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The International Congresses of Mathematicians - politics and mathematics Edmund F Robertson University of St Andrews, Scotland Abstract The International Congresses of Mathematicians began in 1897 and, except for breaks during the two World Wars, has continued to be held regularly ever since. In this lecture I want to look more at the politics behind the organising of the International Congresses of Mathematicians than at the mathematical lectures at these congresses. 1. The lead-up to the Congresses The first International Congress took place in 1897 but before we look at this we will look briefly at the events leading up to this Congress. There were two influential people whose efforts were vital in promoting the idea of international mathematical conferences, namely Felix Klein and Georg Cantor. The first step might be considered to be the founding of the German Mathematical Society in 1890. Alfred Clebsch advocated the founding of such a mathematical society and also a mathematics journal in 1867. He died in 1872 and his role as the leading advocate of a German mathematical society was taken up by Klein, who had been Clebsch's student. However, it was not until Georg Cantor made a strong push for the founding of the Society that eventually the idea turned into reality. Both Klein and Cantor strongly believed in international collaboration in mathematics. Their aims were the same but both were motivated by different personal reasons. Cantor felt his close colleagues were making unfair criticism of his work so he wanted a broader platform to promote his ideas. Klein had strong ideas about teaching mathematics and mathematical research and was a great organiser who wanted to see his ideas placed on a broader stage. The next significant event was the International Mathematical Congress held in conjunction with the World's Columbian Exposition in Chicago in 1893. The University of Chicago had been founded in 1892 and the new Faculty of Mathematics organised an International Mathematical Congress, as part of the World's Columbian Exposition in Chicago, to be held from 21 August to 26 August 1893. Two of the four organisers of this Congress were Germans on the Chicago faculty, Oskar Bolza and Heinrich Maschke. Both had been closely associated with Felix Klein in Germany before going to the United States so it was natural for them to invite Felix Klein to be a main speaker at this Congress. If you look at the papers published in the Proceedings of this 1893 Congress, it appears to have been attended by many leading European mathematicians. This, however, was not the case for only 4 of the 45 participants were not from the United States. Klein brought papers from German, French, Austrian, Italian and Swiss mathematicians for publication in the Proceedings. Klein gave the Opening Address entitled "The Present State of Mathematics." It ends with the following "manifesto" for future international cooperation by mathematicians [2]: A distinction between the present and the earlier period lies evidently in this: that what was formerly begun by a single master-mind, we now must seek to accomplish by united efforts and cooperation. A movement in this direction was started in France some time since by the powerful influence of Poincaré. For similar purposes we three years ago founded in Germany a mathematical society, and I greet the young society in New York and its 'Bulletin' as being in harmony with our aspirations. But our mathematicians must go further still. They must form international unions, and I trust that this present World's Congress in Chicago will be a step in that direction. 2. The 1897 Congress in Zurich Georg Cantor was one of the first to press for international mathematical conferences. In 1888 he proposed a meeting between German and French mathematicians and later, between 1894 and 1896, he contacted several leading mathematicians proposing an international conference. He had support from Felix Klein, Heinrich Weber, Emile Lemoine and others. Cantor proposed that a trial conference be held in 1897, either in Switzerland or Belgium. The choice of countries was, of course, politically motivated. He realised that neutral options were necessary to get both French and German mathematicians to attend. He suggested that the first actual conference be in Paris in 1900. Again this was a political suggestion in that a German proposing a congress in France was most likely to be accepted by both Germans and French. It quickly became clear that of the two options, Switzerland or Belgium, Switzerland was favoured because of its international reputation. The German Mathematical Society and the French Mathematical Society approved these ideas and agreed to contact Karl Geiser in Zurich. The 1897 congress proved so successful that, rather than considering it a trial congress, it became the first International Congress of Mathematicians. Now if Cantor and Klein were the most influential in advocating international congresses, the two people who have been most influential in setting the shape of the whole series of congresses were Karl Geiser and Ferdinand Rudio. Geiser was the Professor of Mathematics at the Polytechnic in Zurich and addressed his colleagues with the following note [1]: As you will know, it has already been suggested several times to unite the mathematicians of different countries at an international congress, which would have to be repeated at appropriate intervals. Recently, it has been proposed specifically (notably by Messrs Weber in Strasbourg and Klein in Göttingen) that a first such meeting should be held in Zurich in 1897. The executive committees of the German Mathematical Society and the Société mathématique de France approved this project and the presidents of the aforementioned societies contacted me to that effect. The chairman of the organising committee was Karl Geiser, who was elected president of the Congress, and Ferdinand Rudio was one of the two secretaries. The Congress was attended by 208 full members and 38 associate members. Although it was truly international, most of the participants were from Switzerland (60), Germany (41), France (23), Italy (20) and Austro-Hungary (17). Only three of those attending were British, E W Hobson, Joseph Larmor, and John S Mackay. The importance of Rudio's contribution is often overlooked. He presented On the tasks and the organization of international mathematical congresses which set out the aims and structures of future congresses. In many aspects, the 21st century congresses are still influenced by these ideas. For example, Article 1 [1]: The congress has the purpose of furthering the personal relations between the mathematicians of various countries. The congress has the purpose of providing, in the talks of the main assemblies and of the section sessions, an overview of the current state of the various fields of mathematical sciences and their applications, as well as the treatment of individual problems of particular importance. 3. The 1900 Congress in Paris In many ways it was David Hilbert's lecture on the future problems of mathematics which became the most famous lecture delivered at any International Congress of Mathematicians. It is sometimes described as a plenary lecture and sometimes it is not; we explain why there is a confusion. Hilbert was invited to give a plenary lecture at the 1900 Congress. He couldn't decide on a topic and discussed what he should talk on with Hermann Minkowski and Adolf Hurwitz. Eventually he decided to discuss outstanding mathematical problems but took a long time to write his lecture. The programme for the 1900 Congress was published before he had things ready and so his talk was not advertised as a plenary lecture. It was delivered at the Congress in a joint session of the Teaching Section and of the History Section. By the time the Proceedings of the conference appeared the organisers decided that, because of its importance, they would put Hilbert's paper in the section with the plenary lectures. Another point worth making is that, because of lack of time, Hilbert only spoke about 10 of his 23 problems in the lecture although all 23 appear in the published paper. Most of this Congress was in French, but there was a discussion about the problem of mathematics being published in such a diverse number of languages. In some ways this Congress fell short of expectations. Attendance was up on Zurich with 250 mathematicians attending and the international aspect increased with more countries represented. It is reported [1]: The Universal Exhibition, which took place in Paris, was so attractive in itself that it would have been difficult to organize successfully for members of Congress special excursions, as had been done in Zurich. The Organizing Committee thought it preferable to leave the delegates complete freedom, and had to confine itself to a few meetings, apart from the sessions proper. Charlotte Scott reported on the Congress to the American Mathematical Society and she was highly critical of certain aspects [3]: One thing very forcibly impressed on the listener is that the presentation of papers is usually shockingly bad. Presumably the reader desires to be heard and understood; to compass these ends, instead of speaking to the audience, he reads his paper to himself in a monotone that is sometimes hurried, sometimes hesitating, and frequently bored. He does not even take pains to pronounce his own language clearly, but slurs or exaggerates its characteristics, so that he is often both tedious and incomprehensible. These failings are not confined to any one nationality; on the whole the Italians, with their clear and spirited enunciation, come nearest to being free from them. She also criticised the organisation [3]: The arrangements excited a good deal of criticism. The committee of organization had doubtless special difficulties to contend with, as M Laisant, to whom the secretarial part had been assigned, was unable to undertake it owing to the pressure of other duties.
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