1962 International Congress of Mathematicians - Stockholm
1. Secretary's Report on Preparations.
Professors O Frostman and A Pleijel were entrusted with the initial preparations for the congress together with Professor H Cramer, at that time Chancellor of the Universities of Sweden, and Professor L Garding, all of whom later constituted the Organising Committee.
The scientific programme was drawn up in close cooperation with the International Mathematical Union, which for this purpose nominated a Consultative Committee with Professor G de Rham as chairman. The Swedish representatives in charge of the scientific programme were Professors L Garding, L Carleson and L Hörmander.
Thus a first meeting was held in Zurich in November 1960 followed by a meeting in Dusseldorf in January 1961. As a result of these two meetings the "International Fields Committee", that elects the two prize winners, was constituted. Furthermore a list was made of speakers to be invited to deliver one-hour addresses on chosen topics in different fields of mathematics. Finally chairmen of international panels were appointed with the task of recommending half-hour speakers who would be able to present recent results within their respective fields. After receipt of the reports from the panels a final meeting was held in Zurich in November 1961; the choice of speakers to be invited to deliver half-hour lectures was then made.
About 1 June 1961 invitations to hold one-hour lectures at the Congress were sent to 19 mathematicians.
An orchestra from the Royal Navy played a selection of Swedish music.
2.1. Welcome from the Chairman of the Organising Committee.
Professor O Frostman, Chairman of the Organising Committee, welcomed the audience with the following words:
Your Majesty, Ladies and Gentlemen:
On behalf of the Swedish mathematicians I wish you welcome to the International Congress in Stockholm, the Opening Session of which is honoured by the presence of His Majesty the King of Sweden. We are very glad that so many from all parts of the world have responded to our invitation and we hope that the addresses given and the new results presented here will be of great value for the development of our science. We also hope that the personal contacts, renewed and established at the Congress, will serve the same purpose and, at the same time, be links in the chain that unites us all.
At the International Congress in Cambridge, England, in 1912, Professor G Mittag-Leffler invited the mathematicians to meet the next time in Stockholm in 1916. Because of the First World War this Congress had to be reduced to a Scandinavian one, and it was not until after the Edinburgh Congress in 1958 that the Swedish mathematicians assumed the responsibility of organising the next Congress. It goes without saying that the decision was a hard one to take. In the first place the number of participants at an international congress of mathematicians would probably have risen to something between 2000 and 3000 by 1962 - in fact, we are over 3000, associated members included - and such figures must inevitably involve difficulties of housing, transportation, too small lecture-rooms, and so on. But the real trouble lies in the development of mathematics itself which is proceeding so rapidly that no man can survey but a part or parts of the front line, and total coverage can only be achieved by joint work on an international basis.
To be able to present a scientific programme worthy of an international congress it was therefore decided at an early stage to seek the assistance of the International Mathematical Union, and at a meeting in Zurich in November 1960 a small Consultative Committee was appointed with Professor de Rham, Lausanne, as chairman. The wide experience and knowledge represented in the Consultative Committee itself and strengthened by contacts with experts from all over the world, made it possible to choose the subjects and speakers for the one-hour addresses and to appoint chairmen of the international panels which have proposed the half-hour speakers. At subsequent meetings the Consultative Committee brought the information gathered to the Swedish representatives and all decisions were made in agreement. It must be clearly stated that the Swedish Committee takes the full responsibility for the organisation of the congress, but without the invaluable help of the panels and the Consultative Committee the scientific programme would not have been adequate.
The part performed by the International Mathematical Union in preparing the scientific programme of this congress is a leading one, and is well suited to act as a precedent for any future international congress. It seems therefore quite natural that the President of the International Mathematical Union should preside over the general sessions of the Congress, and I now have the honour to call upon Professor Rolf Nevanlinna who will declare the Congress open.
2.2. Presidential Address
Professor R Nevanlinna came forward and spoke as follows:
Your Majesty, Ladies and Gentlemen:
One prime characteristic of our age is the highly accelerated pace of its development. This can be felt everywhere in our cultural, social and economic life. It applies with greatest force to technology and science.
Mathematics is no exception. To convince oneself of this, it is sufficient to glance at the questions dealt with in the lectures and discussions of the international mathematical congresses since the beginning of the century.
The expansion and growth of many different branches of science have led to increasing specialisation in the field of research. Today there is no mathematician who can claim to have mastered modern mathematics in its entirety.
This development of science would soon lead to an impossible situation, if there were not another tendency working against it; the tendency towards synthesis. Mathematical development in our century stands out as a shining example of this synthesis, which is necessarily on a conceptually high and abstract level.
What takes place in pure mathematics has its roots in the world of experience. On the other hand, theoretical and general mathematical insight throws light on practical questions, and forms, in fact, the basis of applications in many different fields: in natural science, in technology and, in recent times, in many branches of social and economic life. The astonishing development of electronic computers has contributed enormously to the applicability of mathematical methods.
Thus, mathematics in our time forms a background of ever increasing importance for all cultural life.
Mathematicians from all over the world have come together again after four years to survey the state of our science.
This survey is the principal object of a large Congress, and this opinion has been decisive in the organisation of this Congress.
The most important branches of mathematics will be covered in 16 one-hour addresses, delivered by leading experts. These addresses are meant primarily for those participants of the Congress who are not specialists in these fields. It is my hope that these survey-lectures will contribute towards a better contact between the different branches of mathematics.
About 60 half-hour addresses by invited speakers in the seven sections of the congress will report on the latest advances in their respective fields of work. Freedom of research requires that all mathematicians of the world, and in particular those of the younger generation, should have the opportunity to present briefly their own results during this Congress. For practical reasons, however, the duration of such short communications, of which there are about 800, must be restricted to 10 minutes each.
So I hope that the week beginning today will supply proof that large congresses are still useful and have a task to fulfil as supplements to the smaller meetings at which a small group of specialists discusses their problems.
We are grateful to our Swedish colleagues for having taken over the great burden of organising this Congress and having given us the opportunity of meeting in this beautiful city of Stockholm.
In the name of the International Mathematical Union and of the Swedish Organising Committee I have the honour to declare open the International Congress of Mathematicians in Stockholm.
2.3. The Fields Medals Committee.
After an interval, Professor Nevanlinna in his capacity of chairman of the Fields Medals Committee, read the report of t he Committee which was as follows:
Your Majesty, Ladies and Gentlemen:
During the International Congress of Mathematicians in Zürich 1932, it was made known that J C Fields, chairman of the Organising Committee of the Toronto Congress in 1928 had set up a trust to found two prizes to be presented in connection with the International Congress of Mathematicians that followed. This idea was carried out for the first time at the Congress in Oslo, 1936. At this and at the following Congresses in Cambridge (Harvard) 1950, Amsterdam 1954 and Edinburgh 1958, two gold medals and cash prizes were presented to two young mathematicians in recognition of distinguished achievements in mathematics.
The problem of suggesting names for the award of the Fields medals has, since the last congress, been entrusted to the International Mathematical Union. To prepare the names at this Congress in Stockholm, the Union appointed a Fields medals committee. This committee has the honour to make known its decision here.
The two Fields medals are to be given, also this time, to two young mathematicians for distinguished scientific achievements:
Lars Hörmander, Professor at the University of Stockholm,
John Milnor, Professor at the University of Princeton.
The International Mathematical Union considers it a great honour that His Majesty the King has agreed to be present here and to give the Fields Medals to the winners of the Prizes.
The formal opening ceremony had thus come to an end and His Majesty withdrew from the session.
3.1. President's Closing Remarks.
Professor Nevanlinna opened the session with the following words:
Ladies and Gentlemen
At every international congress of mathematicians since 1950, it has been the custom, on the last day of the Congress, to make an announcement about the International Mathematical Union. Following that custom, I am glad to announce that the Fourth General Assembly of the International Mathematical Union which met in Saltsjöbaden from August 11 to 13 was very successful. The Union, as some of you may know, has as one of its principal objectives the support of the International Congress of Mathematicians. I am glad to say that as a result of the Union's efforts, there has evolved, and become established, a definite pattern of collaboration with the Congress, especially with regard to the Fields Medals, the Scientific Programme, and the choice of location of future Congresses. This, in itself, is by no means a trivial development, since the Union, as the only non-governmental organisation, truly scientific in its intent, and truly international in its scope, offers perhaps the best guarantee of enduring international collaboration among mathematicians the world over.
Professor Nevanlinna then reported that the Executive Committee of the International Mathematical Union for the years 1963-66 would consist of Professors G de Rham, President, H Cartan and K Kuratowski, Vice Presidents, K Chandrasekharan, Secretary, and J C Burkill, F Hirzebruch, M A Lavrentev, D Montgomery, B Segre, and R Nevanlinna (Past President), Members.
He also asked the meeting to join him in wishing the new Executive Committee every success, which was carried by acclamation. Professor Nevanlinna continued:
Ladies and Gentlemen:
As Chairman of the Committee to recommend the choice of location of the International Congress of Mathematicians 1966, I have the honour to request Academician Lavrentev to address this gathering.
M Lavrentev, I have the honour to give you the floor.
3.2. Invitation to ICM 1964.
Professor M A Lavrentev came forward and read an invitation - to hold the next Congress of Mathematicians in the Soviet Union - worded as follows:
Mr President, ladies and gentlemen!
On behalf of the Academy of Sciences of the Soviet Union, I have the honour to invite Congress to convene the next international mathematical congress in the Soviet Union. Over the past decade, world mathematics has achieved introductory successes and there are many here whose efforts have ensured these successes. It is interesting that they received rich spice from the knowledge of technology, even those sections of mathematics that used to seem distracted and distant from life. Mr President, ladies and gentlemen! The rapid growth of mathematics, an increase in the number of its fields and workers in them, all this increases the role of the international mathematical organisation, the role of combining the efforts of mathematics of all countries to solve the most important problems. One of the important forms of international communication is mathematical congresses. Allow me to say here on behalf of the Soviet mathematicians that we will make every effort to prepare and conduct a new congress together with the executive committee of the international union with great benefit and pleasure for members of the congress and their families.
The Russian text of the invitation was followed by an English interpretation given by Professor P S Aleksandrov.
The invitation was carried by acclamation, interpreted by Professor Nevanlinna with the following words:
M Lavrentiev, the Congress unanimously accepts your invitation. I sincerely thank you.
3.3. Professor Eilenberg addresses Congress.
Professor S Eilenberg asked for permission to speak and addressed the meeting as follows:
Mr President, Ladies and Gentlemen:
In the name of the mathematicians of all nations assembled here, I take the liberty to say a few words which I hope represent the feelings of all of us here. First, it is my pleasant duty to ask the Organising Committee to convey expressions of our thanks and gratitude to His Majesty the King of Sweden for having placed this Congress under His high patronage and for having graced the opening session with His presence.
The physical arrangements for this congress were entirely in the capable hands of the Organising Committee composed of Swedish mathematicians. The Swedish mathematical community being relatively small as compared with this huge congress, their task was enormous and the accomplishment most remarkable. I hope that I speak for all of us when I express our sincere thanks to the Organising Committee for their hard task so well carried out.
In preparing the scientific programme, the Organising Committee worked in close cooperation with the Executive Committee of the International Mathematical Union, and enlisted the help of many advisory committees composed of experts of all nations. This truly international effort resulted in a scientific programme of the highest calibre. Let me express here the hope that this procedure constitutes a precedent for future International congresses.
3.4. Professor Nevanlinna addresses Congress.
Having presented his personal thanks in Swedish to the Organising Committee and especially to its Chairman, Professor Frostman, Professor Nevanlinna terminated the session with the following words:
Ladies and Gentlemen:
All good things must come to an end; so must this Congress. It has been a very successful meeting. We have witnessed many brilliant contributions to our science. We have had the pleasure of meeting many eminent personalities. But the dominant characteristic of this Congress has been the vigorous role played by youth. It seems to me that this is the best symbol of its success.
Now is the time to give our thanks to our Swedish Colleagues who made this possible. They have worked hard, and long, and unselfishly; they have been modest and un-obtrusive. But, you will agree, they have been kind, and generous and efficient. The Organising Committee, and especially its chairman Professor Frostman, have placed us in debt. Let us discharge that debt by expressing, publicly, our deep gratitude.
Ladies and Gentlemen, I declare the International Congress of Mathematicians in Stockholm closed.
3.5. Telegram to His Majesty the King.
In compliance with the demand expressed by Professor Eilenberg, the Organising Committee sent the following telegram to His Majesty the King:
On behalf of the mathematicians assembled in Stockholm for the International Congress the Organising Committee thanks Your Majesty most warmly both for becoming patron of the Congress and for graciously attending the opening session and presenting the Fields medals.