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.
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
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.
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
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
11, rue Pierre et Marie Curie
75005 PARIS - FRANCE
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
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
MILTON KEYNES MK7 6AA.
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.
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.
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.
All ideas and propositions are welcome. We suggest the following basic principles :
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).