Mathematics Olympiad?

Tokyo 2020, Rio de Janeiro 2016, London 2012, Beijing 2008, Athens 2004, Sydney 2000… You don’t need to be a sports expert to know the list of the latest Summer Olympic Games (OG). On the other hand, it may be more difficult for you to define the following list: Rio de Janeiro 2018, Seoul 2014, Hyderabad 2010, Madrid 2006, Beijing 2002… This is a list of the latest International Mathematical Congresses (or ICM in its modern English acronym), by far the greatest manifestation of the world mathematical community. Combining JO and ICM may seem bold, as athletic competition and mathematical collaboration seem to be very different human activities.

But it is clear that there are common features between them. First, there is the periodicity: these two events occur every 4 years, floating from city to city, from country to country, but encountering chronic difficulties when passing through developing countries. These two events then undergo the same interruptions (world wars) and similar movements: it is not uncommon for a country to take turns hosting the Olympics and the ICM (think of Brazil with the 2016 Olympics and the 2018 ICM, for example). or China with the 2002 Olympics and the 2008 ICM). Finally, another match appears when we look at the beginning of the list; two events were created simultaneously: 1896 in Athens for the establishment of the Olympic Games of the modern era, 1897 in Zurich for the first congress of mathematicians. This is not very surprising to historians of the late nineteenth century.e century, because this idea of ​​international meetings is part of the concerns of the times.

However, looking more closely, we notice a curious difference: mathematicians do not number congresses; if the Tokyo Olympics are officially the XXXII Gamese The Olympics, the 2018 congress in Rio de Janeiro, the last one scheduled, has no number. When I say maths don’t count, I’m making an inaccuracy: maths don’t count anymore. According to the official page, where you can find the acts of various congresses, the congress in Zurich in 1897 Erster Internationaler Mathematiker-KongressParisian in 1900 Second International Mathematical Congress, Heidelberg in 1904 Dritter Internationaler Mathematiker-Kongressthat in Rome 1908 IV International Congress of Mathematicians…and so on until the interruption due to the First World War. When the congresses returned to Strasbourg in 1920, the congresses no longer had numbers. In the eyes of the interested public, it is difficult to explain this change as a fear of numbers, and the fact becomes intriguing!

On this occasion, the German mathematician Hermann Weyl (1885-1955) allowed himself a certain amount of humor in his speech at the opening of the Zurich Congress in 1932: “Today we are witnessing an unlikely event. For the number n corresponding to the just opened International Congress of Mathematicians, the inequality 7 ≤ n ≤ 9 is satisfied; Unfortunately, our axiomatic foundations do not allow us to give more precise information. » The joke doesn’t shed much light on the reasons for this numbering problem, because it doesn’t specify what is behind Weil’s expression “axiomatic reasons”. To see this more clearly, we must return to the immediate post-war period and its specific geopolitics: in 1919, the United States, France, Great Britain and their allies decided to establishInternational Research Council, an organization whose purpose is to manage international scientific communications through organizations dedicated to each discipline. Unfortunately, this pious desire of the organization was done to the detriment of the vanquished, namely the Central Empires: Germany, Austria-Hungary, Bulgaria, the Ottoman Empire … Thus, the Mathematical Congresses in Strasbourg (the symbolic choice of the Congress of 1920, a city that recently became again French) and Toronto (1924) were held without the participation of Germany and its allies. This unfair measure of exclusion deprives the scientists of these countries of any exchange. An utterly absurd political and symbolic punishment that makes part of the mathematical community not consider these “truncated” congresses to be genuine congresses. We better understand the ambiguity of 1932: which congresses count on the list? Should we restart the countdown from the 1912 Cambridge Congress, or agree to count the shameful conventions? An intermediate solution is preferred: it is better not to decide and stop counting!

In truth, there would be another, even simpler reason for not numbering exits: we forgot one! On the website of the International Mathematical Union, you can get acquainted with the “congress materials” (https://www.mathunion.org/icm/proceedings), heavy books (for 2018, 4 volumes with a total volume of almost 5000 pages). !), which contains both documents about the life of the congress (schedule, list of participants, speeches, etc.), and the texts of the speeches that took place at it. When we reach the end of the chronological list, we find a meeting that corresponds to a meeting of mathematicians that took place in Chicago on the outskirts of World Columbian Exposition 1893 with a large German delegation led by Felix Klein. This event is a prototype of what the official ICM will become in a few years, a kind of zero congress! Finally, if the first congress is no longer the first, then it really seems very reasonable not to keep count.

Roger Mansui

Know more

• Mathematicians of the world, unite! Guillermo P. Courbera, A.K. Peters edition, 2009

Emergence of the American Society for Mathematical Research, 1876-1900 : J. J. Sylvester, Felix Klein, and E. H. Moore, Karen Hanger Parshall, David E. Roe, American Mathematical Society Press, 1994 (pages 295 to 330).

Felix KleinRenate Tobis, Birkhäuser Editions 2019 (pages 401–404)

Image : Poster of the first congress of mathematicians, held in Zurich (Switzerland) from 9 to 11 August 1897 (https://www.e-manuscripta.ch/zut/doi/10.7891/e-manuscripta-43814).