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Home , Felix Klein, John Charles Fields, Joseph Larmor, Oskar Bolza

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 and . The first step might be considered to be the founding of the German Mathematical Society in 1890. 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 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, and Heinrich Maschke. Both had been closely associated with Felix Klein in before going to the 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 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, , 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 '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 . 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 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 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. The mistake was then made of entrusting a part of this responsibility to the firm of Carré and Naud, whereas in such a case personal interest and individual responsibility are indispensable for ensuring proper attention to the various details of organization.

4. The 1904 Congress in Heidelberg

The 1904 Congress was held in Heidelberg and the German Mathematical Society decided to link the Congress to the celebration of the centenary of the birth of Carl Jacobi. Leo Königsberger was asked to give the first lecture on Jacobi's biography and this was printed and given as a gift to all the participants at the Congress. Königsberger also wrote a scientific biography of Jacobi which was available for the participants to purchase at 1/3 of the full price. Another interesting feature of the Congress was a lecture by Julius König in which he 'proved' that Cantor's Continuum Hypothesis was false. Cantor himself attended this lecture and said at the end how grateful he was to have lived to see this answered, even if it did show his conjecture was false. The 'proof' was, however, wrong and some time later Ernst Zermelo found the error in it. The Congress was well organised but, although were up with 336 mathematicians, it was less international with fewer countries represented. There was some confusion over the venue of the next Congress, with the English believing that it would take place in Cambridge but an invitation from the Italians for it to be in Rome was accepted. It became clear that no proper mechanism existed for choosing the next venue.

5. The 1908 Congress in Rome

Perhaps the greatest change in the 1908 Congress from the previous three was the much greater emphasis on applied mathematics. Another innovation at this Congress was the award of an international mathematical prize, the Guccia Medal. This had been announced in 1904 and was awarded at this Congress to Francesco Severi. It has never been awarded at any subsequent Congress. This Congress marks the first attempt to establish an International Mathematical Union which would oversee the congresses but the following 1912 Congress reported failure to achieve this. Also at this Congress, an International Commission on the Teaching of Mathematics was set up and was required to report at the next Congress. This would be highly successful, perhaps due to Henri Fehr who has the remarkable record of attending every International Congress of Mathematicians from this first in 1897 until the 1950 Congress.

Numbers were up considerably with 535 mathematicians attending this successful Congress. The publishing of the Proceedings, however, proved problematic. The Mathematical Typography of Palermo had agreed to print the Proceedings but the printers of Sicily went on strike which presented the organisers with great difficulty. Eventually it was printed by the Typography of Lincea. One sad note here is that Laura Pisati should have been the first woman to deliver a lecture at the International Congresses. She was due to speak in Rome but died eight days before the Congress.

6. The 1912 Congress in Cambridge, England

At the Cambridge, England, Congress as at the previous Congress in Rome, there was a strong emphasis on applications. Four of the eight plenary lectures were on applications of mathematics. The Regulations for the Congress were published in English, French, German and Italian. Indeed, of the four pure mathematics lectures, one was in each of these four languages. The report of the International Commission on the Teaching of Mathematics showed remarkable achievements despite the difficult political situation which would lead to World War I two years after this Congress. The 1916 Congress was awarded to Stockholm and invitations for 1920 in Budapest and 1924 in Athens were made but, in with the regulations, only the 1916 Congress was definite. The outbreak of World War I in 1914 meant these all fell by the wayside.

Sir , President of the Congress, reported on failure to agree on setting up an International Association of Mathematicians [1]:

It was proposed at Rome that a constitution should be formed for an International Association of Mathematicians. I have not heard that any proposal will be made tonight and I do not hesitate to express my own opinion that our existing arrangements for periodical Congresses meet the requirements of the case better than would a permanent organisation of the kind suggested.

The political tensions which would lead in two years to the outbreak of war, were too strong for the mathematicians to agree on this international cooperation. 7. The 1920 Congress in Strasbourg

Although the 1920 International Congress of Mathematicians was called 'International', it was a limited definition of International. Mathematicians from Germany, Austro-Hungary, Bulgaria and Turkey were excluded. This decision, based on the countries 'blamed' for World War I being excluded, was supported by most people but we must say that it was strongly opposed by a small number, most notably G H Hardy and G Mittag-Leffler neither of whom attended. The International Research Council had been founded in Brussels in 1919 and it had decided that the next Congress would be held in Strasbourg and not Stockholm as had been proposed in 1912. This was a highly political decision made to 'celebrate' France regaining Strasbourg from Germany. Strasbourg had been French until the French were defeated in the 1870 Franco-Prussian war. There was a strong nationalistic thread running though the Congress. Mittag-Leffler got the Congress to agree that the Sixth International Congress of Mathematicians was to take place in Stockholm and the Congress in Strasbourg should be the International Congress of Mathematics and not in the agreed series of International Congresses of Mathematicians. The Congress, however, reneged on this agreement and the Proceedings was given the title 'International Congress of Mathematicians'. The concession to Mittag-Leffler was in not using the "Sixth" in the title.

At this Congress a General Assembly of the International Mathematical Union was held. It decided that all countries except Germany, Austria, Hungary and Bulgaria would be invited to join. It was decided to link the International Mathematical Union to the International Congresses of Mathematicians, giving the Union the power to determine the place and date of each International Congress of Mathematicians. Only those from countries which were members of the International Research Council could attend the Congresses.

Numbers were down with only 200 mathematicians attending. The Congress ended by accepting an invitation to hold the 1924 Congress in the United States of America.

8. The 1924 Congress in

The 1920 Congress ended by accepting an invitation to hold the 1924 Congress in the United States of America. This invitation, made by the American mathematicians at the 1920 Congress was made without the approval of the American Mathematical Society. When it was realised by the American Mathematical Society that mathematicians from Germany, Austro-Hungary, Bulgaria and Turkey were to be excluded in 1924, as they were in 1920, they refused to give the Congress financial backing. This attitude by the Americans was very understandable since for many years they had modelled their mathematical research on the German model, had many of their graduates study for doctorates in Germany, and had a number of prominent German mathematicians in leading positions in America. The International Research Council refused to end their exclusion policy so saved the day by inviting the 1924 Congress to Toronto. Some mathematicians, such as G H Hardy, boycotted the Congress because of the exclusion of 'ex-enemy' countries. Applications of mathematics were even more strongly in evidence with only two Sections on pure mathematics topics and five on applications. Numbers were markedly up with 444 mathematicians, with 300 from the United States and Canada.

9. The 1928 Congress in Bologna

Politics played a larger role in organising this Congress than any other. In fact, had it not been for the incredible political skills of Salvatore Pincherle there would have been no 1928 Bologna Congress. Pincherle had been elected President of the International Mathematical Union at the 1924 Congress so his position was even more complicated. The main difficulty with this Congress was the problem over the exclusion of 'ex-enemy' countries. The Organising Committee was put in an almost impossible position and did a remarkable job walking a tightrope between those wanting to continue the exclusions and those desperate to make it truly international again. The Organising Committee set out in detail the extraordinary difficulties it faced and in the end the invitations were issued by the University of Bologna. Notice that on the title page of the Proceedings appears (VI). This Congress considered itself the Sixth International Congress of Mathematicians, meaning that it did not regard the 1920 and 1924 congresses to be International Congresses because they were not open to all. Up to 1916 the Congresses had been numbered 1st, 2nd, 3rd, 4th, 5th. The Proceedings of 1920 and 1924 have no number, 1928 has (VI), and no later Congress numbers itself to avoid the difficulty.

Some Germans were delighted to be allowed to attend. Hilbert attended and addressed the Congress [1]:

It makes me very happy that after a long, hard time all the mathematicians of the world are represented here. That is as it should be and as it must be for the prosperity of our beloved science. ... Mathematics knows no races. ... For mathematics, the whole cultural world is a single country.

Not all Germans agreed, however, and led the opposition calling on German mathematicians to boycott the Congress. Bieberbach did not attend. The International Mathematical Union and the International Research Council declared the Bologna Congress illegal. Mathematicians of the world let their feelings be known by attending in large numbers, 836 mathematicians from 36 countries attended. Pincherle felt he had to resign from the office of President of the International Mathematical Union, despite the members passing the [1]:

The members of the International Mathematical Union are very grateful to Professor S Pincherle for what he has done for the success of the Bologna Congress, and they approve entirely.

The Fascist government of Italy gave the Congress strong financial support looking to impress the international visitors with their political system.

10. The 1932 Congress in Zurich

This Congress put the political difficulties of the 1928 Congress behind it. Ludwig Bieberbach had opposed German participation in the 1928 Congress but was a plenary speaker in the 1932 Congress. Hermann Weyl, in a speech, noted that this was an "extraordinarily improbable event" being the nth International Congress of Mathematicians where 7 ≤ n ≤ 9. This Congress returned to Zurich, the site of the first Congress, and much was made of this in 1932. The main difficulty facing the organisers of this Congress was the world-wide financial crisis following the depression of 1929. Obtaining finance in these difficult times must have been extraordinarily hard. It shows how determined were the organisers and also the participants to make it a success despite these difficulties. It had the second largest number of participants of any of the Congresses up to that time. There were 22 planned plenary lectures but, for some reason which seems a complete mystery, G H Hardy did not deliver his despite being at the Congress. John Charles Fields died a month before the Congress, but it was reported that he had offered to finance the Fields Medals. A Committee was set up to make the first awards in 1936.

The International Mathematical Union, because of its opposition to the 1928 Congress, was highly criticised by most mathematicians and, although it met in Zurich, this is not reported in the Proceedings. The General Assembly of the International Mathematical Union voted to suspend the Union and set up a Commission, chaired by Francesco Severi with Gaston Julia as vice-chairman, to discuss re-establishing it. Julia reported to the International Congress of Mathematicians at Oslo in 1936 that the recommendation was that the Union should not be re-established.

11. The 1936 Congress in Oslo

This Congress is perhaps most famous for being the first at which Fields Medals were presented. This would become an important feature of all futures Congresses. There is a small mystery regarding the award of the to Jesse Douglas. The report in the Proceedings states [1]:

Élie Cartan thanked the President of the Oslo Congress, Carl Stormer, for having kindly let him have the honour of presenting the first two Fields medals to the two winners. He regretted that Jesse Douglas was tired and could not come to receive himself the medal intended for him. He presented two medals to Lars Ahlfors and to Norbert Wiener replacing Jesse Douglas.

We know that Jesse Douglas was at the Congress and we must assume that, like Lars Ahlfors, he was told only hours before the ceremony that he was to receive one of the first two Fields medals ever awarded. I have never seen any explanation as to why he didn't receive the Medal in person; certainly being tired seemed a feeble excuse.

The political situation at this time was very worrying for many and this resulted in a comparatively low attendance of 487 mathematicians. The Italian government did not allow Italians to attend in protest at the sanctions Norway had imposed on Italy following their invasion of Ethiopia. No mathematicians from the Soviet Union attended; clearly a government decision. Notice that the number of plenary lectures at this Congress was 19, each of 45 minutes. This was a slight decrease from the previous Congress. An invitation for the 1940 Congress to be held in the United States was fully supported by the American Mathematical Society, unlike the invitation which had been given in 1920 for the holding the 1924 Congress in the United States.

12. Congresses after World War II

The first Congress after World War II was held in Cambridge, Massachusetts. This followed the pre-war arrangements when at the 1936 Congress the invitation to host the 1940 Congress in the United States had been accepted. Note that this followed quite a different pattern than that following World War I which had caused so many arguments. The Congress was attended by 1686 full members and 616 associate members. Rather surprisingly, the organisers decided to call the 1893 Chicago Congress, an International Congress of Mathematicians, which it certainly wasn't. The Proceedings states [1]:

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.

The American Mathematical Society insisted that they would not organise a Congress until it could be a genuinely international meeting open to everyone [1]:

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.

Although all were invited, no mathematicians from the Soviet Union, Hungary, Czechoslovakia, Poland or Romania attended, prevented by their governments.

Much of the groundwork was done to re-establish the International Mathematical Union during the International Congress of Mathematicians in 1950 in Cambridge, Massachusetts. The International Mathematical Union was formally re-founded in 1951 and the first General Assembly of the new International Mathematical Union was held in 1952. This did not mean that the decision of where to hold the Congresses was always simple. At the 1958 Congress in Edinburgh, the President W V D Hodge, said in his closing speech [1]:

As those who were present at the International Congress in Amsterdam [1954] will remember, a committee consisting of representatives of the International Mathematical Union and of the organisers of the 1958 [Edinburgh] Congress was appointed to consider the location of the Congress of 1962. This committee consisted of Professors Hopf, Chandrasekharan and Mac Lane representing the Union, and Dr Smithies and myself representing this Congress. The committee has discussed with the representatives of a number of countries the possibilities of holding the next Congress in a number of places. I am authorised by the committee to say that while for reasons of a technical nature it is not possible to make any announcement today of the name of the host country for 1962, the prospects of holding a Congress in that year amount to a certainty.

In fact the 1962 Congress was held in Stockholm, honouring the decision to hold the 1916 Congress there. This came about because the committee set up to decide on the venue had several different offers and could not decide which to choose. They decided to approach the Swedish mathematicians at the 1958 Congress, who had not offered to host the 1962 meeting. Unable to accept without consulting back in Sweden and seeing that the financial support would be available, they were unable to give an answer. It was only some time after the 1958 Congress that the venue of Stockholm for 1962 was announced. The number of mathematicians attending the Stockholm Congress was 2107, the first time 2000 was exceeded.

Politics continued to play a part in many later Congresses but we will not look at these later Congresses in this article since we can think of these as being in the "modern" era.

References

1. ICM Proceedings 1893-2018, ICM Proceedings, International Mathematical Union (2020). https://www.mathunion.org/icm/proceedings

2. Felix Klein, The Present State of Mathematics, The Monist 4 (1) (1893), 1-4.

3. Charlotte Angas Scott, The International Congress of Mathematicians in Paris, Bull. Amer. Math. Soc. 7 (2) (1900), 57-79.