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1962 ICM - Moscow
The International Congress of Mathematicians was held in Moscow, USSR from 16 to 26 August 1966. The official number of participants was 4280 from 54 countries. We give below:
Before presenting the material, we make some comments on various matters not mentioned in the Proceedings.
Before presenting the material, we make some comments on various matters not mentioned in the Proceedings.
Comments by JJOC and EFR.
It is worth noting here some things which are missing from the Proceedings. There is no list of participants, not even the number of participants is given. A list giving the number of mathematicians from each country did appear later in Vsemirnii Kongress Matematikov v Moskve (1967). The number actually attending might be one less than the official number since Registered Participant 4397 had the name Nicolas Bourbaki! Of the 64 invited addresses, only 54 appear in the Proceedings. There were many other communications but the Proceedings contains no information at all about these, not even the number. Participants recalled that at times there were almost 40 parallel sessions.
The other event we should mention is much more sensitive and one we would not expect it to be mentioned in the Proceedings. Stephen Smale was to receive a Fields Medal but he had been given an official summons to testify on that same day to the House Committee on Un-American Activities because of his opposition to the Vietnam War. He intended to fly from Athens to Moscow but a problem with his passport made him a day late. He wrote:-
I arrived late in Moscow and rushed from the airport to the Kremlin where I was to receive the Fields medal at the opening ceremonies of the International Congress. Without a registration badge the guards at the gate refused me admission to the palace. Finally, through the efforts of a Soviet mathematician who knew me, I obtained entrance and found a rear seat. René Thom was speaking about me and my work ...In fact he had missed being presented with the Fields Medal. While at the Congress in Moscow, he was invited to a banquet hosted by four Vietnamese mathematicians. Smale wrote:-
At the banquet, I was asked to give an interview to a reporter named Hoang Thinh from Hanoi. I didn't know what to say and struggled with the problem for the next day. I felt a great debt and obligation to the Vietnamese - after all, it was my country that was causing them so much pain. It was my tax money that was supporting the U.S. Air Force, paying for the napalm and cluster bombs. On the other hand I was a mathematician, with compelling geometrical ideas to be translated into theorems. There was a limit to my ability to survive as a scientist and weather further political storms. I was conscious of the problems that could develop for me from a widely publicised anti-U.S. interview given to a Hanoi reporter in Moscow. In particular, I knew that what I said might come out quite differently in the North Vietnamese newspaper, and even more so when translated back into the U.S. press.Here is the text of the statement Smale read at the press conference:-
This was the background for my rather unusual course of action. On the one hand, I would give the interview; on the other hand, I would ask the American reporters in Moscow to be present so that my statements could be reported more directly. I would give the press conference on Friday morning, August 26.
This meeting was prompted by an invitation to an interview by the North Vietnamese Press. ... I would like to say a few words first, afterwards I will answer questions.After the Press Conference Smale was led away by two Soviet officials. He admitted to being frightened but said he was always treated with dignity. The New York Times ran a story under the title Moscow silences a critical American. It began:-
I believe the American military intervention in Vietnam is horrible and becomes more horrible every day. I have great sympathy for the victims of this intervention, the Vietnamese people. However, in Moscow today, one cannot help but remember that it was only 10 years ago that Russian troops were brutally intervening in Hungary and that many courageous Hungarians died fighting for their independence. Never could I see justification for military intervention, 10 years ago in Hungary or now in the much more dangerous and brutal American intervention in Vietnam.
There is a real danger in a new McCarthyism in America, as evidenced in the actions of the House Un-American Activities Committee. These actions are a serious threat to the right of protest, both in the hearings and in the legislation they are proposing. Again saying this in the Soviet Union, I feel I must add that what I have seen here in the discontent of the intellectuals on the Sinyavsky-Daniel trial and their lack of means of expressing this discontent, shows indeed a sad state of affairs. Even the most basic means of protest are lacking here. In all countries it is important to defend and expand the freedoms of speech and the press.
A University of California mathematics professor was taken for a fast and unscheduled automobile ride through the streets of Moscow, questioned and then released today after he had criticised both the Soviet Union and the United States at an informal press conference.
1. Preface to the Proceedings.
The International Congress of Mathematicians in Moscow, as the previous congresses, received organisational and financial support from the International Mathematical Union and from ICSU and UNESCO. This help consisted of financial support for the invited speakers, for some young mathematicians who were delegates of the Congress and for help in the preparation and the printing of the Proceedings of the Congress.
2. Speech of the President of the Academy of Sciences of the USSR Academician M V Keldysh at the Opening of the Congress.
Dear colleagues
Ladies and Gentlemen, Comrades
It gives me great pleasure on behalf of the Academy of Sciences of the Soviet Union to greet all participants in the Congress and convey the wish for successful work at the Congress.
Mathematics, which is the oldest of all sciences, at the same time remains an eternally young, rapidly developing science, constantly expanding the field of its knowledge, developing its connections more widely not only with the natural sciences, but also with the most diverse areas of human activity. I think that the value of mathematical theories is greater, the more closely their roots are associated with the phenomena of the world in which we live, and at the same time, the greater we achieve a degree of abstraction and a common point of view. The success of a theory largely depends on whether we find a degree of generality and a degree of abstraction that are adequate to the phenomenon under study. The value of the theory is determined by the extent to which general provisions allow us to understand specific phenomena and solve specific problems. General mathematical theories allow us to deeply understand the relationship between phenomena. The introduction of mathematical methods transforms the fields of knowledge and not only puts them at the highest level of logical thinking, but opens up new possibilities, new statements of problems, and allows us to look at phenomena in a new way. It is enough to recall what revolutionary, fundamental shifts in the development of natural science were made by the analysis of the infinitely small, the theory of probability, the theory of operators, and, finally, the rapidly developing knowledge of logical processes.
The development of such abstract areas of mathematics as set theory and topology, algebra, functional analysis, etc. that have recently arisen has led not only to the creation of theories of extraordinary beauty, but also to the creation of powerful new methods in all of mathematics. It seems to me that we are experiencing an era when the mathematical method is especially rapidly conquering ever new areas of knowledge. Along with physics, the spirit of mathematical thinking is becoming increasingly important in chemistry, biology, and geology, and it penetrates widely into social sciences, and first of all, into economic science. Studying the fundamentals of logical processes and the theory of operations, methods of discrete mathematics, creating electronic computing devices prepared the foundations for the new greatest scientific and technological revolution in the whole life of mankind, a new level of understanding of many processes in nature and life, and a new stage in the automation of processes that until recently times were considered an area of exclusively intellectual human activity, as well as in the implementation of mathematical processes that we considered feasible only in abstract thinking.
Let me express the hope that the upcoming Congress will be of great importance in mathematical life. The field of mathematics has become so wide that mathematicians speak not only the languages of different nations, but also different mathematical languages and their language is not yet accessible to many scientists of other specialties, but it is precisely because of the breadth and strength of the mathematical method that this Congress will be of great importance for all science and the development human culture.
Let me open the International Congress of Mathematicians.
3. Academician I G Petrovsky delivers the President's Speech at the Opening of the Congress.
Ladies and Gentlemen, Comrades
It gives me great pleasure on behalf of the Academy of Sciences of the Soviet Union to greet all participants in the Congress and convey the wish for successful work at the Congress.
Mathematics, which is the oldest of all sciences, at the same time remains an eternally young, rapidly developing science, constantly expanding the field of its knowledge, developing its connections more widely not only with the natural sciences, but also with the most diverse areas of human activity. I think that the value of mathematical theories is greater, the more closely their roots are associated with the phenomena of the world in which we live, and at the same time, the greater we achieve a degree of abstraction and a common point of view. The success of a theory largely depends on whether we find a degree of generality and a degree of abstraction that are adequate to the phenomenon under study. The value of the theory is determined by the extent to which general provisions allow us to understand specific phenomena and solve specific problems. General mathematical theories allow us to deeply understand the relationship between phenomena. The introduction of mathematical methods transforms the fields of knowledge and not only puts them at the highest level of logical thinking, but opens up new possibilities, new statements of problems, and allows us to look at phenomena in a new way. It is enough to recall what revolutionary, fundamental shifts in the development of natural science were made by the analysis of the infinitely small, the theory of probability, the theory of operators, and, finally, the rapidly developing knowledge of logical processes.
The development of such abstract areas of mathematics as set theory and topology, algebra, functional analysis, etc. that have recently arisen has led not only to the creation of theories of extraordinary beauty, but also to the creation of powerful new methods in all of mathematics. It seems to me that we are experiencing an era when the mathematical method is especially rapidly conquering ever new areas of knowledge. Along with physics, the spirit of mathematical thinking is becoming increasingly important in chemistry, biology, and geology, and it penetrates widely into social sciences, and first of all, into economic science. Studying the fundamentals of logical processes and the theory of operations, methods of discrete mathematics, creating electronic computing devices prepared the foundations for the new greatest scientific and technological revolution in the whole life of mankind, a new level of understanding of many processes in nature and life, and a new stage in the automation of processes that until recently times were considered an area of exclusively intellectual human activity, as well as in the implementation of mathematical processes that we considered feasible only in abstract thinking.
Let me express the hope that the upcoming Congress will be of great importance in mathematical life. The field of mathematics has become so wide that mathematicians speak not only the languages of different nations, but also different mathematical languages and their language is not yet accessible to many scientists of other specialties, but it is precisely because of the breadth and strength of the mathematical method that this Congress will be of great importance for all science and the development human culture.
Let me open the International Congress of Mathematicians.
Dear members of the Congress!
Thank you for your honour. On behalf of the Soviet Organising Committee, allow me to welcome you and wish you success in your work.
In preparing the Congress, the Organisational Committee was greatly assisted by the Advisory Committee of the International Mathematical Union. All its proposals on the number of sections, on hourly and half-hour reports, were completely accepted by the Soviet Organising Committee. We allowed ourselves only to add several reports to the recommendations of the Committee.
On behalf of the Organising Committee, I want to thank the Executive Committee of the International Mathematical Union and its Advisory Committee, chaired by Professor R Nevanlinna. I would especially like to thank Professor R Nevanlinna.
Now let me give the floor to Professor de Rham to report on the decisions of the Fields Medal Award Committee.
4. Report of Professor G de Rham, Chairman of the Fields Medals Committee, at the Opening Ceremony of the Congress.
Thank you for your honour. On behalf of the Soviet Organising Committee, allow me to welcome you and wish you success in your work.
In preparing the Congress, the Organisational Committee was greatly assisted by the Advisory Committee of the International Mathematical Union. All its proposals on the number of sections, on hourly and half-hour reports, were completely accepted by the Soviet Organising Committee. We allowed ourselves only to add several reports to the recommendations of the Committee.
On behalf of the Organising Committee, I want to thank the Executive Committee of the International Mathematical Union and its Advisory Committee, chaired by Professor R Nevanlinna. I would especially like to thank Professor R Nevanlinna.
Now let me give the floor to Professor de Rham to report on the decisions of the Fields Medal Award Committee.
Ladies and Gentlemen
Professor J C Fields, President of the International Congress of Mathematicians held in Toronto in 1924, proposed that two gold medals be awarded at each International Congress, for outstanding achievements in Mathematics. He set up a fund for that purpose, from out of the balance left over at the end of the Toronto Congress. In 1932, after his death, the International Congress held at Zürich decided to accept his proposal with thanks. As is well known, two medals have been presented at every Congress since held: Oslo 1936, Harvard 1950, Amsterdam 1954, Edinburgh 1958 and Stockholm 1962.
Following a tradition which has become well established, the Executive Committee of the International Mathematical Union appoints, in advance of the Congress, a special Committee to select the candidates. This time the Committee consists of Professors H Davenport, M Deuring, W Feller, M A Lavrentev, J P Serre, D C Spencer, R Thorn, and I have been asked to be the chairman. Every one of the members has taken an active part in the deliberations. We have also consulted other experts. I thank them all for their valuable contribution.
The Memorandum of Fields says: "Because of the multiplicity of the branches of Mathematics and taking into account the fact that the interval between such Congresses is four years, it is felt that at least two medals should be available." In view of the vast development of Mathematics during the last forty years, it appears that this number could judiciously be increased to four. The Executive Committee of the International Mathematical Union has therefore viewed with sympathy the generous offer made by an anonymous donor to give this year two more medals. The Organising Committee of this Congress having agreed to this and the Medals Committee having accepted the responsibility to select four names, four medals will be awarded today. The medals have been struck by the Royal Mint in Ottawa. The name of the recipient is engraved on each of them. The name of Fields does not figure on them. Fields himself proposed to call them: "International Medals for outstanding discoveries in Mathematics". Each of them carries with it a cash prize which, this year, amounts to 1,500 Canadian dollars.
The Memorandum of Fields also contains the following: "In coming to its decision, the hands of the International Committee should be left as free as possible. It would be understood, however, that in making the awards, while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievements on the part of the recipients and a stimulus to renewed efforts on the part of the others."
On the basis of this text, and following precedent, we confine our choice to candidates under forty. We prepare a first list of about 30 names. We then looked for those whose work appeared to us the most important and the most striking, irrespective of any other consideration, setting aside any question of nationality. To our regret, we have had to give up several names which would have also deserved this distinction. Several young mathematicians of extraordinary brilliance were among them. But because they are so young, there will be many Congresses before they reach forty and if they continue in their course, they will have every chance of receiving a medal. The choice was thus not easy. Nevertheless, after serious consideration and reflexion, we arrive at a conclusion without undue difficulty. The following four names, in alphabetical order, constitute our choice:
Michael Francis Atiyah
Paul J Cohen
Alexander Grothendieck
Stephen Smale
Unfortunately, A Grothendieck, was unable to come. May I call Messrs Atiyah, Cohen and Smale to come forward and receive these medals from the hands of Academician Keldysh.
Professor J C Fields, President of the International Congress of Mathematicians held in Toronto in 1924, proposed that two gold medals be awarded at each International Congress, for outstanding achievements in Mathematics. He set up a fund for that purpose, from out of the balance left over at the end of the Toronto Congress. In 1932, after his death, the International Congress held at Zürich decided to accept his proposal with thanks. As is well known, two medals have been presented at every Congress since held: Oslo 1936, Harvard 1950, Amsterdam 1954, Edinburgh 1958 and Stockholm 1962.
Following a tradition which has become well established, the Executive Committee of the International Mathematical Union appoints, in advance of the Congress, a special Committee to select the candidates. This time the Committee consists of Professors H Davenport, M Deuring, W Feller, M A Lavrentev, J P Serre, D C Spencer, R Thorn, and I have been asked to be the chairman. Every one of the members has taken an active part in the deliberations. We have also consulted other experts. I thank them all for their valuable contribution.
The Memorandum of Fields says: "Because of the multiplicity of the branches of Mathematics and taking into account the fact that the interval between such Congresses is four years, it is felt that at least two medals should be available." In view of the vast development of Mathematics during the last forty years, it appears that this number could judiciously be increased to four. The Executive Committee of the International Mathematical Union has therefore viewed with sympathy the generous offer made by an anonymous donor to give this year two more medals. The Organising Committee of this Congress having agreed to this and the Medals Committee having accepted the responsibility to select four names, four medals will be awarded today. The medals have been struck by the Royal Mint in Ottawa. The name of the recipient is engraved on each of them. The name of Fields does not figure on them. Fields himself proposed to call them: "International Medals for outstanding discoveries in Mathematics". Each of them carries with it a cash prize which, this year, amounts to 1,500 Canadian dollars.
The Memorandum of Fields also contains the following: "In coming to its decision, the hands of the International Committee should be left as free as possible. It would be understood, however, that in making the awards, while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievements on the part of the recipients and a stimulus to renewed efforts on the part of the others."
On the basis of this text, and following precedent, we confine our choice to candidates under forty. We prepare a first list of about 30 names. We then looked for those whose work appeared to us the most important and the most striking, irrespective of any other consideration, setting aside any question of nationality. To our regret, we have had to give up several names which would have also deserved this distinction. Several young mathematicians of extraordinary brilliance were among them. But because they are so young, there will be many Congresses before they reach forty and if they continue in their course, they will have every chance of receiving a medal. The choice was thus not easy. Nevertheless, after serious consideration and reflexion, we arrive at a conclusion without undue difficulty. The following four names, in alphabetical order, constitute our choice:
Michael Francis Atiyah
Paul J Cohen
Alexander Grothendieck
Stephen Smale
5. Addresses at the Closing Ceremony.
5.1. Address Delivered by Professor G De Rham at the Closing Ceremony of the Congress.
Mr President, Ladies and Gentlemen!
As the retiring President of the International Mathematical Union, it is my pleasant duty to announce that the fifth General Assembly of the Union, which was held at Dubna on 13-15 August 1966, elected the following Executive Committee for a term of four years,
President: Professor H Cartan
Vice-Presidents: Academician M A Lavrentev and Professor D Montgomery
Secretary: Professor O Frostman
Members: Professors M F Atiyah, K Chandrasekharan, G Hajos, G Vesentini and K Yosida.
I am sure that all of you would want me to wish the new Executive Committee every success.
The first object of the International Mathematical Union is to promote international cooperation in Mathematics. In respect to this, the most striking fact during the last years has been the progressive cooperation between mathematicians of the Soviet Union and those of other countries, especially of Western Europe and U.S.A. It is a particular pleasure for me to emphasise the important position occupied by Soviet Mathematicians in our Union. Their contribution to the development of our Science is of the highest significance. This will continue to increase, due to the abundance of brilliant young Soviet Mathematicians. Mathematicians of all countries welcome every opportunity to meet them. May I express the wish that such contacts will grow, for the benefit of all.
It is also my pleasant duty to express the warmest appreciation and thanks of the Union to the Organising Committee of this magnificent Congress. It is the first International Congress of Mathematicians to be held in the Soviet Union and it is the largest of all our Congresses, with a record number of participants from the host country and from abroad. The level of the lectures has been very high. A tremendous amount of work has gone into its organisation. The Union owes special thanks to the President of the Congress, Academician Petrovsky, to the Chairman of the Soviet National Committee of Mathematicians, Academician I M Vinogradov, to Academician Lavrentev and to Professor Mergelyan, for the successful organisation of this huge meeting. To all members of the Organising Committee and to their assistants, we remain grateful, as well to the members of the Consultative Committee and his Chairman Professor R Nevanlinna.
To Academician Keldysh, President of the Academy of Sciences of the Soviet Union, to the Government of the Soviet Union and to the Municipality of Moscow, we are deeply indebted for the hospitality and consideration we have all received.
Now, as Chairman of the Committee to decide the location of the next Congress, I have the pleasure to request the President, Academician Petrovsky, to call upon the delegate from France, Professor Dieudonné, Dean of the Faculty of Sciences of Nice, to address the Congress.
Thank you all.
5.2. Concluding Remarks from Professor J Dieudonné to the Congress.
As the retiring President of the International Mathematical Union, it is my pleasant duty to announce that the fifth General Assembly of the Union, which was held at Dubna on 13-15 August 1966, elected the following Executive Committee for a term of four years,
President: Professor H Cartan
Vice-Presidents: Academician M A Lavrentev and Professor D Montgomery
Secretary: Professor O Frostman
Members: Professors M F Atiyah, K Chandrasekharan, G Hajos, G Vesentini and K Yosida.
I am sure that all of you would want me to wish the new Executive Committee every success.
The first object of the International Mathematical Union is to promote international cooperation in Mathematics. In respect to this, the most striking fact during the last years has been the progressive cooperation between mathematicians of the Soviet Union and those of other countries, especially of Western Europe and U.S.A. It is a particular pleasure for me to emphasise the important position occupied by Soviet Mathematicians in our Union. Their contribution to the development of our Science is of the highest significance. This will continue to increase, due to the abundance of brilliant young Soviet Mathematicians. Mathematicians of all countries welcome every opportunity to meet them. May I express the wish that such contacts will grow, for the benefit of all.
It is also my pleasant duty to express the warmest appreciation and thanks of the Union to the Organising Committee of this magnificent Congress. It is the first International Congress of Mathematicians to be held in the Soviet Union and it is the largest of all our Congresses, with a record number of participants from the host country and from abroad. The level of the lectures has been very high. A tremendous amount of work has gone into its organisation. The Union owes special thanks to the President of the Congress, Academician Petrovsky, to the Chairman of the Soviet National Committee of Mathematicians, Academician I M Vinogradov, to Academician Lavrentev and to Professor Mergelyan, for the successful organisation of this huge meeting. To all members of the Organising Committee and to their assistants, we remain grateful, as well to the members of the Consultative Committee and his Chairman Professor R Nevanlinna.
To Academician Keldysh, President of the Academy of Sciences of the Soviet Union, to the Government of the Soviet Union and to the Municipality of Moscow, we are deeply indebted for the hospitality and consideration we have all received.
Now, as Chairman of the Committee to decide the location of the next Congress, I have the pleasure to request the President, Academician Petrovsky, to call upon the delegate from France, Professor Dieudonné, Dean of the Faculty of Sciences of Nice, to address the Congress.
Thank you all.
On behalf of the French National Mathematics Committee, I have the honour to invite the International Congress of Mathematicians to hold its 1970 session in France. The city of Nice, by its location, its climate, its tourist facilities and the existence of an active University, meets the conditions required for the seat of a Scientific Congress. I therefore propose that the International Congress of Mathematicians be held in 1970 in the city of Nice.
5.3. President's Speech at the Final Meeting of the Congress by Academician I G Petrovsky.
Dear members of the Congress, dear guests!
Let me once again thank you for participating in the Congress.
I would also like to once again thank the Executive Committee of the International Mathematical Union, with whom we have always been in contact and who helped us a lot.
Let me wish you all success in your work and all the best.
Let me once again thank you for participating in the Congress.
I would also like to once again thank the Executive Committee of the International Mathematical Union, with whom we have always been in contact and who helped us a lot.
Let me wish you all success in your work and all the best.
Written by J J O'Connor and E F Robertson (January 2020)