the theory of complexity used in the technical world (computers, planes,...). He can also enter domains using probability theory, statistics, data analysis in economical and social sciences. There are short movies on "Proofs" and "Modelling in Applied Sciences". The staff in charge of the mathematical department hopes to improve the transparency of mathematics in daily life.

Cité des Sciences et de l'Industrie
30, Avenue Corentin Cariou
F-75019 PARIS (France).

## NATMATH

The ECSITE organization plans a travelling exhibition (called NATMATH) on the theme : "Mathematical Modelling of Nature ". The first goal of the exhibition is to cultivate interest in mathematics among the visitors to European museums and science centres, and to instil confidence in their understanding of the value of mathematics and its role in their comprehension of the world around them. NATMATH is planned for stays of three to six months at ECSITE museums.
For information, contact the project leader :

J. Wagensberg,
Director of the Science Museum
Teodor Rovilralta
SP-08022 BARCELONA (Spain).

## A LOGO FOR WMY 2000 ACKNOWLEDGEMENTS

All ideas and propositions are welcome. We suggest the following basic principles :

• all symbols of the abreviation "WMY 2000 " must be used,
• the pictures must represent the notions of  "WORLD " and " MATHEMATICS ".

## ACKNOWLEDGEMENTS

The Editorial board wishes to thank the following institutions for help and sponsorship : UNESCO, IMU, Comité National Français des Mathématiciens, Collège de France, École Polytechnique, Institut des Hautes Études Scientifiques, Institut de mathématiques (Jussieu, Paris).

# Editorial

by

J.L. Lions, President of IMU

This is the second issue of the Newsletter for WMY 2 000. It is specially devoted to developing countries, in connection with the third scope of the Declaration of Rio de Janeiro.

The Newsletter Number 1 has been widely disseminated thanks to the efforts of all the National Committees for IMU, of international organizations such as ICTP, AMU, EMS, AMS and others, and local and individual initiatives.

Many of you have shown interest in its proposals ; ideas are circulating, suggestions are on the way and even constructive criticisms have been made. We thank you for your help and cooperation.

Some initiatives are published in this issue. We shall report on many others in Number 3, which is scheduled at the end of this year, after the International congress of Mathematicians in Zürich.

# Some perspective on WMY 2000

by A.O. Kuku

President of AMU (African Mathematical Union)

• Some AMU aspirations
• Need for debt-for-science campaign

In many developing countries, African countries in particular, the mathematical research scientists are gradually becoming endangered species for obvious reasons, and unless something is done to arrest the situation, the year 2000 and beyond will witness little or no mathematical research activities in these areas of the world. The WMY 2000 can be instrumental in drawing the attention of the International Community to the various problems and co-operate with the local community towards their alleviation.

## Some African Mathematical Union aspirations in the spirit of WMY 2000

### 1. AMU Mathematical Sciences network for Africa

The aims and objectives of the network - which has currently fifteen members - are the following:

• To encourage North-South and South-South co-operation in the area of research and training of graduate students for higher degrees of African Universities, and thus alleviate the problem of brain-drain often resulting from long stay of students outside the continent.
• To bridge the isolation gap among African mathematicians through development of research groups in member Institutions of the network eventually leading to the production of critical mass of mathematical scientists so badly needed in the continent for developmental purpose.
• To produce replacements for the rapidly dwindling staff in Universities, Polytechnics, Colleges of education and research Centers.
• To accelerate the evolution of members of the network as Centres of Excellence for research and training in the mathematical sciences.

The preliminary programme consists of visits by young African researchers to members of the network. During the first year of the programme, the International Center for Theoretical Physics (ICTP) has supported the travelling expenses of young mathematicians while the Association of African Universities (AAU) has supported the local expenses of the researchers at their host Universities.

The long term programme, outlined below, will commence as soon as we find funds to execute any part of it.

• Professors from within and outside the network (especially those from advanced countries) will be invited from time to time to visit members of the network, give lectures and contribute towards the development of research expertise at the host institutions.
• Graduate students and staff from members of the network will be given an opportunity to spend some time - up to a maximum of one year - to get better exposed.
• Special effort will be made to improve the library and others facilities at members of the network.

### 2. AMU tertiary level textbook development

The prices of imported texts at the tertiary level are becoming prohibitive in African countries because of frequent devaluation of the currencies in these countries. So, neither the students nor the teachers nor sometimes the libraries can afford to buy them. Thus, as soon as the AMU is able to mobilize enough funds, we shall organize writing workshops for our membership to produce text books across linguistic and geo-political barriers. It is our strong belief that producing books locally will reduce costs as well as make the texts more relevant to the needs and background of African students.

### 3. Journals/books for Africa

The AMU is currently exploring ways of co-operating with Organisa-tions/Individuals who are interested in getting mathematics journals/books across to African Institutions. We like to seize this opportunity to appeal to Professional Organizations like the AMS, CMS, LMS.MAA, etc, publishing journals/books to donate journals/ books to members of the network. We also like to appeal to reputable publishers of journals/books to donate some and /or sell some at highly reduced rates.

### 4. Electronic mail

We are aware of the dire need for electronic mail all over the continent to reduce the isolation problems of African Mathematicians and we are joining forces with other scientific organizations within and outside Africa to put pressure on our various Governments and tertiary Insti-tutions to make this a reality. We do hope that by the year 2000, all tertiary Institutions in Africa will have e-mail.

## Need for Debt-for-Science campaign

Many third world countries are, at the moment so overwhelmed by their debt burdens that it is absolutely impossible for them to find financial resources necessary to make meaningful progress in the direction of mathematics, science and technology.

There is currently a mounting pressure on the creditor nations to write off a lot of these debts. While it is indeed desirable to write off quite a lot of these debts for various reasons, it is also desirable to ensure that the money that these countries would otherwise have used to service debts is spent on concrete developmental projects. The International Scientific Community should spearhead a Debt-for-Science campaign whereby Third world countries that show evidence of willingness to use its debt-servicing funds to further the progress of mathematics, science and technology would have such debts written off.

This way, the creditor countries will be contributing to global development of mathematics, science and technology without giving new loans. The Third world countries involved will also be able to make scientific progress without much pain. It should not be too difficult for WMY 2000 to co-operate with other scientific organisations like ICSU, TWAS, UNESCO, to promote an effective campaign, and succeed.

# Bordeauxthèque

by J.F. Jaulent, BMI director

Bordeauxthèque is a documentation service for mathematicians and computer scientists working in French speaking universities. It is supported by the BMI (Research Library for Mathematics and Computer Science of Bordeaux).

This service has been growing extensively since its foundation in 1988 by J.L. Joly, and now concerns over forty African universities. As a result of its success it has obtained the support of CIRUISEF and CIMPA which will cover most of its expenditure in the future.

Operating a modern research library requires a big investment and continuous expenditure. So in spite of the fact that, especially in mathematics, up to date documentation is of outmost importance, this documentation is often non available even to active mathematics departments, because of financial reasons. The aim of Bordeauxthèque is to help the researchers of countries lacking proper bibliographical resources, by offering them access to scientific literature at no cost in a simple, regular and efficient way. To do this, Bordeauxthèque relies on the remarquable wealth of the BMI.

## How does Bordeauxthèque work?

The documentation service Bordeauxthèque produces two volumes a year, each consisting of 250 pages of summaries of about 60 periodicals which have been chosen according to the wishes of our correspondents (for consideration, a periodical has to be requested by at least two correspondents). These summaries allow our users to ask us photocopies of recent papers, which are then made by our staff and sent to our correspondents free of charge Each request must be checked by the head of the correspondent's department in order to avoid sending the paper twice. For this, some request forms are sent with the two volumes of the summaries.

Bordeauxthèque also publishes on a regular basis two lists : a list of fundamental books covering the main topics of mathematics ; and a list of titles recently acquired by the BMI. This keeps researchers informed on the ressources available in Bordeaux. Moreover our users acknowledge with pleasure that our library's staff is always ready to answer any queries concerning addresses of journals, references, and so on...

## Some data

The three volumes published by Bordeauxthèque in 1988, 1989 and 1990 have been distributed to some 70 French speaking universities (essentially in Africa). Each subsequent issue has been updated with more summaries at the request of our correspondents : the two biannual volumes produced since 1991 consist of the summaries of about 60 journals. The number of photocopies sent by the service has steadily increased since its creation, as follows:

• in 1988, 4500 copies concerning 09 universities
• in 1989, 6000 copies concerning 15 universities
• in 1990, 7000 copies concerning 18 universities
• in 1991, 8500 copies concerning 29 universities
• in 1992, 10200 copies concerning 43 universities
• in 1993, 11800 copies concerning 47 universities

For instance, in 1991, some 668 requests from 153 researchers have been answered, each request amounting to an average of 13 copies. Of these requests 517 concerned very recent summaries.

## Plans for the future

From the first six years of activity, it appears that Bordeauxthèque has been a success and has proven that there is a real need for such a service. Of course it is clear that there is room for improvement in its perfomances. For instance, starting 1994, we will be able to collect by scanner the information on the summaries we publish. Our publications will be available on electronic support. However one has to keep in mind that most of our correspondents do not have access to electronic mail ...

To conclude we shall mention that Bordeauxthèque runs on a budget of about 70.000FF. Even though this amount only represents between 5 and 10 % of the library's total expenditure, it allows the BMI to count among its users more out -of -town researchers than mathematicians working in Bordeaux.

# The CDE

by P. Bérard, Secretary of the CDE

The CDE (Commission on Development and Exchange of the International Mathematical Union) currently runs two programmes in order to promote mathematical research in developing countries.

The first programme offers partial travel support to mathematicians from developing countries who make an extended research visit in an advanced mathematical center ; it also applies to mathematicians from advanced countries who make an extended research visit in a mathematical center in a developing country. It is required that the host center commits itself to bearing the local expenses.

The second programme offers (limited) financial support to conferences of regional interest organized in developing countries.

The CDE has also begun to identify research teams of high quality in developing countries and to offer support on a three year basis (two teams have been supported so far).

Although CDE could address itself to a limited number of needs required in the development of Mathematics, it seems to us that CDE's support to Mathematics in the Third World is important both for its psychological and practical impact.

The CDE benefits from IMU funds, from grants awarded by ICSU and UNESCO as well as from donations by some mathematical societies. CDE's actions need continuity in order to be meaningful and hence a reasonable level of regular funding. WMY 2000 should be a unique opportunity to achieve this goal. Using the dynamics of WMY 2000 and the help of all the organizations already supporting CDE - especially UNESCO - a Trust Fund, which would ensure the financial stability of CDE, should be raised.

For more information on CDE actions or to make donations in support of CDE programmes, please write to: the Secretary of CDE, Professor P. Bérard

# EMS sub-committee

by P. Bérard

The Executive Committee of the European Mathematical Society has recently set up a sub-committee on developing countries, under the chairmanship of Professor Pierre Bérard (Grenoble, France).

This sub-committee will make proposals towards collaboration with developing countries that seem more appropriate in the European framework. One such proposal would be to facilitate access to scientific information in the spirit of Bordeauxthèque (see this Newsletter).

# Miscellaneous

## Unesco

UNESCO will renew in 1995, as part of the CDE activities, its help to developing countries. Further developments are under study.

## Philately and WMY 2000

A proposal, supported by the Société Mathématique de France and the Société de Mathématiques Appliquées et Industrielles, to edit for the year 2 000 four or six stamps with the effigy of French mathematicians has been submitted to La Poste in order to illustrate, on the French side, the World Mathematical Year 2 000. We hope that such an initiative could be taken in other countries all over the world.

## How to use

Many libraries, and individuals, all around the world, have asked for copies of the Newsletter Nb. 1. We thank you very much for your interest, and we shall add your demand to our mailing list. But we would like to ask you, when-ever possible, to first apply to the National Committee or the Learned Society in your country, in order to avoid a too huge centralization of demands. Besides, some National Committees have offered to translate the Newsletter ; this also could help to circulate ideas and initiatives!

## Call for initiative

We hope many mathematical Societies will relay the Declaration of Rio de Janeiro.

We shall mention all the initiatives all over the world in the forthcoming Newsletter.

This Newsletter, sent to all the National Committees and National Adhering Organizations of IMU, can be reproduced and we hope it will be widely spread.

# Editorial

by

J.L. Lions, President of IMU

The declaration of Rio de Janeiro on Mathematics, the text of which is to be found in the next columns of this Newsletter, has declared year 2000 to be World Mathematical Year-in short WMY 2000.

I am glad to present the first issue of this Newsletter, the purpose of which is being intended to give the largest possible audience all informations related to this initiative.

Dissemination of this Newsletter is made possible thanks to the very kind help of the I.H.P. (Institut Henri Poincaré) and the École Polytechnique. All suggestions, remarks and correspondence, must be sent to the address given at the end of this Newsletter. Documentation and preparation for the first issue have been realized by Mrs. H.Gispert and Mrs. A.Theis, who is assisting me in my responsability as President of the International Mathematical Union.

Mrs. H.Gispert will gather all further information and will be in charge of preparing the next issues.

This Newsletter is sent to all the National Committees and National Commissions-ICMI, CDE, ICHM, and to the CTP, the Third World Academy of Sciences, ICPAM, adhering Organizations of IMU, as well as to the IMU and to other Mathematical Societies.

We thank in advance all these Committees and Institutions to help spreading this Newsletter as widely as possible, among their members and surroundings. We very much hope the tool we are just setting will greatly help encouraging this initiative.

# DECLARATION of RIO de JANEIRO on MATHEMATICS

On May 6th, 1992, in Rio de Janeiro, during the celebration of the 40th anniversary of the world-wide reputed Institute of Pure and Applied Mathematics (IMPA), Professor Jacques-Louis Lions, President of the International Mathematical Union (IMU) declared in the name of this Union, that the year 2000 will be the World Mathematical Year.

WMY 2000 is set under the sponsorship of UNESCO (Professor Federico Mayor), of the Third World Academy of Sciences (Professor Abdus Salam and Professor Carlos Chagas, who took part in the declaration of Rio de Janeiro), of the French Ministry of Research and Space (Professor Hubert Curien), of the Brazilean Academy of Sciences (Professor Israel Vargas) and of the Swiss Federal Counsellor (Dr.Flavio Cotti), the next International Congress of Mathematicians being organized in Zürich in August 1994. The declaration of Rio de Janeiro sets three aims:

## 1. First aim : the great challenges of the 21st century

During his conference in Paris in 1900, David Hilbert listed a series of the main problems that the now ending century had to challenge.

The American Mathematical Society suggested in 1990, at the last General Assembly of IMU in Kobe (Japan), that first class mathematicians, to be represented within the Turn of the Century Committee, organize the efforts to envision what the great challenges of the year 2000 would be. This Committee is chaired by Professor Jacob Palis Jr, IMPA (Brazil), Secretary of IMU.

## 2. Second aim : Mathematics, keys for Development

Pure and Applied Mathematics are one of the main keys of the understanding of the world and of its development.

That is why it is essential that countries which are members of UNESCO be gradually able to reach a level enabling their admission to IMU, the members of which are 50 nations for the time being. Therefore, the second aim of the Declaration of Rio de Janeiro is that most countries which are members of UNESCO reach such level by the turn of century.

That implies great additional efforts in the fields of Education, of Training, and-a very sensitive point for countries that face difficulties in having currency ressources-of access to Scientific Information.

Such efforts which have already been widely undertaken, will be confirmed and raised by the two main commissions of IMU : ICMI (International Commission on Mathematical Instruction), which is chaired by Professor M. de Guzman from Madrid and whose Secretary is Professor M. Niss from Denmark, and the CDE (Commission on Development and Exchange), which is presided by Professor M.S. Narasimhan from Bombay and whose Secretary is Professor P. Bérard from Grenoble, France. Both commissions are linked with UNESCO which was represented in Rio de Janeiro by Professor A. Marzollo, responsible for mathematics.

## 3. Third aim : the Image of Mathematics

The Declaration of Rio de Janeiro sets as third goal, which is also of great importance, a systematic presence of mathematics in the `Information Society" thanks to examples and applications which will be scientifically exact and open to the largest number.

That will be developed in connection with such efforts which have been already undertaken by many countries that are members of IMU. The declaration of Rio de Janeiro on Mathematics announcing the World Mathematical Year 2000 was warmly supported not only by all the mathematicians present in Rio and who had come from all continents, and of course many of the Brazilian most eminent mathematicians, but also by professors in other subjects too, and especially Professor Carlos Chagas, former President of the Pontifical Academy of Sciences.

# FOLLOW UP OF THE DECLARATION

Among the three aims of the Rio de Janeiro declaration, if considering the great challenges for the 21st century proceed with more specific approach of IMU, no doubt the realization of the two other aims has to be as broad and open as possible. So, UNESCO's sponsorship is specially significant.

UNESCO plans to reinforce in 1994-1995 its cooperation with the International Mathematical Union (IMU), in the framework of its sponsoring of the World Mathematical Year 2000 launched in Rio de Janeiro in May 1992. This cooperation, established since 1986 with the International Commission for Mathematical Instruction (ICMI) of IMU, has mainly consisted in:

1. Joint publications of a selected Mathematical Bibliography for the Third World, and of a Directory of Mathematicians from Developing Countries.
2. The IMU/CDE-UNESCO programme of visiting professors and researchers.
3. UNESCO support to participation of representatives of mathematical communities from developing countries in international events.

In line with the long term objectives of the IMU WMY 2000, and in particular with the one of creating the prerequisites for broadening national representations in IMU, UNESCO will endeavour in 1994-1995 to strenghten its support of aims 1 and 2 above.

Moreover, UNESCO efforts will be devoted to the gradual establishment of regional mathematical information and documentation centres, trying to meet in this way a crucial problem for mathematicians from the Third World. (A. Marzollo, UNESCO director)

## Turn of the Century

### Turn of the Century Committee

On August 1990, in Kobe, during the last International Congress of Mathematicians, the following resolution was voted:

"Whereas the IMU wishes to mark the turn of the century in a appropriate manner to the standard set by David Hilbert in 1900, the General Assembly directs the Executive Committee to set up a Committee to report to the adhering bodies by September 1991 how to accomplish that in 1994 the Assembly can discuss it and decide how to proceed".

The composition of the Committee which will address a first report in Zürich in 1994 is the following:

Chairman : J. Palis Jr. (Brazil), Members : V.I. Arnold (Russia), F. Hirzebruch (Germany), L. Lovasz (Hungary), B. Mazur (USA), , S. Mizohata (Japan), G.D. Mostow (USA), J. Tits (France), W. Thurston (USA), S. Varadhan (USA).

### ICHM

The International Commission on History of Mathematics, believing that it would be appropriate, in the year 2000, to assess the significance and fate of Hilbert's famous lecture of 1900 on seminal, as-of-then unsolved problems in mathematics (just at the Turn of the Century Committee will project its own vision to devise a new set of seminal problems for the 21st century), is organizing an historical Symposium for the Zürich Congress in 1994. This will be devoted to a rigourous examination of the history of congresses from Zürich to Zürich, including the Paris Congress in 1900.

## Mathematical keys for Development

### ICMI

ICME-7 (Quebec, 1992) and WMY 2000

The announcement of IMU's initiative which was made at the opening address of ICME-7 was very well received.

The Executive Committee and General Assembly of ICMI have discussed of ICME-9 which will take place in year 2000, a global congress on mathematical education-a central congress with regional satellite congresses held at the same time being linked to the central one by means of communication technology. The Executive Committee agreed to stimulate the publication of a survey book on "what happened in mathematical education in the last 40 years?"

In the meantime, ICME-8 will take place in 1996 in Sevilla. In the very spirit of the declaration of Rio de Janeiro, it has been decided to raise registration fees thus enabling to exempt people from some countries.

### Sevilla 1996 global communication

Projects are developing to make Sevilla a test-bench, at a small scale, for the world meeting ICME-9. Among them, an agreement in principle is acquired on the use of the new Spanish satellite Hispasat launched in September 1992 which covers in particular Spain, Portugal and America (USA, Mexico, Central and South America).

### CDE

The activity of the CDE which tries to promote the place and the role of mathematics in collaboration with developing countries, is fully in keeping with the second aim of the declaration of Rio de Janeiro.

More precisely, with the support of ICSU, UNESCO, IMU and some scientific societies, the CDE grants travel fellowships in research advanced centers and partially subsidizes congresses according to scientific level on a somewhat reciprocal commitment. Future activity of CDE will certainly find some profit in the dynamic WMY 2000 is going to create.

### CDE-UNESCO dissemination centres

One of CDE projects, the programm of dissemination of mathematical information and documentation in developing countries elaborated with UNESCO in December 1990, is of particular importance. This programm consists in setting up three libraries-documentation centres in Asia, Latin America, Africa, in institutions where fairly well developed libraries already exist as well as a group of active mathematicians. The programm intends to provide additional inputs for completing the collections of core mathematical books and important mathematical journals, as well as reprints. Moreover, the new imputs should facilitate the acquisition of essential electronic data bases and communication systems. The centres shall provide their services to mathematicians in the region to facilitate access to both latest and classical mathematical literature.

## Image of Mathematics

### ICMI

Among numerous propositions about WMY 2000, some deal with the image of mathematics with the general public. Professors M. de Guzman and M. Niss (President and Secretary of ICMI) have suggested to emphasize three ideas : the role of mathematics in culture and society, an overview of the impacts of mathematics on technology (old, modern and future technology), a general effort to counteract wrong images of mathematics with the general public.

### ICHM

One of the best ways to establish a "systematic presence" of mathematics in the "Information Age" is through the history of mathematics, which can effectively demonstrate the significance of mathematics in cross-cultural ways in the widest possible variety of different contexts.

Local meetings, international symposia, special exhibitions and long-range publications can all help to create a higher public awareness of mathematics and the crucial role they have played in world history.

Two efforts in which the ICHM is already engaged have a direct relation to the aims of WMY 2000. One is the maintenance of an archive of slides and photographs of mathematics; one goal of the Commission in light of WMY 2000 might be publication of a catalogue of all known portraits or photographs and where they may be found.

The second project is the production of a "Historiography of the history of Mathematics" to which more than forty historians from all over the world are collaborating to describe the history of history of mathematics from the first historical writings about mathematics by the ancient Greeks and Chinese, to the present. Publication of this work in anticipation of WMY 2000 would be a realistic goal of the Commission, and one that would be very much in keeping with aims 2 and 3 as stated in the Rio Declaration. (J.Dauben, ICHM Chairman)

# WMY 2000, FIRST ECHOES

Some associations and societies have already shown their interest and their support for WMY 2000.

## ICSU

The International Council of Scientific Unions has published in the fall issue of Science International an article from Professor Lions presenting the Declaration of Rio de Janeiro.

## AMU

The African Mathematical Union is already involved in WMY 2000, several of its own projects being connected with the second aim of the Declaration of Rio de Janeiro. It is in particular the proposal for Mathematical Sciences Network for Africa. Its aims are, first, to encourage South-South cooperation in the area of research and the training of graduate students, second, to have the University centres included in the network used as regional mathematical centres.

Another important project of AMU which could be pushed under WMY 2000 is a Mathematical Communication Network within Africa and between Africa and the rest of the world.

The Journal, Journal Afrika Mathematika created in 1978 which publishes regularly since several years first rate papers of African mathematicians, is a first essential tool to avoid isolation of mathematicians in Africa.

## SMF and SMAI

Last year in May, the Société Mathématique de France and Société de Mathématiques Appliquées et Industrielles organized in Paris a workshop on "Les Mathématiques au Futur" which intended to echoes to the Rio declaration about "World Mathematical Year 2000". This initiative, welcomed by the French Ministry of Research and Space who patronized the launching of WMY 2000, was addressed to the scientific press and the mathematical community. After an interview of J.L.Lions in which were described the three major aims of WMY 2000, several talks were given on the topic "Mathematics as an Historical adventure". The first one, referring to the work of the "Turn of the Century Committee", dealt with the actuality of the Hilbert program listing the great mathematical challenges of the twentieth century. Then, mathematicians and physicians of the generation of the thirties-forties exposed their vision of mathematics of their times, telling what they thought important for the next years to come. The mathematical fields mentionned were Number Theory and Topology, Geometry and Physics, Statistical Mechanics, Applied Mathematics, Dynamical Systems and Analysis. At last, P.Bérard, Secretary of the Commission on Development and Exchanges spoke of the second aim of WMY 2000, the great challenge of mathematical alphabetisation, explaining the formation and teaching problems in mathematics, in particular among Developing Countries, and the support that could be brought to them.

## ISRAËL ACADEMY OF SCIENCES AND HUMANITY

The Israël Academy informed the IMU that it strongly supports the aims of the Rio Declaration considering it was a privilege to promote this cause.

## EMS

During its first Congress in Paris in July 1992, the European Mathematical Society (EMS) organized a round table "Collaboration with Developing Countries" to which participated several members of the CDE including its President. Recommendations, akin to the aims and activities of the CDE, have been drawn for future actions : 1. make governments aware of the importance of mathematics, 2. training at graduate level and PhD or postdoctoral research, 3. develop local research, 4. multiply local initiatives to develop communications, libraries and scientific documentation. EMS is now thinking how to take care of these recommendations in the future.

# Call for initiatives

We hope many scientific centers and organizations will relay the Declaration of Rio de Janeiro. We shall mention all the initiatives all over the world in the next Newsletters. UNESCO will renew in 1995, as part of the CDE activities, its help to developing countries. Further developments are under study.

Directeur de la publication : Professeur Jacques-Louis LIONS Institut Henri Poincaré (IHP) - 11 rue Pierre et Marie Curie 75231 Paris Cedex 05 FRANCE

This Newsletter, sent to all the National Committees and National Adhering Organizations of IMU, can be reproduced and we hope it will be widely spread.

La Sociedad Central de Arquitectos ha auspiciado, acompañada por la Facultad de Arquitectura, Diseño y Urbanismo, Correo Argentino, Metrovías y otras entidades, dos concursos organizados por la Asociación de Matemática y Diseño: “2000 – Año Mundial de la Matemática”.

La realización de este concurso surgió a raíz de que UNESCO ha declarado el año 2000 como el año Mundial de la Matemática. Y el Instituto “Henri Poincaré” de París, que centraliza toda una serie de eventos en el ámbito internacional ha convocado a la Asociación presidida por la Dra. Vera W. de Spinadel, profesora titular consulta de la Facultad de Arquitectura, Diseño y Urbanismo de la U.B.A., a realizar una actividad conmemorativa en la República Argentina. La Asociación de Matemática y Diseño, buscando organizar un evento que excediera los límites de la “comunidad matemática”, y promovió dos concursos de diseño:

Un concurso de diseño de afiche, cuya obra ganadora fuera expuesta en las estaciones de tren subterráneo de Buenos Aires, de Metrovías S.A. y otro concurso de diseño de sello postal, cuya obra ganadora fuera emitida por Correo Argentino S.A. como filatelia oficial durante el año 2000. De este modo, se gestaron dos actividades, no sólo con fines de difusión, sino también como estímulo para los participantes.

Los concursos fueron lanzados en Junio de 1999 y recibiéndose obras hasta el día 15 de noviembre de 1999. El 29 de Noviembre último, tuvo lugar en la sede de la Sociedad Central de Arquitectos el acto del jurado, integrado por la Dra. Vera W. de Spinadel, los arquitectos Juan Carlos Fervenza, Carlos Mendez Mosquera, Hernán Busso, Horacio Levit y Martín Benarroch, la diseñadora gráfica Mariana Scotto y el profesor Jorge Blumenfarb, el Sr. Daniel Similichis, representante de Corel Corp. y el Sr. Julio C. Sáenz, de la gerencia de sellos postales y filatelia de Correo Argentino.

Se realizó el acto de entrega de premios en el salón microcine de Correo Argentino, el 15 de Diciembre de 1999, al que asistieron todos los ganadores y aquellos que tuvieron menciones, invitados por la Asociación M&D y las empresas auspiciantes a la Ciudad de Buenos Aires a participar del evento. Estuvieron presentes, además de los miembros del jurado, autoridades de las entidades auspiciantes y de la organización.

Los participantes ganadores son los siguientes:

Concurso de sellos postales:

1er. Premio: Erica Palatnik, FADU – UBA

3er. Premio: Luciana Manarini, FADU – UBA

Tres menciones:

• Andrea Verónica Paredes Rudaitis, Fac. de Arquitectura, Urbanismo y Diseño, Córdoba
• Eduardo Carlos Machnicki, Instituto de Estudios Superiores, Córdoba
• Luciana Maqueda (con Tomas Medici y Carlos Ferrando), Facultad de Arquitectura y Urbanismo – UNLP

Concurso de afiches

1er Premio: Griselda Druetto, Escuela Superior de Diseño Gráfico, Rosario, Sta. Fe

2do. Premio: Erica Palatnik, FADU – UBA

3er. Premio: Luciana Manarini, FADU – UBA

Seis Menciones:

• Martín Fasani, FADU – UBA
• Julia Tristana Barassi (con Andrés Wilhelm), FADU – UBA
• Luciana Maqueda (con Tomas Medici y Carlos Ferrando),  FAU – UNLP
• Eduardo C. Machnicki, Instituto de Estudios Superiores, Córdoba
• Eugenia Frías Moreno, FADU – UBA

La Sociedad Central de Arquitectos ha auspiciado, acompañada por la Facultad de Arquitectura, Diseño y Urbanismo, Correo Argentino, Metrovías y otras entidades, dos concursos organizados por la Asociación de Matemática y Diseño: “2000 – Año Mundial de la Matemática”.

La realización de este concurso surgió a raíz de que UNESCO ha declarado el año 2000 como el año Mundial de la Matemática. Y el Instituto “Henri Poincaré” de París, que centraliza toda una serie de eventos en el ámbito internacional ha convocado a la Asociación presidida por la Dra. Vera W. de Spinadel, profesora titular consulta de la Facultad de Arquitectura, Diseño y Urbanismo de la U.B.A., a realizar una actividad conmemorativa en la República Argentina. La Asociación de Matemática y Diseño, buscando organizar un evento que excediera los límites de la “comunidad matemática”, y promovió dos concursos de diseño:

Un concurso de diseño de afiche, cuya obra ganadora fuera expuesta en las estaciones de tren subterráneo de Buenos Aires, de Metrovías S.A. y otro concurso de diseño de sello postal, cuya obra ganadora fuera emitida por Correo Argentino S.A. como filatelia oficial durante el año 2000. De este modo, se gestaron dos actividades, no sólo con fines de difusión, sino también como estímulo para los participantes.

Los concursos fueron lanzados en Junio de 1999 y recibiéndose obras hasta el día 15 de noviembre de 1999. El 29 de Noviembre último, tuvo lugar en la sede de la Sociedad Central de Arquitectos el acto del jurado, integrado por la Dra. Vera W. de Spinadel, los arquitectos Juan Carlos Fervenza, Carlos Mendez Mosquera, Hernán Busso, Horacio Levit y Martín Benarroch, la diseñadora gráfica Mariana Scotto y el profesor Jorge Blumenfarb, el Sr. Daniel Similichis, representante de Corel Corp. y el Sr. Julio C. Sáenz, de la gerencia de sellos postales y filatelia de Correo Argentino.

Se realizó el acto de entrega de premios en el salón microcine de Correo Argentino, el 15 de Diciembre de 1999, al que asistieron todos los ganadores y aquellos que tuvieron menciones, invitados por la Asociación M&D y las empresas auspiciantes a la Ciudad de Buenos Aires a participar del evento. Estuvieron presentes, además de los miembros del jurado, autoridades de las entidades auspiciantes y de la organización.

Los participantes ganadores son los siguientes:

Concurso de sellos postales:

1er. Premio: Erica Palatnik, FADU – UBA

3er. Premio: Luciana Manarini, FADU – UBA

Tres menciones:

• Andrea Verónica Paredes Rudaitis, Fac. de Arquitectura, Urbanismo y Diseño, Córdoba
• Eduardo Carlos Machnicki, Instituto de Estudios Superiores, Córdoba
• Luciana Maqueda (con Tomas Medici y Carlos Ferrando), Facultad de Arquitectura y Urbanismo – UNLP

Concurso de afiches

1er Premio: Griselda Druetto, Escuela Superior de Diseño Gráfico, Rosario, Sta. Fe

2do. Premio: Erica Palatnik, FADU – UBA

3er. Premio: Luciana Manarini, FADU – UBA

Seis Menciones:

• Martín Fasani, FADU – UBA
• Julia Tristana Barassi (con Andrés Wilhelm), FADU – UBA
• Luciana Maqueda (con Tomas Medici y Carlos Ferrando),  FAU – UNLP
• Eduardo C. Machnicki, Instituto de Estudios Superiores, Córdoba
• Eugenia Frías Moreno, FADU – UBA

Oct. 25, 2000 - Nov. 27, 2000

In accordance with the "Rio De Janeiro" Declaration on May 6, 1992 by the International Mathematical Union, the Department of Mathematics, Fatima Mata National College, Quilon celebrated the World Mathematical Year 2000 by conducting several programmes. The main focus was on the young talents at the High School level ( 8 th grade) and College level rather than Higher level or Research level. On Oct. 25, 2000 we conducted an essay competition on "Image of Mathematics" at the under graduate level. Atheesh Kumar, J. of I BSc. Mathematics won the first prize. The second and third prizes were awarded to Neeti C. Joseph of II BSc. Chemistry and Nripan Das P.A. of II BSc. Mathematics respectively. A Poster Designing Competition was conducted on Oct. 27, 2000 on "World Mathematical Year 2000" . The first prize went to Mathew Kurian of II B. Com. and the second and third prizes were awarded to Parwathy K. Nair of Final BSc. Mathematics and Alphonse Justus of II BSc. Mathematics respectively. In order to spot out and foster young talents at High School level, we conducted a Scholarship Examination in Mathematics. Forty-six young talents from twenty-six High Schools attended the examination and Deepthi Luke of Lourde Matha High School, Kovilthottam, Quilon won the first prize. Archa Prabhan of Vimala Hridaya School, Quilon and Ancy Rajan of St. Margaret's High School won the second and third prizes respectively. The Closing Ceremony of the World Mathematical Year 2000 was held on Nov. 27, 2000. The chief guest was Dr. E. Krishnan ( Deptatment of Mathematics, University College, Trivandrum). On the same day, we conducted the Prof. N.T. Jose Memorial Inter Collegiate Quiz Competition on Mathematics and General Knowledge. The quiz programme was jointly conducted by Dr. E. Krishnan and Prof. A.S. Francis (Department of English, Fatima Mata National College, Quilon) . the meeting was inaugurated by Rev.Sr. Adolph Mary, Vice Principal of the College and Presided over by Prof. A. Telveenus, H.O.D. Math. of the College. Dr. E. Krishnan distributed the prizes.

A.Telveenus
Head,Dept. of Mathematics Fatima Mata National College
Quilon- 691001 Kerala State, S.India
Email This email address is being protected from spambots. You need JavaScript enabled to view it.

Noszvaj (Hungary) June 11 to June 18, 2000

The 38th International Symposium on Functional Equations (ISFE), held at Noszvaj (Hungary), June 11 to June 18, 2000 was included into the activities of WMY 2000, in particular since in its program a series of seven talks was scheduled, giving surveys of significant open problems related to functional equations and their applications which could form a collection of topics for future research in the 21st century and whose solutions could be considered as a substantial progress. The idea to have such a series of problem talks came from János Aczél (Waterloo, Ontario) who convinced the Scientific Committee and the Organizing Committee to plan the series. The topics presented were inconnection to some, through not all of the most active fileds of present research in functional equations. The recently renewed study of functional equations in the complex domain could unfortunately not be presented.

A list of the speakers and titles of the problem talks follows.

• Claudi Alsina (Barcelona): Problems on associativity, related functional equations and generalizations.
• Walter Benz (Hamburg): Functional equation problems in applications to geometry.
• Jean-Claude Falmagne (Irvine, CA): Functional equations problems in the social and behavioral sciences.
• Roman Ger (Katowice): A collection of problems in stability theory.
• Zsolt Páles (Debrecen): Problems in the regularity theory of functional equations.
• Jürg Rätz (Bern): Functional equations problems concerning orthogonality.
• Ludwig Reich (Graz): Problems concerning algebraic aspects of functional equations.

Also the survey talk „Schilling’s equation and related problems“ by Roland Girgensohn (Neuherberg, Germany) was partly devoted to open problems on functional equations in a single variable.

Detailed versions of the problem talks will appear in forthcoming volumes of Aequationes Mathematicae (Birkhäuser Verlag, Basel).

For more information on the 38th International Symposium on Functional Equations see http://riesz.math.klte.hu/~isfe2000/.

Written by Ludwig Reich (Graz)

Organizers: Joseph W. Dauben (New York) and Yvonne Dold (Heidelberg)
Rockefeller Foundation, Bellagio Study and Conference Center (Italy)
May 8-12, 2000

The purpose of the Bellagio conference was to bring together an international team of scholars, some of whom had worked together before, to allow thorough discussion of the transmission of mathematics between cultures across Europe and Asia. During an intensive week of lectures and discussion, participants focused their attention on early mathematical works, especially those in China, India, the Arabic/Islamic world, and the late Middle Ages/Renaissance in Europe, in order to explore evidence of direct and indirect influences, possible connections, and various means by which the problems or methods devised in one particular place and time found their way to other points, often very far apart in place and time.

The Rockefeller Foundation's Bellagio Conference Center, the Villa Serbelloni, provided a quiet, reflective atmosphere in which we were able to accomplish a substantial amount of work in a relatively short period of time. In the course of seven morning and afternoon sessions, twenty-one studies were presented and discussed in detail by the group.

The list of participants with the titles of their contributions can be found at http://www.iwr.uni-heidelberg.de/transmath.

In response to the comments and suggestions made during the course of the meeting, the papers prepared for the Bellagio conference will be further revised over the next few months. This proceedings will appear as a volume of Boethius, a series published by Steiner Verlag in Stuttgart, Germany. The Editorial Board is comprised of Joseph W. Dauben, New York, Yvonne Dold-Samplonius, Heidelberg, and Menso Folkerts, Munich.

Written by Yvonne Dold-Samplonius

The "Fifth Forum of Young Women Mathematicians" ("Cinquième Forum des Jeunes Mathématiciennes") was held at the Institut Henri Poincaré in Paris, France, on Friday and Saturday, January 21-22, 2000. This annual meeting is an excellent occasion for scientific exchange and gives young researchers the opportunity to present their work in a stimulating environment. This year, it was part of the French program for the WMY2000 Project (World Mathematical Year 2000), also sponsored by UNESCO. The forum always consists of a scientific part, which gives an overview of the current state of mathematical research, and a historical-sociological part, which is intended to stimulate debates on current issues of women in the scientific community. This year, the scientific talks were given by twelve young mathematicians and six established mathematicians from all over France and Europe. The first debate was introduced by historians Delphine Gardey and Michelle Perrot, and followed the talk "Historical approach to relations between women, science and technology" by Delphine Gardey. The second debate, "Parity in the scientific community", was introduced by Claudine Hermann (Professor at the Ecole Polytechnique and member of E.T.A.N.) who reported on the activity of the European community about the question of Women and Science.

The forum program is available at the web-site: http://www.desargues.univ-lyon1.fr/home/fem/agjan00.html

This meeting was organized by the association "femmes et mathématiques"

http://www.desargues.univ-lyon1.fr/home/fem/fem.html