# 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.