1950 International Congress of Mathematicians - Cambridge, Massachusetts

The International Congress of Mathematicians was held in Cambridge, Massachusetts, from 30 August to 6 September 1950. The Congress was attended by 1686 full members and 616 associate members. We give below a version of the report by the Secretary on Preparations, a report on the Opening Ceremonies held in the Sanders Theatre of Harvard University on the afternoon of Wednesday 30 August 1950, and a report on the Closing Ceremonies held in the Sanders Theatre of Harvard University on the morning of Wednesday, 6 September.

1. Secretary's Report on Preparations.

From 30 August 30 to 6 September 1950, an International Congress of Mathematicians was held at Harvard University under the auspices of the American Mathematical Society. In addition to the principal host, Harvard University, the following acted as co-hosts: The American Academy of Arts and Sciences, Boston College, Boston University, The Massachusetts Institute of Technology, and Tufts College.

This was the first International Congress of Mathematicians held in the United States since that assembled in connection with the Chicago World's Fair in 1893. At that time an international gathering of mathematicians met at Northwestern University under the presidency of Professor William E Story of Clark University. Professor Felix Klein of the University of Göttingen attended this Congress as the official representative of the German government and brought with him a number of papers by prominent foreign mathematicians. These papers formed an important part of the program of the meetings. The nations represented among the authors of papers submitted to the Congress were as follows: Austria, France, Germany, Italy, Russia, Switzerland, and the United States. There were twenty-five mathematicians in attendance. In the two weeks immediately following the Congress, Professor Klein, who had taken such a prominent part in the Congress, gave a series of Colloquium Lectures at Northwestern University. These twelve lectures were published under the title The Evanston Colloquium Lectures on Mathematics.

The 1950 Congress was the first International Congress of Mathematicians held on the North American continent since that in Toronto in 1924.

At the International Congress in Oslo in 1936, the American delegation invited the mathematicians of the world to hold their next general gathering in the United States in 1940. Plans had been practically completed for such a gathering at Harvard University when the outbreak of World War II necessitated the cancellation of the Congress. At the close of the war in 1945, the Council of the Society at once began discussion concerning the possibility of a gathering of the mathematicians of the world. Those guiding the policies of the American Mathematical Society were insistent that there should be no international congress until such a time that the gathering could be truly international in the sense that mathematicians could be invited irrespective of national or geographic origins. On December 10, 1947, the Council of the Society voted unanimously to accept the recommendation of the Emergency Committee for the International Congress of Mathematicians that steps be taken at once to elect officers and committees for the next congress.

Early in 1948, the following officers of the Congress were elected: President Designate: Oswald Veblen, Institute for Advanced Study; Secretary: J R Kline, University of Pennsylvania; Associate Secretary: R P Boas, Jr., Mathematical Reviews.

Garrett Birkhoff was elected chairman of the Organising Committee with W T Martin as vice chairman. The other members of this committee, as finally constituted, were: A A Albert, J L Doob, G C Evans, T H Hildebrandt, Einar Hille, J R Kline, Solomon Lefschetz, Saunders Mac Lane, Marston Morse, John von Neumann, Oswald Veblen, J L Walsh, Hassler Whitney, D V Widder, and R L Wilder. R G D Richardson and J L Synge were also originally members of this Committee. Dean Richardson died July 17, 1949, while Professor Synge resigned from the Committee when he left the United States to assume his position at the Institute for Advanced Studies in Dublin in August 1948.

Invitations to send delegates to the Congress were sent to national academies and royal societies, universities and colleges, and to the mathematical societies throughout the world. In the case of all national academies and royal societies of countries with which the United States Government maintained diplomatic relations, these invitations were transmitted through the diplomatic mail pouch of the State Department. The various mathematical societies cooperated by distributing to their members invitations to and literature about the Congress which was furnished to them by the Secretariat. In attempting to maintain the non-political nature of the Congress, many serious difficulties had to be overcome. In the solution of these problems, officers of the Congress found the various officials of the Department of State most sympathetic and helpful. As a part of the effort to keep the Congress apolitical, they tried to secure a visa for every mathematician who notified them about any visa difficulties before cancelling his passage. As far as they know only one mathematician from any independent nation was prevented from attending the Congress because he failed to pass a political test and this man did not notify the officers of the Congress about his difficulties. Only two mathematicians from occupied countries failed to secure visas. Mathematicians from behind the Iron Curtain were uniformly prevented from attending the Congress by their own governments which generally refused to issue passports to them for the trip to the Congress. Their non-attendance was not due to any action of the United States Government.

2. The Opening Ceremonies.
Just before the opening of the Congress there was received from the President of the Soviet Academy of Sciences the following cablegram:
USSR Academy of Sciences appreciates receiving kind invitation for Soviet scientist take part in International Congress of Mathematicians to be held in Cambridge. Soviet Mathematicians being very much occupied with their regular work unable attend congress. Hope that impending congress will be significant event in mathematical science. Wish success in congress activities.

S Vavilov, President, USSR Academy of Sciences.

This cablegram was read at the opening plenary session of the Congress which was held on Wednesday afternoon, August 30, in the Sanders Theatre of Harvard University.

2.1. Official opening of the Congress.

The Congress was officially opened by Professor Garrett Birkhoff as chairman of the Organising Committee of the Congress. Professor Birkhoff spoke as follows:

Fellow Mathematicians:

It gives me great satisfaction to see you all assembled here. The organising of a successful International Congress at such a time of political tensions, and after a gap of fourteen years, has had its anxious moments, as many of you know. Your presence here promises that our efforts will be crowned with success.

It is needless to say that the organisation of the Congress would have been impossible without the generous and loyal assistance of many people. I wish I could mention them individually, by name, but time does not permit this. Those who did the work are quite cognisant of the fact, I am sure, and do not need to be reminded of it.

In fact, our scientific program is so full that there will not even be time to listen, in this first preliminary session, to the official greetings from the representatives of many countries and learned societies which have sent delegates here. Therefore, it will be necessary for these greetings to be conveyed informally; I am sure that they are appreciated nonetheless.

To save time I shall say no more, but shall call immediately upon Mr Skolem, as the delegate of President Størmer of the Oslo Congress in 1936, to nominate the President of this Congress.

2.2. The Presidential Address.

Professor T A Skolem of the University of Oslo presented the name of Professor Oswald Veblen for the Presidency of the Congress. Professor Veblen was unanimously elected and then delivered his presidential address, which follows:

Opening Address of Professor Oswald Veblen.

In taking the chair today I feel that I am just acting as deputy for my friend, George Birkhoff, whose untimely death has kept him from performing this duty. It was he who could have best welcomed the mathematicians of the world both on behalf of his University and on behalf of the American Mathematical Society.

If this Congress could have been held, as originally planned, in 1940 it would have marked in rather a definite sense the coming of age of mathematics in the United States. At the time of the International Congress in Chicago, in 1893, there was no indigenous mathematical tradition in this country, but there were a few active mathematicians, some of whom were beginning to diverge a bit from the lines laid down, by their European teachers. By the time of the Oslo Congress, which was so admirably conducted by our Norwegian colleagues, a notable growth and transformation had taken place. Important discoveries had been made by American mathematicians. New branches of mathematics were being cultivated and new tendencies in research were showing themselves. Some American universities were receiving students and research workers from overseas, and interchanges of all sorts tended to be more and more on terms of equality. The colonial period was ending. At the same time mathematics had attained a small but growing amount of recognition from the rest of the American community - enough, at least, to encourage us to invite the mathematicians of the world to a congress in this country in 1940.

Now, fourteen years have elapsed since the invitation was issued, and we are approaching the end of another epoch. I mean the period during which North America has absorbed so many powerful mathematicians from all over the world that the indigenous traditions and tendencies of mathematical thought have been radically changed as well as enriched. These American gains have seemed to be at the cost of great losses to European mathematics. But there are so many signs of vitality in Europe that it is now possible to hope that the losses will be only temporary while the American gains will be permanent.

We are holding the Congress in the shadow of another crisis, perhaps even more menacing than that of 1940, but one which at least does allow the attendance of representatives from a large part of the mathematical world. It is true that many of our most valued colleagues have been kept away by political obstacles and that it has taken valiant efforts by the Organising Committee to make it possible for others to come. Nevertheless, we who are gathered here do represent a very large part of the mathematical world. I will also venture the much more hazardous statement that we represent most of the currents of mathematical thought that are discernible in the world today. I hope that this remark will be dissected and, if possible, pulverised in the private conversations that are so valuable a part of any scientific meeting.

I have referred to the political difficulties which have harassed this Congress, but think that if there are to be future international congresses, an even more serious difficulty will be the vast number of people who have a formal, and even an actual, reason for attending. This makes all meetings, even for very specialised purposes, altogether too large and unwieldy to accomplish their purposes.

Mathematics is terribly individual. Any mathematical act, whether of creation or apprehension, takes place in the deepest recesses of the individual mind. Mathematical thoughts must nevertheless be communicated to other individuals and assimilated into the body of general knowledge. Otherwise they can hardly be said to exist. But the ideal communication is to a very few other individuals. By the time it becomes necessary to raise one's voice in a large hall some of the best mathematicians I know are simply horrified and remain silent.

The Organising Committee of the present Congress has tried to meet this problem by means of a series of conferences, more informal than the regular program, but even in the conferences the problem of numbers will remain. It is to be hoped that our colleagues who have been meeting in New York to consider organising an International Mathematical Union will have something to say to us on this and other problems before this Congress adjourns.

The solution will not be to give up international mathematical meetings and organisations altogether, for there is a deep human instinct that brings them about. Every human being feels the need of belonging to some sort of a group of people with whom he has common interests. Otherwise he becomes lonely, irresolute, and ineffective. The more one is a mathematician the more one tends to be unfit or unwilling to play a part in normal social groups. In most cases that I have observed, this is a necessary, though definitely not a sufficient, condition for doing mathematics. But it has made it necessary for mathematicians to group themselves together as mathematicians. The resultant organisations of various kinds have accomplished many important things known to us all. Of these accomplishments I am sure that the most important is the maintenance of a set of standards and traditions which enable us to preserve that coherent and growing something which we call Mathematics.

To our non-mathematical friends we can say that this sort of a meeting, which cuts across all sorts of political, racial, and social differences and focuses on a universal human interest will be an influence for conciliation and peace. But the Congress is, after all, just a meeting of mathematicians. Let us get about our business.

2.3. The Fields Medals.

Immediately after the address by Professor Veblen, Professor Harald Bohr of the University of Copenhagen spoke on behalf of the Committee to award the Fields Medals. At the International Congress at Toronto in 1924 it was decided that at each international mathematical congress two gold medals should be awarded. Professor J C Fields, the Secretary of the 1924 Congress, presented a fund to subsidise these medals. They were first awarded in Oslo in 1936. The Committee to select the winners of the 1950 medals was: Professor Harald Bohr (Chairman), Professors L V Ahlfors, Karol Borsuk, Maurice Fréchet, W V D Hodge, A N Kolmogorov, D Kosambi, and Marston Morse. The medals were awarded to

Professor Laurent Schwartz of the University of Nancy

and to

Professor Atle Selberg of the Institute for Advanced Study.

Professor Bohr gave an excellent résumé of the work of Schwartz on distributions and of the work of Selberg on the Riemann zeta function and his elementary proof of the celebrated prime number theorem. Professor Professor Bohr's address follows:

2.4. Address of Professor Professor Harald Bohr.

At a meeting of the organising committee of the International Congress held in 1924 at Toronto the resolution was adopted that at each international mathematical congress two gold medals should be awarded, and in a memorandum the donor of the fund for the founding of the medals, the late Professor J C Fields, expressed the wish that the awards should be open to the whole world and added that, while the awards should be a recognition of work already done, it was at the same time intended to be an encouragement for further mathematical achievements. The funds for the Fields' medals were finally accepted by the International Congress in Zürich in 1932, and two Fields medals were for the first time awarded at the Congress in Oslo 1936 to Professor Ahlfors and Professor Douglas. And now, after a long period of fourteen years, the mathematicians meet again at an international congress, here in Harvard.

In the fall of 1948 Professor Oswald Veblen, as nominee of the American Mathematical Society for the presidency of the Congress in Harvard, together with the chairman of the organising committee, and with the secretary of the Congress, appointed an international committee to select the two recipients of the Fields medals to be awarded at the Congress in Harvard, the committee consisting of Professors Ahlfors, Borsuk, Fréchet, Hodge, Kolmogorov, Kosambi, Morse, and myself. With the exception of Professor Kolmogorov, whose valuable help we were sorry to miss, all the members of the committee have taken an active part in the discussions. As chairman of the committee I now have the honour to inform the Congress of our decisions and to present the gold medals together with an honorarium of $1,500 to each of the two mathematicians selected by the committee.

The members of the committee were, unanimously, of the opinion that the medals, as on the occasion of the first awards in Oslo, should be given to two really young mathematicians, without exactly specifying, however, the notion of being "young." But even with this principal limitation the task was not an easy one, and it was felt to be very encouraging for the expectations we may entertain of the future development of our science that we had to choose among so many young and very talented mathematicians, each of whom should certainly have been worthy of an official appreciation of his work. Our choice fell on Professor Atle Selberg and Professor Laurent Schwartz, and I feel sure that all members of the Congress will agree with the committee that these two young mathematicians not only are most promising as to their future work but have already given contributions of the uttermost importance and originality to our science; indeed they have already written their names in the history of mathematics of our century.

Before having the honour of presenting the medals to Professor Selberg and Professor Schwartz, I shall try briefly, and in a very general way, to emphasise some of the most important results obtained by the two recipients and those which have especially attracted the admiration of the committee.

Atle Selberg who studied and took his doctor's degree in his native country Norway, with its great mathematical traditions since the days of Abel, some years ago followed a call to the modern centre of mathematics, the Institute for Advanced Study in Princeton. His scientific production is very extensive, his interests centring on the theory of numbers, including the theory of those functions which dominate the analytical theory of numbers. Of great importance is his generalisation of the method of his very original and ingenious countryman Viggo Brun, the Eratosthenes sieve method; I shall not, however, enter into any details of this part of Selberg's work ...

And now I turn to the work of the other, slightly older, of the two recipients, the French mathematician Laurent Schwartz. Having passed through the old celebrated institution École Normale Supérieure in Paris, he is now Professor at the University of Nancy. He belongs to the group of most promising and closely collaborating young French mathematicians who secure for French mathematics in the years to come a position worthy of its illustrious traditions. Like Selberg, Schwartz can look back on an extensive and varied production, but when comparing the work of these two young mathematicians one gets a strong impression of the richness and variety of the mathematical science and of its many different aspects. While Selberg's work dealt with clear cut problems concerning notions which, as the primes, are, so to say, given a priori, one of the greatest merits of Schwartz's work consists on the contrary in his creation of new and most fruitful notions adapted to the general problems the study of which he has undertaken. While these problems themselves are of classical nature, in fact dealing with the very foundation of the old calculus, his way of looking at the problem is intimately connected with the typical modern development of our science with its highly general and often very abstract character. Thus once more we see in Schwartz's work a confirmation of the words of Felix Klein that great progress in our science is often obtained when new methods are applied to old problems. In the short time at my disposal I think I may give the clearest impression of Schwartz's achievements by limiting myself to speak of the very central and most important part of his work, his theory of "distributions." The first publication of his new ideas was given in a paper in the Annales de l'Université de Grenoble, 1948, with the title Généralisation de la notion de fonction, de dérivation, de transformation de Fourier et applications mathématiques et physiques, a paper which certainly will stand as one of the classical mathematical papers of our times. As the title indicates it deals with a generalisation of the very notion of a function better adapted to the process of differentiation than the ordinary classical one. ...

I have the honour to call upon Professor Selberg and Professor Schwartz to present to them the golden medals and the honorarium.

In the name of the committee, I think I dare say of the whole Congress, I congratulate you most heartily on the awards of the Fields medals. Repeating the wish of Fields himself I may finally express the hope that the great admiration of your achievements of which the medals are a token may also mean a encouragement to you in your future work.

2.5. The Congress banquet.

The Congress banquet was held on Tuesday evening, September 5, in the Sever Quadrangle. Professor Marston Morse was the Toastmaster and Dr Detlev Bronk, President of the National Academy of Sciences, gave the principal address. Other speakers were Edward Crane, the Mayor of Cambridge; Dr James R Killian, the President of Massachusetts Institute of Technology; Professor W V D Hodge of Cambridge University; and Professor Percy Bridgeman of Harvard University. Professor Hodge expressed the sincere appreciation of our foreign members of the Congress to their American hosts for their splendid hospitality. Dr Bronk's address follows:

2.6. Address of Dr Detlev Bronk President, National Academy Of Sciences.

Professor Morse, Professor Veblen, and colleagues of the Congress. As a mere biologist, I accepted the invitation to come here this evening with great trepidation; for I was reminded of the first time that I met Lord Rutherford in company with my good friend, E B Hill, who had been a senior wrangler, I believe, at Cambridge. To me, Lord Rutherford said, "It is interesting to find another physicist and mathematician who has ventured into biology." Indeed, when I was cruising in the fogbound waters of Maine during these past few weeks, I had one consolation in the difficulties of navigation. For I felt that could I not escape from my fogbound visitations, I would escape the duties that now confront me. But I regret to say that although I never reached the peaks of mathematical ability, I could do the simple arithmetic of dead reckoning that brought me back in time.

It is my pleasant privilege to bring to you the greetings of the National Academy of Sciences of the United States of America. It is especially appropriate that we your colleagues, who work in other fields of science, do so, for we are keenly conscious of our debt to you for intellectual tools we all require. In these days of increasing specialisation, mathematics is a unifying focus. We recognise in your deliberations which we may not comprehend, the genesis of thoughts and concepts which will increase the acuity of our own investigations. We perceive in this great Congress the furtherance of intellectual powers that will facilitate increased understanding of natural forces without regard of the boundaries of scientific discipline. To you from other nations I bring the cordial welcome of my colleagues. It is a welcome filled with gratitude from the scientists of a youthful nation. At a time when men and women who have come from your several countries were absorbed in pioneers' practical duties on geographic Frontiers, we benefited from the endeavours of your scientific ancestors. Now that our geographical frontiers are passed, we may join with you in exploring the endless frontiers of knowledge. We would thus pay back to you the debt for the basic facts and concepts which enabled us to satisfy our needs in technology in the applications of science. Having benefited thus, we clearly recognise science as a universal heritage of all men and women in all nations. That you have thus gathered with your distant colleagues without regard for race or tongue or nation is reaffirmation of your faith in the international amity of science. To be an isolationist in science is to handicap one's own achievements. The course of new discoveries starts from the territory of established knowledge. The genesis of new ideas is catalysed by the work and thought of others. Recognising this, scientists were among the first to realise the practical dependence of their own work on the efforts of those in distant lands. Together with the trades in rare goods, they have sought intellectual products and new discoveries wherever they were to be found. Out of this desire for the advantages which can be gained from the work of others has come that admirable phrase "my foreign colleague," so frequently heard in scientific circles and so seldom heard in others. It is worthy of emphasis that this desire for international cooperation derives from no unique nobility of spirit but comes rather from the simple realisation of the advantages that derive from a free exchange of ideas. If scientists are better prepared for the acceptance of the principles of world unity, it is because we have long ago realised the benefits that come from such cooperation. The desire for world-wide dissemination of thoughts on science and of scientific discoveries motivated those who shaped the earliest association of scientific workers.

The Academia de Scientia of Rome, first of the academies of sciences, in 1609 laid plans for the establishment of common scientific non-clerical monasteries, not only in Rome, but in the four quarters of the globe. In each house, every observation, every discovery, was to be communicated without delay to the head house and to all the sister houses. A similar purpose was subsequently found in Bacon's proposal for the creation of the House of Solomon wherein there were to be twelve fellows who were to sail into foreign countries and return with the books and abstracts and the patterns of experiments made in other nations. These we call, significantly said Bacon, merchants of might. This international idea was an essential motive in the early activities of the Royal Society of London. That may be judged from the lines of William Glanville, written in 1660, while the Society was forming at Gresham College, that "Gresham College shall hereafter be the whole world's university." This was not an unfulfilled aspiration. Oldenburg, the first secretary of the Royal Society, lists among his duties, "I write all letters abroad and answer received thereto, entertaining correspondence with at least some thirty persons." Because the reading of these communications from foreign scientists became so important a part of the meetings of the Society, one of their fellows got the sum of five hundred pounds for the support of a fellow to carry on a foreign correspondence. Science has facilitated the movements of scientists by means of swift transportation. The exchange of information is speeded by new methods of communication. But two recent wars and the present conflicts of national purpose show how insecure is our privilege to exercise that freedom upon which depends the furtherance of science. As scientists we have a precious stake in the preservation of personal liberties that do not infringe the liberties of others. But our freedom of thought, of opinion, and of debate will be guaranteed only by a social system which guarantees to all such freedoms. In these times when stress, bewilderment, and fear encourage few to gain control of many, we must couple with our scientific efforts vigorous defences of freedom, of undistorted science uncontrolled except by experimental test and reason. These are times that challenge us to double effort. These are times that challenge our loyalty to those ideals that made possible the intellectual adventures of the past which led to scientific progress.

In these times when national conflicts threaten human welfare, the scientist will not forget that the social value of his accomplishments makes him a citizen of all free nations. A new chemical agent, or the treatment of disease, is of potential benefit to all men. The laws of electromagnetic induction, discovered by Faraday, the Englishman, relieve the labours of the citizens of many lands. The observations of Galileo, Copernicus, and Newton have increased the intellectual horizons of no one national group. Scientific research conducted in a spirit of freedom and published without restriction increases the welfare and the resources of all nations. To further scientific investigations is a common responsibility and a common advantage for all countries. As Francis Bacon did foresee, science enlarges the bounds of human empire and the effecting of all things possible from a knowledge of the causes and secret motions of things. Science gives to those who would limit the bounds of human empire awful power over others. Because of this, the progress of science is endangered by others who would use scientists and science to achieve their selfish ends. To do so, they would restrict the free statement of ideas and information. But science cannot flourish if the discoveries and thoughts of scientists are the secret knowledge of the few. Science cannot increase the understanding and improve the welfare of all men unless free access to knowledge is recognised as a fundamental human right. To deserve that right, the peoples of the world must restore regard for truth and for the democratic determination of individual and national action. The spirit of science will not long survive in a world half free to think and speak, to investigate and question, half slave to prejudice and dictation. So long as wars are waged to gain advantage and control, science will be used to implement aggression, and to fortify the defence of freedom. Thus will the proper purpose of scientists be deflected, inquiry to satisfy curiosity and increase understanding will be subordinated. The mere application of scientific facts, freedom for discussion, will be curtailed, and truth will bow to propaganda.

In these days, we as scientists are challenged to adhere to our traditional ideals of intellectual freedom, to align ourselves with those who would guarantee the freedom of peoples everywhere. Great though our temporary sacrifice may be, our future right to inquiry demands it. The use of modern science gives a nation tremendous power and material advantage. Since science is developed more in some than in other countries, there will be a further imbalance in the intellectual and material welfare of different peoples. There lies a grave threat to peace and wholesome progress. This accents the responsibility of the scientists of more favoured nations to share their knowledge and their methods with all people, and especially with those who are victims of poverty and disease and ignorance. For scientists have an important role in shaping world cultures suitable for these times.

In these days of international tension, American scientists like to recall that one of our greatest statesmen was also one of our first and greatest scientists. Benjamin Franklin was fitted for his tasks in foreign capitals by many qualifications; but not the least of these was his eminence as a man of science. Because of this, we know that he was heard as one who contributed to the welfare of all peoples while seeking as a patriot to improve the material and political circumstances of his own countrymen. Of especial importance was the fact that he carried through his tasks an instinct for internationalism, which had been developed through his scientific career. It is not unreasonable to assume that this gave him a tolerance and a breadth of outlook that favoured the course for which he pled and gave it reasonableness.

It was this quality which prompted him in March of 1779 to address to all captains and commanders of armed ships, acting by permission from the Congress of the United States of America, then at war with Great Britain, this directive: "Gentlemen, A ship having been fitted out from England before the commencement of this war to make discoveries in unknown seas, within the conduct of that most celebrated discoverer and navigator Captain Cook, which is an undertaking laudable in itself as the increase in geographical knowledge facilitates the communication between distant nations, and sciences of other kinds are increased which have benefit for mankind in general; this, then, is to recommend to you that in case the said ship should fall into your hands, you should not consider her as an enemy, nor permit any plunder of her effects, nor obstruct her return to England." Would that we had more statesmen that possessed this attitude toward the international values of science. Would that we had more scientists who would participate in the international affairs of nations. As you bring to a close your distinguished Congress, I would, on behalf of the Academy I represent, express our gratitude for your visit to our country and to our colleagues, and to pledge anew our devotion to the fraternity of free scholars.

3. Closing Ceremonies.
On Wednesday evening, 6 September, the mathematicians were the guests of the Director and Board of Trustees of Gardner Museum at a farewell party.

On Wednesday morning, September 6, there was held a final plenary session of the Congress in Sanders Theatre. Professor M H Stone gave a report on the conference which had been held in New York City immediately preceding the International Congress for the purpose of considering the formation of an International Mathematical Union, He reported that Statutes and By-Laws had been adopted and that these would be submitted to the proper scientific groups in the various national or geographic areas in which there was significant mathematical activity. When a specified number of groups have signified their acceptance of these Statutes and By-Laws, the Union will be declared in existence and a meeting of the General Assembly arranged.

3.1. Invitation to ICM 1954.

Professor van der Corput, on behalf of the delegation from the Netherlands, presented a cordial invitation to the International Congress to hold its next meeting in the Netherlands in 1954. The Congress unanimously voted to accept the gracious invitation of our Dutch colleagues. After addresses, there was an address of appreciation by President Harald Cramér of the University of Stockholm. After Professor A A Albert had presented a resolution of thanks to Harvard University and to the various committees of the Congress, which resolution was unanimously adopted, the Congress adjourned.

The Congress was undoubtedly the largest gathering of persons ever assembled in the history of the world for the discussion of mathematical research. However, the real measure of its success lies not in the large number of persons present, but in the excellence of its scientific program and in the contributions which it made to the cause of closer cooperation among scientists and to the cause of international good will.

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