# 1974 ICM - Vancouver

## 1974 International Congress of Mathematicians - Vancouver

The International Congress of Mathematicians was held in Vancouver, Canada, from 21 August to 29 August 1974. There were 3121 registered ordinary members from 73 countries. We give below:

**1. Preparations for the Congress.**

The 1974 International Congress of Mathematicians was held in Vancouver, Canada, at the invitation of the Canadian Mathematical Congress, representing the Canadian mathematical community, and with the approval of the International Mathematical Union, representing the international mathematical community. As official hosts the Canadian Mathematical Congress assumed the responsibility for all the arrangements and appointed the Organising Committee whose members were A H Cayford, Aubert Daigneault, T E Hull, R D James (Chairman), Maurice Sion (Deputy Chairman). The International Mathematical Union maintained control over the scientific programme and appointed, in consultation with the Canadian Mathematical Congress, the Consultative Committee whose members were G A Gratzer, H A Heilbronn, F E P Hirzebruch, L Hörmander (Chairman), T E Hull, T Husain, S V Jablonskii, N Jacobson, L Schwartz.

The main organiser of the Congress at the practical level was Maurice Sion who, as Chairman of the Local Arrangements Committee, took direct responsibility for all aspects of the Congress with the exception of the list of invited speakers. The other members of the Local Arrangements Committee were G W Bluman, A H Cayford, Armin Frei, S S Page, J V Zidek. Nominally the Local Arrangements Committee was under the supervision of the Organising Committee. In fact the composition and the responsibilities of the two committees overlapped to a considerable extent. Special subcommittees were established as the time of the opening of the Congress approached. Notable assistance on these subcommittees was given by G W Bluman, James Carrell, A H Cayford, John Coury, T E Cramer, Armin Frei, Virginia Green, Lome Halabisky, Ronald Harrop, Rene Held, Erhard Luft, George Maxwell, L A Mysak, S S Page, L G Roberts, Dennis Sjerve, Keith Wales, J V Zidek, and the graduate students in the Department of Mathematics, University of British Columbia.

The main organiser of the Congress at the practical level was Maurice Sion who, as Chairman of the Local Arrangements Committee, took direct responsibility for all aspects of the Congress with the exception of the list of invited speakers. The other members of the Local Arrangements Committee were G W Bluman, A H Cayford, Armin Frei, S S Page, J V Zidek. Nominally the Local Arrangements Committee was under the supervision of the Organising Committee. In fact the composition and the responsibilities of the two committees overlapped to a considerable extent. Special subcommittees were established as the time of the opening of the Congress approached. Notable assistance on these subcommittees was given by G W Bluman, James Carrell, A H Cayford, John Coury, T E Cramer, Armin Frei, Virginia Green, Lome Halabisky, Ronald Harrop, Rene Held, Erhard Luft, George Maxwell, L A Mysak, S S Page, L G Roberts, Dennis Sjerve, Keith Wales, J V Zidek, and the graduate students in the Department of Mathematics, University of British Columbia.

**2. Opening Ceremonies.**

The inaugural session of the Vancouver Congress took place in the Queen Elizabeth Theatre on the morning of August 21, 1974. Professor K Chandrasekharan opened the proceedings by proposing that Professor H S M Coxeter be elected President of the Congress by acclamation. Following his election, Professor Coxeter announced that a telegram would be sent to His Excellency, the Right Honourable Jules Leger, C. C., C.M.M., Governor General of Canada, Patron of the Congress. The text of the telegram is as follows:

We much appreciate your agreeing to serve as Patron of the first meeting in Vancouver of the International Congress of Mathematicians. We regret your inability to be present and we convey our warmest wishes for a complete recovery.Professor Coxeter then called on His Honour, the Honourable Walter S Owen, Lieutenant Governor of British Columbia who welcomed members of the Congress to Canada and to British Columbia.

**2.1. Presidential Address.**

Professor Coxeter then gave his presidential address to the Congress.

The last congress meeting in Canada was in August 1924, almost exactly fifty years ago. That was when the Fields Medals were established. Professor Fields was the president, and gave a long address on

In opening the 1954 congress in Amsterdam, Professor Schouten declared that "The place of mathematics in the world has changed entirely after the second war." What he meant was that, whereas formerly mathematics was studied by exceptional people, in ivory towers, the subject had become immensely popular. Even sport was affected: footballs (for soccer) began to be made to look like truncated icosahedra, electronic computers were springing up everywhere, and departments of mathematics in all universities were expanding to accommodate crowds of eager students. As soon as they graduated, the best students were urged to write original papers. The slogan was "publish or perish." Although some of the resulting work was second-rate, much of it was excellent. In fact, the accumulation of mathematical knowledge has been so rapid that, as Professor Nevanlinna remarked at Stockholm in 1962, no one of us can appreciate all its branches.

Why, then, do we now come together from all the countries on earth? What do we have in common? Perhaps it is our appreciation of patterns of abstract ideas, our striving for order and truth and beauty in a world full of confusion and deceit and pollution. We understand, with William Wordsworth, that mathematics is "An independent world created out of pure intelligence" or, as Alfred North Whitehead put it, "The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit."

To see the extent of the feverish activity mentioned by Schouten and Nevanlinna, we merely have to measure the volumes of Mathematical Reviews on our shelves. (This is reasonable because it is usually the most important books and papers that deserve the longest reviews.) The volumes from 1941 to '51 measure 21 inches, 1952 to '62 45 inches, and 1963 to '73, 87 inches. Thus each period of eleven years produces twice as much as the preceding period. Such a proliferation of mathematical research, if continued in the future, would make the number of writers surpass the number of readers, the same discoveries would be made over and over again, and all the libraries in the world would not suffice to accommodate the mass of material.

However, such a calamity may now have been averted in an unexpected manner. The present generation has been engulfed by a wave of anti-intellectualism, with the result that most universities are short of students. Young people find that the problem of looking for a job is not facilitated by a university education. The idea of "art for art's sake" is less prevalent than it used to be, and pure mathematics is abandoned in favour of applied mathematics, statistics, or computing. Thus the editors of pure mathematical journals may soon be able to relax and get rid of their terrifying backlog of papers waiting to be assessed for possible publication.

What, then, should be our advice to a student who is wondering whether to specialise in mathematics? In view of the present scarcity of suitable jobs, I would advise him to take up some other subject, unless his love for mathematics is so intense that he finds himself doing it in almost all his spare time, even thinking about it while sleeping, or between dreams. For such a person, as Hermann Minkowski declared, "The purpose of life is to behold the truth, to understand it well, and to expound it perfectly."

Some of the mathematicians who attended the Congress in Nice are no longer with us. I think especially of Abraham Robinson, who died so tragically a few months ago, at the height of his powers. He made contributions to applied mathematics as well as to algebra and logic, on which he spoke at Nice. Since that time, his nonstandard analysis has opened up new vistas in both research and pedagogy. When I was a boy, I was introduced to calculus the "easy" way, using infinitesimals. At college I was told to put away childish things and become rigorous. How wonderful it is that the name "infinitesimal calculus" has been restored to respectability!

Before sitting down, I wish to propose a vote of thanks to the Consultative Committee, appointed by IMU to plan the academic program, namely Professors L Hormander, F Hirzebruch, S V Jablonski, N Jacobson, L Schwarz, G A Gratzer, T Husain, T E Hull, H Heilbronn.

And now it is my pleasure to call upon Professor Chandrasekharan, the president of IMU to make an important announcement.

*A foundation for the theory of ideals*. He was editor of the PROCEEDINGS, which contained a nice photograph of La Vallée Poisson presenting a commemorative wreath to the University of Toronto. There was also a map of Canada showing the route of the Transcontinental Excursion, which included a stop in Vancouver. Perhaps one or two of you can still remember that occasion.In opening the 1954 congress in Amsterdam, Professor Schouten declared that "The place of mathematics in the world has changed entirely after the second war." What he meant was that, whereas formerly mathematics was studied by exceptional people, in ivory towers, the subject had become immensely popular. Even sport was affected: footballs (for soccer) began to be made to look like truncated icosahedra, electronic computers were springing up everywhere, and departments of mathematics in all universities were expanding to accommodate crowds of eager students. As soon as they graduated, the best students were urged to write original papers. The slogan was "publish or perish." Although some of the resulting work was second-rate, much of it was excellent. In fact, the accumulation of mathematical knowledge has been so rapid that, as Professor Nevanlinna remarked at Stockholm in 1962, no one of us can appreciate all its branches.

Why, then, do we now come together from all the countries on earth? What do we have in common? Perhaps it is our appreciation of patterns of abstract ideas, our striving for order and truth and beauty in a world full of confusion and deceit and pollution. We understand, with William Wordsworth, that mathematics is "An independent world created out of pure intelligence" or, as Alfred North Whitehead put it, "The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit."

To see the extent of the feverish activity mentioned by Schouten and Nevanlinna, we merely have to measure the volumes of Mathematical Reviews on our shelves. (This is reasonable because it is usually the most important books and papers that deserve the longest reviews.) The volumes from 1941 to '51 measure 21 inches, 1952 to '62 45 inches, and 1963 to '73, 87 inches. Thus each period of eleven years produces twice as much as the preceding period. Such a proliferation of mathematical research, if continued in the future, would make the number of writers surpass the number of readers, the same discoveries would be made over and over again, and all the libraries in the world would not suffice to accommodate the mass of material.

However, such a calamity may now have been averted in an unexpected manner. The present generation has been engulfed by a wave of anti-intellectualism, with the result that most universities are short of students. Young people find that the problem of looking for a job is not facilitated by a university education. The idea of "art for art's sake" is less prevalent than it used to be, and pure mathematics is abandoned in favour of applied mathematics, statistics, or computing. Thus the editors of pure mathematical journals may soon be able to relax and get rid of their terrifying backlog of papers waiting to be assessed for possible publication.

What, then, should be our advice to a student who is wondering whether to specialise in mathematics? In view of the present scarcity of suitable jobs, I would advise him to take up some other subject, unless his love for mathematics is so intense that he finds himself doing it in almost all his spare time, even thinking about it while sleeping, or between dreams. For such a person, as Hermann Minkowski declared, "The purpose of life is to behold the truth, to understand it well, and to expound it perfectly."

Some of the mathematicians who attended the Congress in Nice are no longer with us. I think especially of Abraham Robinson, who died so tragically a few months ago, at the height of his powers. He made contributions to applied mathematics as well as to algebra and logic, on which he spoke at Nice. Since that time, his nonstandard analysis has opened up new vistas in both research and pedagogy. When I was a boy, I was introduced to calculus the "easy" way, using infinitesimals. At college I was told to put away childish things and become rigorous. How wonderful it is that the name "infinitesimal calculus" has been restored to respectability!

Before sitting down, I wish to propose a vote of thanks to the Consultative Committee, appointed by IMU to plan the academic program, namely Professors L Hormander, F Hirzebruch, S V Jablonski, N Jacobson, L Schwarz, G A Gratzer, T Husain, T E Hull, H Heilbronn.

And now it is my pleasure to call upon Professor Chandrasekharan, the president of IMU to make an important announcement.

**2.2. The Fields Medals Committee.**

Professor Chandrasekharan, chairman of the Fields Medals Committee, then presented the following report:

The proposal to institute two gold medals, to be awarded "for outstanding discoveries in mathematics," at successive International Congresses of Mathematicians, was first mooted by Professor J C Fields, President of the International Congress of Mathematicians held in Toronto in 1924. The fund for the founding of the medals was constituted by a balance left over after financing the Toronto Congress. That proposal was accepted with thanks, after the death of Professor Fields, by the International Congress of Mathematicians which met in Zurich in 1932.The first two such medals were presented at the Oslo Congress in 1936. After an interruption, caused by the war, two medals were presented at each of the following Congresses: at Harvard in 1950, Amsterdam 1954, Edinburgh 1958, and Stockholm 1962; while four medals were presented at the Moscow Congress in 1966, and at the Nice Congress in 1970. Each medal carries with it a cash prize of 1500 Canadian dollars. The medals are struck at the Royal Canadian Mint. It is expressly provided that there should not be attached to them, in any way, the name of any country or institution. Although, in common parlance, they are known as the Fields medals, the name of Fields does not appear on them.

Following established practice, the Executive Committee of the International Mathematical Union appointed, about two years ago, an international committee to adjudicate the award of the medals at this congress. The Committee consists of Professors J F Adams, K Kodaira, L S Pontryagin, B Malgrange, A Mostowski, J Tate, A Zygmund, and myself, as Chairman. May I take this opportunity to convey to all the members of the Committee the appreciation and thanks of the Union for the service they have rendered. The Committee, in turn, is indebted to many individual mathematicians whose expert knowledge provided valuable assistance.

The Committee decided, at the outset, and not without discussion, to confine the award to mathematicians under forty, as in the past. The names of some who have done brilliant work in recent years, but who are now on the wrong side of forty, have had regrettably to be omitted. Even so, more than a score of names figured on our first list. The task of reducing that number was by no means easy. There was a great deal of consultation, deliberation, and reflection. The Committee elected finally to select two names for the award. That decision was reached as unanimously as one could reasonably expect. We are aware of the very strong claims of many of those not selected, some of them so young that many Congresses will meet before they are forty. Nevertheless, we are convinced that the two selected are mathematicians of exceptional merit, whose work has advanced the development of important branches of our science. May I offer them our warmest congratulations, and invite them to come forward to receive the medals from the hands of His Honour, the Lieutenant Governor of British Columbia. They are, in alphabetical order,

and

His Worship, Mayor Art Phillips of Vancouver gave a short address in which he welcomed members of the Congress to the City of Vancouver.

Professor Coxeter announced that reports of the work of the Fields medalists would be given in the evening. Professor Chandrasekharan would report on the work of Enrico Bombieri and Professor J Tate on the work of David Mumford. The inaugural session was then declared closed.

Following established practice, the Executive Committee of the International Mathematical Union appointed, about two years ago, an international committee to adjudicate the award of the medals at this congress. The Committee consists of Professors J F Adams, K Kodaira, L S Pontryagin, B Malgrange, A Mostowski, J Tate, A Zygmund, and myself, as Chairman. May I take this opportunity to convey to all the members of the Committee the appreciation and thanks of the Union for the service they have rendered. The Committee, in turn, is indebted to many individual mathematicians whose expert knowledge provided valuable assistance.

The Committee decided, at the outset, and not without discussion, to confine the award to mathematicians under forty, as in the past. The names of some who have done brilliant work in recent years, but who are now on the wrong side of forty, have had regrettably to be omitted. Even so, more than a score of names figured on our first list. The task of reducing that number was by no means easy. There was a great deal of consultation, deliberation, and reflection. The Committee elected finally to select two names for the award. That decision was reached as unanimously as one could reasonably expect. We are aware of the very strong claims of many of those not selected, some of them so young that many Congresses will meet before they are forty. Nevertheless, we are convinced that the two selected are mathematicians of exceptional merit, whose work has advanced the development of important branches of our science. May I offer them our warmest congratulations, and invite them to come forward to receive the medals from the hands of His Honour, the Lieutenant Governor of British Columbia. They are, in alphabetical order,

**Enrico Bombieri**and

**David Mumford**.His Worship, Mayor Art Phillips of Vancouver gave a short address in which he welcomed members of the Congress to the City of Vancouver.

Professor Coxeter announced that reports of the work of the Fields medalists would be given in the evening. Professor Chandrasekharan would report on the work of Enrico Bombieri and Professor J Tate on the work of David Mumford. The inaugural session was then declared closed.

**3. Closing Ceremonies.**

The closing session of the Vancouver Congress took place in the Frederick Wood Theatre, University of British Columbia, on the afternoon of August 29, 1974. Professor H S M Coxeter, President of the Congress, was in the chair.

Professor Coxeter read a message from His Excellency the Governor General of Canada expressing his thanks for the telegram sent on behalf of the Congress at the inaugural session. He then called on Professor K Chandrasekharan, President of the International Mathematical Union, to present the following report:

It is my pleasant duty to announce that the Seventh General Assembly of the International Mathematical Union, which met at Harrison Hot Springs, from August 17 to 19, 1974, elected the following Executive Committee for a term of four years beginning January 1, 1975.

President:

Professor Deane Montgomery (Princeton, N.J., U.S.A.).

Vice Presidents:

Professor J W S Cassels (Cambridge, U.K.),

Academician M Nicolescu (Bucharest).

Secretary:

Professor J-L Lions (Paris).

Members:

Professor E Bombieri (Pisa),

Professor M Kneser (Göttingen),

Professor O Lehto (Helsinki),

Professor M Nagata (Kyoto),

Academician L S Pontryagin (Moscow).

I am sure you will join me in wishing the new Committee every success in the work ahead.

The main object of the International Mathematical Union is "to promote international co-operation in mathematics," and, in particular, "to support and assist the International Congress of Mathematicians." May I, on behalf of the Union, express our gratitude to the Canadian Mathematical Congress for having played host to this International Congress in such a beautiful place as Vancouver. Our warmest thanks go to the members and staff of the Organising Committee headed by Professor R D James, and to the members and staff of the Local Arrangements Committee headed by Professor M Sion, for having ministered to our needs unobtrusively and efficiently, both at Harrison Hot Springs and at Vancouver.

The Congress has brought together mathematicians from many lands, united in a friendship which stems from a common devotion to mathematics, transcending the stresses of politics, and happily free from the strains of competitive sport. We trust that the next Congress in 1978 will be a worthy successor. May I, as Chairman of the Committee to select a site for the next Congress, request you, Mr President, to invite Professor Rolf Nevanlinna to speak on behalf of the National Committee for mathematics in Finland.

President:

Professor Deane Montgomery (Princeton, N.J., U.S.A.).

Vice Presidents:

Professor J W S Cassels (Cambridge, U.K.),

Academician M Nicolescu (Bucharest).

Secretary:

Professor J-L Lions (Paris).

Members:

Professor E Bombieri (Pisa),

Professor M Kneser (Göttingen),

Professor O Lehto (Helsinki),

Professor M Nagata (Kyoto),

Academician L S Pontryagin (Moscow).

I am sure you will join me in wishing the new Committee every success in the work ahead.

The main object of the International Mathematical Union is "to promote international co-operation in mathematics," and, in particular, "to support and assist the International Congress of Mathematicians." May I, on behalf of the Union, express our gratitude to the Canadian Mathematical Congress for having played host to this International Congress in such a beautiful place as Vancouver. Our warmest thanks go to the members and staff of the Organising Committee headed by Professor R D James, and to the members and staff of the Local Arrangements Committee headed by Professor M Sion, for having ministered to our needs unobtrusively and efficiently, both at Harrison Hot Springs and at Vancouver.

The Congress has brought together mathematicians from many lands, united in a friendship which stems from a common devotion to mathematics, transcending the stresses of politics, and happily free from the strains of competitive sport. We trust that the next Congress in 1978 will be a worthy successor. May I, as Chairman of the Committee to select a site for the next Congress, request you, Mr President, to invite Professor Rolf Nevanlinna to speak on behalf of the National Committee for mathematics in Finland.

**3.1. Invitation to ICM 1978.**

Professor Coxeter called on Professor Nevanlinna who spoke as follows:

On behalf of the Finnish National Committee of Mathematics, I have the honour to invite you to the next International Congress of Mathematicians in Helsinki.

Finland is a small country and it may seem risky to undertake the organisation of such big meeting, the more so as many previous congresses have been so splendidly run like this fine meeting in Vancouver. But we know that the International Mathematical Union will help us, and support has also been promised to us by the Finnish Government and by the University of Helsinki. Therefore we feel confident that we shall be able to organise the Congress in a satisfactory manner.

Ladies and Gentlemen: Hoping that you will accept our invitation, I welcome you all to the next International Congress of Mathematicians to be held in August 1978 in Helsinki.

The invitation was accepted by acclamation.
Finland is a small country and it may seem risky to undertake the organisation of such big meeting, the more so as many previous congresses have been so splendidly run like this fine meeting in Vancouver. But we know that the International Mathematical Union will help us, and support has also been promised to us by the Finnish Government and by the University of Helsinki. Therefore we feel confident that we shall be able to organise the Congress in a satisfactory manner.

Ladies and Gentlemen: Hoping that you will accept our invitation, I welcome you all to the next International Congress of Mathematicians to be held in August 1978 in Helsinki.

Speaking on behalf of the members of the Congress, Professors J Tits and B Szökefalvi-Nagy expressed their thanks to those who had participated in the arrangements for the Congress. Professors R D James and Maurice Sion replied for all concerned.

Professor Coxeter then declared the Vancouver Congress closed.