1990 International Congress of Mathematicians - Kyoto

The International Congress of Mathematicians was held in Kyoto, Japan, from 21 August to 29 August 1990. The Congress was attended by 3,954 full members and 452 associate members. We give below a version of the report by the Secretary on Preparations, a report on the Opening Ceremonies held in the Event Hall of the Kyoto International Conference Hall, starting at 9:30 a.m. on 21 August 1990, and a report on the Closing Ceremonies held in the Main Hall of the Kyoto International Conference Hall, starting at 1:15 p.m. on 29 August.

1. Secretary's Report on Preparations.

The International Congress of Mathematicians 1990 was held in Kyoto at the invitation of the Science Council of Japan (JSC) and the Mathematical Society of Japan under the co-sponsorship of the Japan Society of Mathematical Education, the History of Science Society of Japan, the Institute of Actuaries of Japan, the Japan Society for Software Science and Technology, the Japan Statistical Society, and the Operations Research Society of Japan. The Congress was also supported by the Ministry of Education, Science and Culture, by Kyoto Prefecture, Kyoto City, Kyoto University, and the Information Processing Society of Japan.

The members of the Organising Committee and its subcommittees were appointed one year before the Congress was held. Until the Organising Committee was established on 14 August 1989, however, all preparations were carried out by the Committee of ICM-90, which was set up in the Mathematical Society of Japan in December, 1986.

The scientific program of the Congress was in the hands of the Program Committee, which was appointed by the International Mathematical Union in May, 1987. Its members were Nicolaas H Kuiper (Chairman), Vladimir I Arnold, Alain Connes, Ronald L Graham, Heisuke Hironaka, Masaki Kashiwara, Robert P Langlands, Sigeru Mizohata, and Daniel G Quillen.

Recipients of the Fields Medals and the Rolf Nevanlinna Prize were selected by the respective committees appointed by the IMU in April, 1988. The Fields Medal Committee consisted of Ludwig D Faddeev (Chairman ex officio), Michael F Atiyah, Jean-Michel Bismut, Enrico Bombieri, Charles L Fefferman, Kenkichi Iwasawa, Peter D Lax, and Igor Shafarevich. The Rolf Nevanlinna Prize Committee consisted of László Lovász (Chairman), Alexandre J Chorin, Michael Rabin and Volker Strassen.

2. Opening Ceremonies.
The opening ceremonies of the Congress were held in the Event Hall of the Kyoto International Conference Hall, starting at 9:30 a.m. on August 21, 1990, The Gagaku Club of Tenri University entertained the participants with a Gagaku (court music) recital entitled Etenraku. Academician Ludwig D Faddeev, President of the International Mathematical Union, opened the Congress with the following speech:

After this symbolic opening let me formally declare the International Congress of Mathematicians (ICM-90) in Kyoto open.

This is the first Congress in the history of the International Mathematical Union to take place outside of Europe and North America. This is consonant with the main goal of the Union - the promotion of mathematical research throughout the world. For this reason, the proposal of the Japanese Committee of Mathematicians to hold the Congress in Kyoto was enthusiastically accepted by the General Assembly of the IMU four years ago. I believe that I can already express admiration for the efforts being made by the Organising Committee to make the Congress work effectively. It appears that the attendance is the highest in the history of ICM.

The scientific program of ICM is traditionally in the hands of the Program Committee appointed by the Executive Committee of IMU. Let me disclose to you the list of its members. Professor Nicolaas H Kuiper was appointed as chairman. Professors Vladimir I Arnold, Alain Connes, Ronald L Graham, Heisuke Hironaka, Masaki Kashiwara, Robert P Langlands, Sigeru Mizohata, and Daniel G Quillen served as members. We shall witness the effectiveness of their choice of speakers in the coming days.

Now I come to the important duty of designating the President of the Congress. Let me nominate Professor Hikosaburo Komatsu for this post.

Acclamation.

I take this as confirmation of the proposal. Thank you.

2.1. Presidential Address.

Professor Komatsu, as President of the Congress, made the following address:

Thank you Mr President. I am honoured to serve as President of the Congress.

Ladies and Gentlemen,

On behalf of the Organising Committee I would like to welcome you to the International Congress of Mathematicians 1990 (ICM-90). I very much hope that your stay in the historical city of Kyoto will be a pleasant one.

First of all, let me explain how the Congress has been prepared. It was more than seven years ago that the Liaison Committee for Mathematics in the Science Council of Japan (JSC), which is the Committee for Mathematics in Japan, and the Mathematical Society of Japan started planning to host ICM-90. After the Feasibility Committee chaired by Professor Kiyosi Ito made a careful initial investigation of this issue, MSJ decided in 1985 to invite ICM-90 to Kyoto. Fortunately this invitation was accepted by the Site Committee of IMU and was approved by the General Assembly of IMU at Oakland in 1986.

The actual preparations started when MSJ formed the Committee of ICM-90 in December, 1986. Its Executive Committee consists of the following:

President: Kunihiko Kodaira
Vice Presidents: Kiyosi Ito, Heisuke Hironaka
Chairman: Hikosaburo Komatsu
Secretary: Huzihiro Araki
Treasurer: Hirosi Toda
Members: Shigeru Iitaka, Sigeru Mizohata, Masayoshi Nagata.

The full Committee of ICM-90 had an additional 29 members.

By the end of 1987, the Japan Society of Mathematical Education, the History of Science Society of Japan, the Institute of Actuaries of Japan, the Japan Society for Software Science and Technology, the Japan Statistical Society, and the Operations Research Society of Japan decided to sponsor the Congress and elected their representatives to the Committee of ICM-90 and its Science Committee.

In June, 1989, JSC made the final decision of sponsoring ICM-90 with the consent of the Government. Then, according to the general rules of MSJ, the Committee of ICM-90 was reorganised into the Organising Committee in August, 1989.

Second, as the President of IMU reported, the scientific program of the Congress and, in particular, the list of invited speakers were prepared by the Program Committee, appointed by the Executive Committee of IMU. However, a few additional speakers working in Japan, and also substitutes for speakers who declined, were invited by the Organising Committee on its own initiative, in which the latter were selected from the list of alternatives made by the Program Committee.

Finally 15 speakers were invited to give one-hour Plenary Addresses. Among them two declined and were replaced by other choices. Also 144 speakers were invited to give 45-minute Section Lectures, 19 were substituted, and 6 lectures were cancelled. In addition, the International Commission on Mathematical Instruction invited five 45-minute speakers.

We have benefited very much by the recent reconciliation in the world politics and the prosperity of the Japanese economy. As far as I know, no invited speakers declined for political or economic reasons.

Adopting Professor Mary Rudin's proposal, the last General Assembly of IMU in 1986 recommended that Subfields of Mathematics, Women, and Mathematicians in Small Countries should not be overlooked when speakers to the ICM are selected. I believe both the Program Committee and the Organising Committee have respected this recommendation.

The selection of additional speakers and the scheduling of scientific program were carried out by the Science Committee in the Organising Committee, chaired by Sigeru Mizohata.

Thirdly, the budget of this Congress amounted to approximately 300,000,000 Yen (approximately US$2,000,000). One third of the revenue is the registration fees, one third the donations from private corporations, and the rest consists of subventions from IMU, JSC and MSJ, the donations by individual members of MSJ, and the miscellaneous income (here the donations by 1138 members of MSJ are actually more than the total of all the other subventions). We are very sorry that we had to set a high registration fee of 30,000 Yen but we were forced to do so because the Japanese tax regulations do not allow us to receive tax-exempted donations exceeding the total amount of registration fees.

In addition to the budget of the Organising Committee, the Japan Association for Mathematical Sciences, MSJ, the Oriental Life Insurance Cultural Development Centre, the Commemorative Association for the Japan World Exposition (1970), and The Kajima Foundation allocated a total of 60,000,000 Yen to support 269 foreign participants mostly from developing countries or countries with foreign currency restrictions. This number includes 47 IMU Scholars whose travel expenses are supported by the Special Development Fund of IMU.

Most funds from these foundations also originated from donations solicited from enterprises by the Organising Committee.

The biggest contributors are insurance and electronic companies. On behalf of all the participants, I would like to thank all these bodies for their generous donations. A list of donors is in the Program and will be published in the Proceedings.

It is not an easy task to raise so much money. But I must confess that it was a pleasant one, too, because every executive I met for this purpose showed a liking for mathematics and appreciated that mathematics had played an important role in the development of the Japanese economy.

The Fund Raising Committee is chaired by Kiyosi Ito and its office was set up in Gakushuin University with Shigeru Iitaka in charge.

Assistance with visa applications was carried out by Shinichi Kotani at the office located in the University of Tokyo.

The other preparations have been planned and implemented by General Secretary Huzihiro Araki, Treasurer Hirosi Toda and the Local Committee chaired by Masayoshi Nagata. The Secretariat was set up in the Research Institute for Mathematical Sciences, Kyoto University.

The Proceedings of the Congress will be edited by the Publications Committee with Ichiro Satake as the chairman. Its office is in Tohoku University. I would like to thank these institutions and, in particular, Kyoto University for their kind cooperation.

Today, 4,000 mathematicians from 83 countries have assembled here to review our scientific achievements over the last few years and to set goals for the future in all fields of mathematics ranging from pure mathematics through applied mathematics to mathematical education. This seems to be an almost megalomaniac dream at this time of specialisation. I do not know any other discipline which attempts to hold this kind of congresses regularly.

I have often wondered why mathematicians do have Congresses and what Congresses mean to them. My answer is that Congresses are to mathematicians what Bon and New Year Festivities are to Japanese, in which they abandon their daily life completely.

Japanese are believed to work continuously without vacations, but that is not true. Even in the Edo Period there were two one-week long holidays. One is the New Year Festivities and the other is the Bon Festivities which take place a week earlier than this time of the year,

On these holidays people are relieved from labour and go back to their native home. People are not allowed to cook on the first days of the Festivities, so that they have a busy time preparing all meals before the holidays start.

New Year Festivities are associated with the future. We renew everything we can and start again, Bon Festivities are for the past, We receive ancestors' ghosts, make conversations with them, and then send them back. In cities like Kyoto people decorate their entrance halls with their treasures and keep the doors open. The whole city becomes a big museum. In the countryside people gather in the village square and dance. There is no distinction between performers and spectators; all dance. That is the way Japanese refresh themselves, inherit their traditions and unite. Bon and New Year Festivities also give young people the opportunity to meet together to make a new family. I would like to ask all speakers at the Congress to make their lectures accessible to a wide audience, and not just to the specialists, at least in the first part. This is certainly not the time to work in a daily manner.

I hope you all enjoy this big event.

Thank you.

2.2. Address by the President of the Mathematical Society of Japan.

Professor Akio Hattori, President of the Mathematical Society of Japan, spoke as follows :

Mr Chairman, Distinguished Guests, Ladies and Gentlemen,

I should like to extend a warm welcome to you all for having gathered from all parts of the world to attend this Congress. The Japanese mathematical community is proud of a pioneer; I am referring to Professor Kiyosi Ito, a renowned probabilist. He has been instrumental in bringing this Congress to Japan and in its organisation. I propose that Professor Ito be elected Honorary President of this Congress.

2.3. Professor Ito's Address.

Professor Ito was elected by acclamation and spoke as follows :

Mr Chairman, Distinguished Guests, Ladies and Gentlemen,

It is my great honour to speak to you as Honorary President of the Congress. Before now, some Japanese mathematicians have tried to bring the Congress to Japan. As early as the 1960s, Professors S Iyanaga and Y Kawada began campaigning for the Congress to be held in Japan. Now that this Congress is starting, I feel a certain nostalgia for their pioneering efforts.

When we formed the Organising Committee chaired by Professor Kunihiko Kodaira, the first Japanese Fields medalist, our big problem was how to raise funds. In this respect, I would like to give credit to Professor Kodaira. Impressed by his fame and his fine personality Mr H Tanimura, Professor Kodaira's friend, together with Messrs R Ishikawa and M Kitoku set up a fund-raising program for us and appealed to leading companies. We thank them for their tremendous efforts, which enabled us to make concrete plans for the Congress. To our great regret, Professor Kodaira is unable to come here today. I would like to express our sincere gratitude to him on this occasion.

The next problem was that we anticipated there would be less participants than usual because of Japan's geographic location and the worldwide economic upheaval. Professor H Komatsu proposed to make a grant available to help participants from abroad. This idea was welcomed by several foundations whose support contributed to the increase in the number of participants.

In Japan, people have been more concerned with science and technology than with mathematics. Despite this, we are proud of two exceptional projects which have helped mathematicians: the International Symposia supported by Mr Toyosaburo Taniguchi and secondly, the Exchange Program of the Japan Association for Mathematical Sciences established by Professor H Hironaka, the second Japanese Fields medalist. Through these projects many Japanese mathematicians have acquired a sense of international cultural exchange, which is perhaps one of the main aims of the Congress.

A large number of members of the Mathematical Society of Japan helped the Organising Committee in many respects, academically or non-academically. At the final stage of preparation a tremendous amount of business had to be carried out within a limited time. We are very grateful to Professors H Komatsu, H Araki, H Toda, S Iitaka, S Kotani, and their secretaries for all their hard work.

We are very happy to welcome you here in Kyoto. Please enjoy the lectures and participate as much as possible in the informal discussions.

Thank you.

2.4. Address by the President of the Science Council of Japan.

Professor Jiro Kondo, President of the Science Council of Japan, gave the following welcome address:

Mr Chairman, Distinguished Guests, Ladies and Gentlemen,

It is a great pleasure to have this opportunity, on behalf of the Science Council of Japan, to speak to all of you who have gathered here from as many as 80 countries, at the opening of the International Congress of Mathematicians 1990.

The Science Council of Japan was established in 1949 as a government organisation representing qualified Japanese scientists both internally and internationally, covering all scientific fields consisting of Cultural, Social and Natural Sciences. The aim of the Council is to promote scientific development and to improve administration, industry and living standards through science.

Since that time, we have been working to contribute to the progress of science in cooperation with the academic organisations of the world by sponsoring many international congresses here in Japan, and by sending Japanese delegations to international congresses held overseas. We do this because we believe that the promotion of international scientific exchanges is one of our most important duties.

We have opened today the International Congress of Mathematicians in cooperation with the Mathematical Society of Japan, the Japan Society of Mathematical Education, the History of Science Society of Japan, the Institute of Actuaries of Japan, the Japan Society of Software Science and Technology, the Japan Statistical Society, and the Operations Research Society of Japan. It is an extraordinary pleasure for me to have this opportunity to be with so many distinguished scientists from around the world, and to listen to your lectures and presentations on the recent achievements.

The first Meeting of the International Congress of Mathematicians was held in Zürich in 1897. Since then, the Congress has been held nearly every four years somewhere in the world, and this is the first Congress to be held outside Europe and North America. I offer my heartfelt congratulations on the remarkable growth of the Congress in terms of both quality and number of participants and at the same time I express my great pleasure in being able to welcome the Congress to Japan for the first time. Since I graduated from the Department of Mathematics, Imperial University of Kyoto in 1940, I am very happy to hold this Congress here in Kyoto. After my graduation I worked mostly in the field of mathematical applications, such as theoretical aerodynamics, operations research, systems engineering and environmental sciences.

Recent international trends clearly indicate the importance of basic research in science and technology. In particular, mathematical sciences are entrusted with the crucial mission of providing the backbone for all sciences and the theoretical basis for the new era of information science in the twenty-first century, and they must also live up to people's high expectations. Moreover, because of the rapid progress in computer technology, many scientists in other fields, as well as engineers and businessmen, are coming to expect a greater contribution from mathematicians.

As researchers of all branches of mathematics gather from all over the world at this International Congress, it is expected that much interaction among the different branches will be made and that this will result in a new development of mathematics as a unified discipline. While we see recently a strong tendency of specialisation in all branches of science, I have learned that essential progress in mathematics has often arisen out of the unexpected connection of different areas. The interaction of researchers with different cultural backgrounds is also expected to produce such an effect. I hear that this Congress is organised with an emphasis on interdisciplinary and international interactions and efforts have been made to provide various opportunities for contact among participants. I hope that through the interaction with neighbouring fields of science which will inject new blood into mathematics and through friendship among participants crossing the boundaries of different branches of mathematics and different countries, this Congress serves as a stepping stone towards active worldwide research cooperation in the future.

I earnestly hope that everyone who participates in this Congress, will gain worthwhile experience in both fundamental and applied aspects of mathematics.

In closing, I sincerely hope for the great success of the Congress. I also hope that all of you from abroad will enjoy their stay in Japan. I believe that this Congress will become truly memorable for you through contact with fellow scientists, and I wish this to be a chance for you to learn more about Kyoto, the ancient capital of Japan, and about Japanese culture.

Thank you.

2.5. Prime Minister's telegram.

The following congratulatory telegram from Prime Minister Toshiki Kaifu was read both in Japanese and in English by Professor Huzihiro Araki:

PLEASED TO EXTEND A HEARTY WELCOME TO ALL DELEGATES FROM AROUND THE WORLD AT THE OPENING OF THE 11TH GENERAL ASSEMBLY OF THE INTERNATIONAL MATHEMATICAL UNION AND THE INTERNATIONAL CONGRESS OF MATHEMATICIANS 1990 HELD IN JAPAN UNDER THE COSPONSORSHIP OF THE SCIENCE COUNCIL OF JAPAN, MATHEMATICAL SOCIETY OF JAPAN, JAPAN SOCIETY OF MATHEMATICAL EDUCATION, THE OPERATIONS RESEARCH SOCIETY OF JAPAN, THE HISTORY OF SCIENCE SOCIETY, JAPAN SOCIETY FOR SOFTWARE SCIENCE AND TECHNOLOGY, THE JAPAN STATISTICAL SOCIETY AND THE INSTITUTE OF ACTUARIES OF JAPAN.

I WISH A GREAT SUCCESS IN THIS INTERNATIONAL CONGRESS.

TOSHIKI KAIFU

PRIME MINISTER

2.6. Minister of Education's Address.

Mr Kosuke Hori, Minister of Education, Science and Culture gave a congratulatory address as follows:

Distinguished Delegates, Ladies and Gentlemen of the Audience,

It is a real pleasure and privilege for me to be afforded this opportunity to address congratulatory greetings to this distinguished audience at the opening of the Twenty-first International Congress of Mathematicians.

First of all, I would like to extend my sincerest welcome to you all, especially to those who have travelled far in order to come to Japan. At the same time, I am deeply grateful and wish to pay respect to all the people who have made great efforts in mathematical research.

Recently, pure mathematics, applied mathematics, mathematical education, and other fields of mathematics have achieved remarkable progress in research. This International Congress has been held every four years since 1897 for the purpose of bringing together mathematicians in all fields from all over the world in order to share the significant progress achieved in each area of mathematics and to help further new progress in mathematics. In these respects, the International Congress of Mathematicians has attained excellent achievements.

I am told that this International Congress is the first to be held in Asia, and distinguished mathematicians from Japan and abroad who participate in it will present many new discoveries in mathematics. I am confident that this Congress will further enrich the knowledge that is common property to all human beings.

I hope that those participants who have travelled from overseas will have the opportunity to acquaint themselves with some aspects of Japanese culture and society and that they will have a pleasant stay in Japan.

Finally, I would like to pay our deepest respects to those people who have already worked so hard in Organising this Congress and I anticipate that it will be highly successful.

Thank you very much for your attention.

2.7. Address by the Governor of Kyoto Prefecture.

Mr Teiichi Aramaki, Governor of Kyoto Prefecture, gave a congratulatory address as follows:

Distinguished Delegates, Ladies and Gentlemen of the Audience,

As Governor of Kyoto Prefecture, I would like to extend my sincerest congratulations for the Twenty-first International Congress of Mathematicians to be held here in Kyoto from today, with distinguished mathematicians assembled from various countries of the world.

The First International Congress of Mathematicians was held in Zürich, Switzerland in 1897 and since then, the Congress has produced excellent results, establishing a long history and tradition. The fact that the Fields Medal, which is said to be the Nobel Prize of mathematics, and the Nevanlinna Prize have been awarded to superb mathematicians has attracted the attention of not only the people concerned but also many others.

It is a great pleasure and privilege for us living in Kyoto Prefecture that this authoritative International Congress is being held in Kyoto which itself is recognised as an academic and scientific centre. On behalf of the people of Kyoto Prefecture, I would like to extend a cordial welcome to all of you. The International Congress of Mathematicians has been held only in western cities so far and so it is a great pleasure and honour that this is the first International Congress of Mathematicians to be held outside Europe and North America. I am sure that this fact will further encourage many Japanese mathematicians.

Finally, I would like to pay our deepest respects to the scientists of the Research Institute for Mathematical Sciences, Kyoto University and to those who have gone to great pains in organising this International Congress. I anticipate that each of the participating mathematicians will take an active role in the discussions and that the Congress will be highly successful.

Thank you for your attention.

2.8. Mayor of Kyoto City's Address.

Dr Tomoyuki Tanabe, Mayor of Kyoto City, gave the following congratulatory address:

Ladies and Gentlemen,

Firstly, please let me welcome you all to Kyoto.

I am delighted that the Twenty-first International Congress of Mathematicians is starting today and on behalf of the citizens of Kyoto, I would like to extend a cordial welcome to you all.

As you may know, Kyoto is an ancient city with a history that looks back on 1,200 years of culture and tradition. This is why Kyoto is said to be the spiritual root of Japan.

Kyoto is rich in cultural heritage and a variety of time-honoured customs based on Japanese tradition still exist as part of our everyday way of life. Traditional industries which embody the quintessence of Japanese folk art and technology can also be found.

On the other hand, Kyoto is a scientific city which has produced several superb Nobel Prize winners and Fields Medalists. At the same time, Kyoto is an industrial city which has given birth to world leaders in high-tech industries.

About ten years ago, we declared Kyoto as a City Open to the Free Exchange of World Cultures. In this connection, it is a profound feeling of pleasure and privilege that the International Congress of Mathematicians is being held here in Kyoto.

I am confident that everyone who has travelled from afar to participate in this International Congress, will renew old friendships as well as begin new acquaintances. I also hope that you will enjoy the mixture of traditional Japanese culture and the modern atmosphere of our city.

Let me close my greetings by wishing the International Congress of Mathematicians success and combine this with a wish for your good health and happiness.

Thank you for your attention.

2.9. President of Kyoto University's Address.

Dr Yasunori Nishijima, President of Kyoto University, delivered this congratulatory address:

Ladies and Gentlemen,

It is my honour and great pleasure to greet this distinguished gathering at the opening of the International Congress of Mathematicians.

I have learned that this Congress had its first meeting in 1897. That is also the year that Kyoto University was founded as the Kyoto Imperial University and this marked the establishment of the modern academe in the old capital. Ninety-four years have passed since then and today Kyoto welcomes this gathering of the world's notable mathematicians to Japan for the first time, Kyoto is most honoured to be the chosen site.

Last week, the General Conference of the International Association of Universities took place in Helsinki, Finland. It was very cool and dry, unlike the hot and wet weather here. The Chancellor, Professor Olli Lehto, and all the members of the University of Helsinki, including the most delightful of students, made the meeting a great success.

The theme of the Conference was "The Mission of the University: Universality, Diversity, and Interdependence," and I had the opportunity to chair the whole-day commission on "Diversity within Universality." In this rapidly and dramatically changing world, Diversity tends to be emphasised. However, at the same time, Universality is the human aspiration to create a higher degree of wisdom for the future and this is the mission of the world's academic community.

After the exciting and fruitful meeting in Helsinki, I returned to Japan a few days ago. In the airport transit lounge, I met Chancellor Lehto, who was on his way to this Congress. He was holding a small bag on his lap with great care. I thought it was the medal for the Rolf Nevanlinna Prize which will be presented at today's Ceremony. I said, "Is that top secret?" Chancellor Lehto simply smiled and nodded. We boarded the same airplane for the last stretch of our long journey from Helsinki to Kyoto. This morning, following the performance of a classic Japanese court dance, Bugaku, the presentation of the Fields Medals and the Rolf Nevanlinna Prize will reveal all the secrets. I really think mathematics is the core of the universality of human wisdom. Mathematics has since ancient times conveyed wisdom throughout the history of human endeavour. At the same time, mathematics covers all branches of knowledge and leads us along the road to Truth and Reason.

David Hilbert said, "Mathematics is an organism for whose vital strength the indissoluble union of the parts is a necessary condition."

I would like to congratulate all those who have worked so hard to prepare and organise this most important meeting. I anticipate it will be a great success.

I wish all participants a most fruitful and pleasant meeting in Kyoto.

2.10. Commemorative stamps.

On behalf of Takashi Fukaya, Minister of Posts and Telecommunications, Mr Tomoyuki Onozawa, Director General of Posts, presented a sheet of commemorative stamps with the following letter:

To Professor Hikosaburo Komatsu, President of the International Congress of Mathematicians.

It is of high significance and a matter for congratulations that the Twenty-first International Congress of Mathematicians is being held here in Kyoto, for the first time in Asia.

The Ministry of Posts and Telecommunications has issued a specially designed postage stamp to commemorate this event, and the first sheet of stamps is now presented to you.

From Takashi Fukaya, Minister of Posts and Telecommunications

On August 21, 1990.

Kyoto Gagaku-Kai then performed a Bugaku (court dance) entitled Gosechi no Mai accompanied by the Gagaku Club of Tenri University which played a Gagaku (court music).

2.11. Award of Fields Medals.

Academician Ludwig D Faddeev, Chairman of the Fields Medal Committee, announced the recipients of the Fields Medals as follows:

The Fields Medal and Prize Committee is appointed by the Executive Committee of the IMU. For this term the following people were appointed and worked for the Committee: Professors M Atiyah, J M Bismut, E Bombieri, C Fefferman, K Iwasawa, P D Lax and I Shafarevich. Since it is the duty of the President of the IMU to chair the work of this Committee, I served as chairman.

After thorough consideration of the material at our disposal, we decided to award four Medals. The recipients are

Vladimir G Drinfeld,

Vaughan F R Jones,

Shigefumi Mori,

Edward Witten.

I believe that these names are well known to the mathematical community throughout the world. Their scientific contributions will be described during the afternoon session.

Let me proceed to the pleasant task of presenting the awards. I ask the Honourable Minister Hori to do this.

The winners came forward and received their medals and prize cheques from Mr Kosuke Hori, Minister of Education, Science and Culture.

2.12. Award of the Rolf Nevanlinna Prize.

Professor László Lovász announced the recipient of the Rolf Nevanlinna Prize as follows:

The Nevanlinna Prize Committee consisted of Alexandre Chorin from Berkeley, Michael Rabin from Jerusalem, Volker Strassen from Konstanz, and László Lovász from Budapest as chairman. After considering a number of outstanding candidates, the Committee decided to award the Rolf Nevanlinna Prize to Alexander A Razborov from the Steklov Institute in Moscow, for his ground-breaking work on lower bounds for circuit complexity.

The winner came forward and received his medal and prize cheque from Mr Kosuke Hori, Minister of Education, Science and Culture.

The opening ceremonies adjourned at 11:00 a.m.

3. Closing Ceremonies.
The closing ceremonies were held in the Main Hall of the Kyoto International Conference Hall, starting at 1:15 p. m. on August 29, 1990.

Academician Ludwig D Faddeev, President of the International Mathematical Union, began the closing ceremonies with the following words:

Time runs very fast and we have come to the end of our Congress. I believe that we can now judge very highly the results of the scientific program and congratulate the Program Committee on their success. Personally, I was glad to observe how prominently Mathematical Physics was represented in its connections with other domains of Mathematics.

The work of the Congress has been so smooth that some of you did not notice the efforts of the Organising Committee to achieve this. We are all highly indebted to our Japanese colleagues for their excellent job.

Let me also add that the general atmosphere of the Congress has been very friendly and this has allowed us to concentrate on purely mathematical problems.

It is my pleasure to inform you that the Emperor and Empress of Japan invited the winners of the Fields Medals and the Nevanlinna Prize to visit them in Tokyo. The Honorary President of the Congress, Professor Ito, as well as Professor Hironaka and I were also present. The interest expressed by the Imperial Family in the work of our Congress is a great honour to us all.

Let me now inform you of the results of the General Assembly which took place in Kobe just before the Congress. It represented 52 members of the IMU most of whom attended the meeting.

During the last few years Saudi Arabia has been accepted as a new member. Spain and Israel have upgraded their membership to Group III.

The General Assembly elected new Committees and Commissions.

The new Executive Committee is composed as follows:

President: J L Lions
Vice-Presidents: J Coates, D Mumford
Secretary: J Palis
Members: J Arthur, A Dold, H Komatsu, L Lovász, E Zehnder.

I shall remain on the Executive Committee as the past President.

Half of the Executive Committee has changed. So it is appropriate to cite one of the resolutions adopted at the General Assembly: "The General Assembly gives special thanks to Professor Olli Lehto for his excellent work as Secretary to the IMU during the last eight years, ably assisted by Mrs Mäkeläinen. It also thanks the University of Helsinki and the Finnish Ministry of Education for their generous support of the IMU secretariat over this period.

The General Assembly also appointed the Commissions.

The ICMI Executive Committee:

President: M de Guzmán
Vice-Presidents: J Kilpatrick Lee Peng-Yee
Secretary: M Niss
Members: Yu L Ershov, E Luna, A Sierpinska.

The ex-officio members are: the past President of ICMI, the President of IMU, the Secretary of IMU and the IMU representative at CTS (ICSU). The next ICME will take place in 1992 in Quebec.

Commission on Developments and Exchange:

Chairman: M S Narasimhan
Members: P Bérard, C Camacho, A Grunbaum, A O Kuku, J Mawhin, T Ochiai, P L Papini, Wu Wen Tsun.

The ex-officio members are: the past Chairman of CDE, the President of IMU, the Secretary of IMU and the IMU representative at COSTED (ICSU).

Besides the administrative business, there was lively and important discussion at the General Assembly on the role of Applied Mathematics and its balance in the program of the ICM, the increasing relevance of Mathematics in Industry, and related problems of mathematical education.

Finally the Site Committee made its proposal to the General Assembly on the time and location of the next Congress, which was adopted after some discussion. The next Congress, ICM-94 will be held in Zürich, Switzerland. I shall now step down and give the floor to Professor Chatterji.

3.1. Invitation to ICM-94.

Professor S D Chatterji of the Ecole Polytechnique Fédérale de Lausanne invited the audience to the next International Congress of Mathematicians with these words:

Ladies and Gentlemen,

On behalf of the Swiss Mathematical Society and the entire Swiss mathematical community, it is my great privilege to invite you all to the 1994 International Congress of Mathematicians in Zürich. As you know, the honour and responsibility of Organising the Congress have fallen on Zürich twice before in the past: in 1897 and 1932. Zürich is an important financial, commercial and cultural centre of Switzerland; it is also the seat of two of our important institutions of higher education - the Swiss Federal Institute of Technology (ETH) and the University of Zürich. Situated in beautiful natural surroundings in the heart of Europe, Zürich is easily accessible by rail, road and air.

Our Japanese hosts have set such high levels of hospitality and efficiency at this Congress that it would be difficult to match them. However, we shall do our best to make your participation at the 1994 Congress agreeable and fruitful.

Rendezvous then for August 1994 in Zürich.

Dr Jose Felipe Voloch of the Instituto de Matemática Pura e Aplicada, Brazil, and Professor Carol Wood of Wesleyan University, USA, President-Elect of the Association of Women in Mathematics, were invited to give comments on ICM-90.

3.2. President's Closing words.

Professor Hikosaburo Komatsu, President of the Congress, closed the meeting and the Congress with these words:

Thank you for your kind remarks. The organisers of the Congress are really rewarded to hear them. However, all praise should go to Professors Kenji Ueno, Masaki Maruyama, and Chiaki Tsukamoto, as well as to Miss Tanaka, Mrs Ichiki, Miss Ishii to name just a few of the people who have carried out all the plans of the Congress so perfectly.

Our thanks are also due to Professors Gleason and Mesirov for sending us the material they prepared for the last Congress in Berkeley. This was of great help to us.

This Congress has been admired for its smooth organisation but this was true only in appearance. In spite of all the devoted works, I often had to remain in the Secretariat to solve many minor problems. Even when I was attending a lecture, the buzzer, you might have heard, called me back there. Therefore, I must admit that my impression of the Congress is very partial. Nevertheless, I felt that we are at another turning point in the history of mathematics. The previous one was marked at the Second Congress in 1900 when Hilbert gave his famous lecture, Since then we have obtained an enormous number of general results by axiomatisation and abstract formulation, often at the hands of mathematical giants. This time it is a transition from abstract simplification to more concrete synthesis. We are now in a fortunate time when we can solve many problems which remained open for many years in spite of all the efforts of past generations of mathematicians. We no longer have a single genius but many people work together developing new strong streams. It was only many brooks last time at the Congress in Berkeley. They meet together and now we see a big river or a sea or even an ocean.

On behalf of all participants, I would like to praise Professor Kuiper and the other members of the Program Committee for their outstanding work in selecting the invited speakers. I would also like to thank the speakers for their admirable efforts.

At our time of democracy, international cooperation is indispensable and so is the unity of mathematics. We are proud of the fact that this Congress has helped these goals.

As reported in the Daily Bulletin, the Congress has been attended by 3,954 ordinary members, 452 accompanying members, and 92 child members from 76 countries.

Unfortunately, all the preregistered members from 7 countries were unable to attend because of the crisis in the Persian Gulf. World politics has once again cast its shadow on the Congress. I do hope that the next Congress in 1994 will be a truly universal one.

I declare the Congress closed.

The closing ceremonies adjourned at 1:45 p.m.


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