The Congress at Zürich.

A not unnatural consequence of my having complied with a request to act as a Delegate of the Mathematical Association at the International Congress of Mathematicians, which was held at Zurich during the week September 4-12, is that I have been asked to write a short account of the Congress for the Gazette. It is a little difficult to avoid giving merely an epitome of the official programme; and my difficulties are somewhat increased by my having, like many others, deliberately abstained from attending the Congresses at Strasbourg and Toronto in 1920 and 1924, for reasons which are now, happily, a matter of past history, and by my having been unavoidably prevented from going to Bologna in 1928; in fact my only previous experience of a Congress was gained at Cambridge in 1912.

A rough count of the official list gave the number of members of the Congress as about 680 (though a few of these were not present), and they were accompanied by about 180 members of their families; so far as I could ascertain, not more than about 150 out of the 680 were Swiss. The corresponding figures for the Congress at Bologna were 836 members, accompanied by 280 members of their families; and 336 out of the 836 were Italians. In view of the economic circumstances, it is a little remarkable that the number of foreign mathematicians at Zurich should exceed the number at Bologna, though one can see that there was a tendency for people to economise at the expense of their families.

This is the first occasion on which the Congress has paid a return visit, the first Congress having been held at Zurich in 1897; there were then 204 members accompanied by 38 ladies, and about seventeen of the members of the first Congress, including the President of the first Congress, Prof Geiser, also attended the Congress in 1932.

A substantial change in procedure has been made since 1928; it has been decided not to print all communications in full, but to issue two comparatively small volumes of Proceedings only; the first will contain the records of the meetings and the formal lectures, while the second will contain abstracts (limited to about 300 words) of other communications. While this change may be partly due to financial considerations, it certainly seems desirable for the reason that, for ease of reference, mathematicians ought to be encouraged to publish their most important work in standard periodicals which are to be found in all important libraries rather than in Proceedings of Congresses which are apt to become exceedingly scarce. It may be a relief to some mathematicians to realise that they are not receive anything resembling the six substantial volumes which followed the Congress at Bologna.

The Congress opened with an informal reception at the Studentenheim on the Sunday evening, and more formally with addresses of welcome by the President of the Organising Committee, Prof Fueter, and by representatives of the Canton on Monday morning. The mornings throughout the week were devoted to formal lectures in the Technische Hochschule, the lecturers being Fueter (Theory of Ideals), Caratheodory (Functions of several complex variables), Julia (Development of the theory of functions of a complex variable), Pauli (Mathematical methods of Quantum Mechanics), Tschebotarow (Galois Theory), Carleman (Linear integral equations), Cartan (Riemannian spaces), Bieberbach (Fundamental regions in the theory of functions), Morse (Calculus of variations), Noether (Hypercomplex systems), Bohr (Almost periodic functions), Severi (Functions of several variables and Algebraic Geometry), R Nevanlinna (Riemann Surfaces), Wavre (Planetary figures), Alexander (Topology), F Riesz (Derivates of functions of a real variable), Valiron (The Borel-Julia theorem on meromorphic functions), Sierpinski (Sets of points which are effectively definable), Bernstein (Aleatory quantities), Menger (Modern methods and problems in Geometry), Stenzel (Modes of thought in Greek Mathematics); a lecture by Hardy on Additive Theory of Numbers was announced, but was not given.

Four afternoons were occupied at the University by the meetings of the Sections, of which there were ten (1, Algebra and Theory of Numbers; 2, Analysis; 3, Geometry; 4, Probability; 5, Mechanics and Physics; 6, Astronomy; 7, Engineering; 8, Logic and Philosophy; 9, History; 10, Pedagogy); Sections 2, 3 and 6 were further subdivided. At these meetings, communications were limited to 15 minutes, and the number of papers read in all the Sections was nearly 200. Among the English mathematicians who read papers were Hardy, Linfoot, Milne-Thomson, Mordell, Neville, Paley, Winn, and Miss Cartwright. Section 2 was the most popular with about 60 papers, while Sections 3 and 5 had over thirty each, Section 1 about twenty, Sections 4 and 8 had about a dozen each, and Section 6 about eight. Sections 7 and 10 were apparently represented by one paper each, and I did not discover Section 9. I got the impression that the Committee transferred papers from Section 2 to Section 1 whenever practicable in order to avoid a still greater preponderance of papers in Section 2; at any rate, rather to my surprise, I found on most afternoons that I would feel rather more at home in Section 1 than in any of the subdivisions of Section 2.

The Congress inevitably suffered from two disadvantages; limitations of time usually made it necessary for two lectures to be given simultaneously in the mornings (though the actual selection of simultaneous lectures had evidently been carefully arranged by the Committee so as to cause as little inconvenience as possible), and, of course, there were usually at least half a dozen Sectional meetings taking place simultaneously in the afternoons. The other disadvantage was that due to the confusion of tongues; a fair number of the speakers bore in mind the fact that a large proportion of their audience was listening to a foreign language and took care to speak as clearly as possible (for example, I was able to follow the lectures of Caratheodory and Julia almost as well as if they had been speaking in English), but others, I am sure, were comprehensible only to their own countrymen.

The atmosphere of the Sectional meetings (as opposed to the formal Lectures) tended to be a little frigid; discussion was invited on each paper, but often nobody said anything, and then the Chairman usually called on the author of the next paper; at one meeting which I attended, however, Hahn, who was in the Chair, made a short commendatory speech after each paper, and the audience's appreciation of his action seemed to me to be an ample justification of the trouble which he must have taken in discovering something appropriate to say on each paper.

Enough has now been said concerning what took place inside the lecture rooms, and I now turn to the pleasanter side of the week. On Tuesday afternoon the official delegates were all invited to tea by Herr von Schulthess-Bodmer and his wife at their estate on the island (or rather peninsula) of Au, about a dozen miles from Zurich across the lake; some of the party stayed on the peninsula rather longer than they had originally intended. Thursday was devoted to excursions, of which four were arranged, a drive to the Klausen Pass, the ascents of Pilatus and the Rigi, and a steamboat trip across Lake Lucerne from Flüelen (at the foot of the ascent to the St Gotthard tunnel) to Lucerne. On Monday there was a concert at the Tonhalle (I did not attend it, since, like the late Master of Christ's, I am "immune to music").

On Saturday there was a social gathering at the Municipal Theatre; we were there entertained by speeches by members of the Federal Council; these were followed by a ballet, an informal dinner and a dance; in connection with the dinner we were each presented with a book of coupons (presumably for the committee to be able to check the amounts consumed with the amounts supplied with the caterers), and the effect of seeing in this book possibilities of all the things which we might have was really overwhelming. A very eminent mathematician (I hold him in too much respect to mention his name) told me that this was one of the few books of which he had read every word from cover to cover, his wonder increasing with every page that he turned. Coupons 1-4 each provided a course; 5, 8, 11, 12, 15 and 17-19 were merely advertisements of the various caterers (but they all added to the effect); 6 and 7 each produced a half-bottle of wine; 9 and 10 respectively told one that coffee and beer could be obtained ad lib. (a slight snag here was that the programme stated that those who wanted beer were requested to go to the Cellar-Restaurant for it); 13, 14, and 16 provided respectively a liqueur, fruit or cheese, and pastry.

Finally it was requested that we should not dance except on the stage. While on the subject of food, I might mention that many of us made our first acquaintance with the American cafeteria system at lunch at the Studentenheim, and some of us, when confronted with the necessity of getting a whole meal on to a tray, made hopelessly bad shots as to the amounts that we would require, some in excess, others in defect.

For most of us the Congress ended on the Sunday afternoon when we were entertained to tea at the Hotel Dolder by representatives of the city of Zürich; there was, however, a party which visited the Observatory on the Jungfraujoch on the Monday and Tuesday.

It is understood that the next Congress, in 1936, will be held at Oslo, the first visit to a Scandinavian country; there are probably many of us who have already decided to go there to renew the friendships which were made at Zürich and which will have to be kept up by correspondence in the meantime.

I cannot conclude without expressing my appreciation of the excellence of the organisation of the Congress and the hospitality of our hosts; in particular, English members of the Congress have special cause to be grateful to Dr Gut who, whenever advice or information was wanted, seemed certain to be found in the Reception Room, ready to resolve one's difficulties in a moment.