International Congress of Mathematicians | |
---|---|

Status | Active |

Genre | Mathematics conference |

Frequency | Quadrennial |

Country | Varies |

Years active | 1897–present |

Inaugurated | August 1897 |

Founder | Felix Klein Georg Cantor |

Most recent | August 2018 |

Previous event | 2018 |

Next event | 6-14 July 2022 Saint Petersburg, Russia |

Activity | Active |

Website | www |

The **International Congress of Mathematicians** (**ICM**) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).

- History
- ICMs and the International Mathematical Union
- Soviet participation
- List of Congresses
- See also
- References
- Further reading
- External links

The Fields Medals, the Nevanlinna Prize, the Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being invited to talk at the ICM has been called "the equivalent [...] of an induction to a hall of fame."^{ [1] }

Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.^{ [2] }^{ [3] } The first International Congress of Mathematicians was held in Zurich in August 1897.^{ [4] } The organizers included such prominent mathematicians as Luigi Cremona, Felix Klein, Gösta Mittag-Leffler, Andrey Markov, and others.^{ [5] } The congress was attended by 208 mathematicians from 16 countries, including 12 from Russia and 7 from the U.S.A.^{ [3] } Only four were women (none of them speakers): Iginia Massarini, Vera von Schiff, Charlotte Scott, and Charlotte Wedell.^{ [6] }

During the 1900 congress in Paris, France, David Hilbert announced his famous list of 23 unsolved mathematical problems, now termed Hilbert's problems. Moritz Cantor and Vito Volterra gave the two plenary lectures at the start of the congress.^{ [7] }

At the 1904 ICM Gyula Kőnig delivered a lecture where he claimed that Cantor's famous continuum hypothesis was false. An error in Kőnig's proof was discovered by Ernst Zermelo soon thereafter. Kőnig's announcement at the congress caused considerable uproar, and Klein had to personally explain to the Grand Duke of Baden (who was a financial sponsor of the congress) what could cause such an unrest among mathematicians.^{ [8] }

During the 1912 congress in Cambridge, England, Edmund Landau listed four basic problems about prime numbers, now called Landau's problems. The 1924 congress in Toronto was organized by John Charles Fields, initiator of the Fields Medal; it included a roundtrip railway excursion to Vancouver and ferry to Victoria. The first two Fields Medals were awarded at the 1936 ICM in Oslo.^{ [8] }

In the aftermath of World War I, at the insistence of the Allied Powers, the 1920 ICM in Strasbourg and the 1924 ICM in Toronto excluded mathematicians from the countries formerly part of the Central Powers. This resulted in a still unresolved controversy as to whether to count the Strasbourg and Toronto congresses as true ICMs. At the opening of the 1932 ICM in Zürich, Hermann Weyl said: "We attend here to an extraordinary improbable event. For the number of *n*, corresponding to the just opened International Congress of Mathematicians, we have the inequality 7 ≤ *n* ≤ 9; unfortunately our axiomatic foundations are not sufficient to give a more precise statement”.^{ [8] } As a consequence of this controversy, from the 1932 Zürich congress onward, the ICMs are not numbered.^{ [8] }

For the 1950 ICM in Cambridge, Massachusetts, Laurent Schwartz, one of the Fields Medalists for that year, and Jacques Hadamard, both of whom were viewed by the U.S. authorities as communist sympathizers, were only able to obtain U.S. visas after the personal intervention of President Harry Truman.^{ [9] }^{ [10] }

The first woman to give an ICM plenary lecture, at the 1932 congress in Zürich, was Emmy Noether.^{ [11] } The second ICM plenary talk by a woman was delivered 58 years later, at the 1990 ICM in Kyoto, by Karen Uhlenbeck.^{ [12] }

The 1998 congress was attended by 3,346 participants. The American Mathematical Society reported that more than 4,500 participants attended the 2006 conference in Madrid, Spain. The King of Spain presided over the 2006 conference opening ceremony. The 2010 Congress took place in Hyderabad, India, on August 19–27, 2010. The ICM 2014 was held in Seoul, South Korea, on August 13–21, 2014. The 2018 Congress took place in Rio de Janeiro on August 1–9, 2018.

The organizing committees of the early ICMs were formed in large part on an *ad hoc* basis and there was no single body continuously overseeing the ICMs. Following the end of World War I, the Allied Powers established in 1919 in Brussels the International Research Council (IRC). At the IRC's instructions, in 1920 the *Union Mathematique Internationale* (UMI) was created.^{ [8] } This was the immediate predecessor of the current International Mathematical Union. Under the IRC's pressure, UMI reassigned the 1920 congress from Stockholm to Strasbourg and insisted on the rule which excluded from the congress mathematicians representing the former Central Powers. The exclusion rule, which also applied to the 1924 ICM, turned out to be quite unpopular among mathematicians from the U.S. and Great Britain. The 1924 ICM was originally scheduled to be held in New York, but had to be moved to Toronto after the American Mathematical Society withdrew its invitation to host the congress, in protest against the exclusion rule.^{ [3] } As a result of the exclusion rule and the protests it generated, the 1920 and the 1924 ICMs were considerably smaller than the previous ones. In the run-up to the 1928 ICM in Bologna, IRC and UMI still insisted on applying the exclusion rule. In the face of the protests against the exclusion rule and the possibility of a boycott of the congress by the American Mathematical Society and the London Mathematical Society, the congress's organizers decided to hold the 1928 ICM under the auspices of the University of Bologna rather than of the UMI.^{ [8] } The 1928 congress and all the subsequent congresses have been open for participation by mathematicians of all countries. The statutes of the UMI expired in 1931 and at the 1932 ICM in Zurich a decision to dissolve the UMI was made, largely in opposition to IRC's pressure on the UMI.^{ [8] }

At the 1950 ICM the participants voted to reconstitute the International Mathematical Union (IMU), which was formally established in 1951. Starting with the 1954 congress in Amsterdam, the ICMs are held under the auspices of the IMU.

The Soviet Union sent 27 participants to the 1928 ICM in Bologna and 10 participants to the 1932 ICM in Zurich.^{ [11] } No Soviet mathematicians participated in the 1936 ICM, although a number of invitations were extended to them. At the 1950 ICM there were again no participants from the Soviet Union, although quite a few were invited. Similarly, no representatives of other Eastern Bloc countries, except for Yugoslavia, participated in the 1950 congress. Andrey Kolmogorov had been appointed to the Fields Medal selection committee for the 1950 congress, but did not participate in the committee's work. However, in a famous episode, a few days before the end of the 1950 ICM, the congress' organizers received a telegram from Sergei Vavilov, President of the USSR Academy of Sciences. The telegram thanked the organizers for inviting Soviet mathematicians but said that they are unable to attend "being very much occupied with their regular work", and wished success to the congress's participants.^{ [13] } Vavilov's message was seen as a hopeful sign for the future ICMs and the situation improved further after Joseph Stalin's death in 1953. The Soviet Union was represented by five mathematicians at the 1954 ICM in Amsterdam, and several other Eastern Bloc countries sent their representatives as well. In 1957 the USSR joined the International Mathematical Union and the participation in subsequent ICMs by the Soviet and other Eastern Bloc scientists has been mostly at normal levels.^{ [13] } However, even after 1957, tensions between ICM organizers and the Soviet side persisted. Soviet mathematicians invited to attend the ICMs routinely experienced difficulties with obtaining exit visas from the Soviet Union and were often unable to come. Thus of the 41 invited speakers from the USSR for the 1974 ICM in Vancouver, only 20 actually arrived.^{ [3] } Grigory Margulis, who was awarded the Fields Medal at 1978 ICM in Helsinki, was not granted an exit visa and was unable to attend the 1978 congress.^{ [3] }^{ [14] } Another, related, point of contention was the jurisdiction over Fields Medals for Soviet mathematicians. After 1978 the Soviet Union put forward a demand that the USSR Academy of Sciences approve all Soviet candidates for the Fields Medal, before it was awarded to them.^{ [3] }^{ [14] } However, the IMU insisted that the decisions regarding invited speakers and Fields medalists be kept under exclusive jurisdiction of the ICM committees appointed for that purpose by the IMU.^{ [3] }^{ [14] }

Year | City | Country |
---|---|---|

2022 | Saint Petersburg | |

2018 | Rio de Janeiro | |

2014 | Seoul | |

2010 | Hyderabad | |

2006 | Madrid | |

2002 | Beijing | |

1998 | Berlin | |

1994 | Zürich | |

1990 | Kyoto | |

1986 | Berkeley | |

1982 (met during 1983) | Warsaw | |

1978 | Helsinki | |

1974 | Vancouver | |

1970 | Nice | |

1966 | Moscow | |

1962 | Stockholm | |

1958 | Edinburgh | |

1954 | Amsterdam | |

1950 | Cambridge, Massachusetts | |

1936 | Oslo | |

1932 | Zürich | |

1928 | Bologna | |

1924 | Toronto | |

1920 | Strasbourg | |

1912 | Cambridge | |

1908 | Rome | |

1904 | Heidelberg | |

1900 | Paris | |

1897 | Zürich |

**Alain Connes** is a French mathematician, currently Professor at the Collège de France, IHÉS, Ohio State University and Vanderbilt University. He was an Invited Professor at the Conservatoire national des arts et métiers (2000).

The **Fields Medal** is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.

The **International Mathematical Union** (**IMU**) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports the International Congress of Mathematicians. Its members are national mathematics organizations from more than 80 countries.

The **Rolf Nevanlinna Prize**, known from 2022 as the **IMU Abacus Medal**, is awarded once every four years at the International Congress of Mathematicians, for outstanding contributions in Mathematical Aspects of Information Sciences including:

- All mathematical aspects of computer science, including computational complexity theory, logic of programming languages, analysis of algorithms, cryptography, computer vision, pattern recognition, information processing and modelling of intelligence.
- Scientific computing and numerical analysis. Computational aspects of optimization and control theory. Computer algebra.

**Heinz Hopf** was a German mathematician who worked on the fields of topology and geometry.

**Jean-Christophe Yoccoz** was a French mathematician. He was awarded a Fields Medal in 1994, for his work on dynamical systems.

**Victor Gershevich** (**Grigorievich**) **Kac** is a Soviet and American mathematician at MIT, known for his work in representation theory. He co-discovered Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. He is also known for the Kac–Weisfeiler conjectures with Boris Weisfeiler.

**Nicolai Yuryevich Reshetikhin** is a mathematical physicist, currently a professor of mathematics at the University of California, Berkeley and a professor of mathematical physics at the University of Amsterdam. His research is in the fields of low-dimensional topology, representation theory, and quantum groups. His major contributions are in the theory of quantum integrable systems, in representation theory of quantum groups and in quantum topology. He and Vladimir Turaev constructed invariants of 3-manifolds which are expected to describe quantum Chern-Simons field theory introduced by Edward Witten.

The **International Commission on Mathematical Instruction** (**ICMI**) is a commission of the International Mathematical Union and is an internationally acting organization focussing on mathematics education. ICMI was founded in 1908 at the International Congress of Mathematicians (ICM) in Rome and aims to improve teaching standards around the world, through programs, workshops and initiatives and publications. It aims to work a great deal with developing countries, to increase teaching standards and education which can improve life quality and aid the country.

**Jean-Michel Bismut** is a French mathematician who has been a Professor at the Université Paris-Sud since 1981. His mathematical career covers two apparently different branches of mathematics: probability theory and differential geometry. Ideas from probability play an important role in his works on geometry.

**Robert "Bob" Osserman** was an American mathematician who worked in geometry. He is specially remembered for his work on the theory of minimal surfaces.

**Yakov Eliashberg** is an American mathematician who was born in Leningrad, USSR.

**Artur Avila Cordeiro de Melo** is a Brazilian mathematician working primarily on dynamical systems and spectral theory. He is one of the winners of the 2014 Fields Medal, being the first Latin American to win such an award. He has been a researcher at both the IMPA and the CNRS. Since September 2018 he is a professor at the University of Zurich.

The **Chern Medal** is an international award recognizing outstanding lifelong achievement of the highest level in the field of mathematics. The prize is given at the International Congress of Mathematicians (ICM), which is held every four years.

**Georges Jean Marie Valiron** was a French mathematician, notable for his contributions to analysis, in particular, the asymptotic behaviour of entire functions of finite order and Tauberian theorems.

**Christophe Soulé** is a French mathematician working in arithmetic geometry.

**Benny Sudakov** is an Israeli mathematician, who works mainly on Hungarian-style combinatorics. He received his PhD from Tel Aviv University under the supervision of Noga Alon. Until 2014, he was a professor at the University of California, Los Angeles. In July 2013 Benny Sudakov joined ETH Zurich as a professor.

**Isabelle Gallagher** is a French mathematician. Her research concerns partial differential equations such as the Navier–Stokes equations, wave equation, and Schrödinger equation, as well as harmonic analysis of the Heisenberg group.

**Marie Charpentier** (1903–1994) was the first woman to obtain a doctorate in pure mathematics in France, and the second woman, after Marie-Louise Dubreil-Jacotin, to obtain a faculty position in mathematics at a university in France.

**Michèle Artigue** is a French expert in mathematics education, a professor emeritus at Paris Diderot University and the former president of the International Commission on Mathematical Instruction.

- ↑ Castelvecchi, Davide (7 October 2015). "The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof".
*Nature*.**526**: 178–181. doi:10.1038/526178a. PMID 26450038. - ↑ THE INTERNATIONAL MATHEMATICAL UNION AND THE ICM CONGRESSES. www.icm2006.org. Accessed December 23, 2009.
- 1 2 3 4 5 6 7 A. John Coleman. "Mathematics without borders": a book review.
*CMS Notes*, vol 31, no. 3, April 1999, pp. 3-5 - ↑ C., Bruno, Leonard (2003) [1999].
*Math and mathematicians : the history of math discoveries around the world*. Baker, Lawrence W. Detroit, Mich.: U X L. p. 56. ISBN 0787638137. OCLC 41497065. - ↑ In the section
*Vorgeschichte des Kongresses*(prehistory of the congress) of the 1st ICM proceedings, 21 prominent organizers were cited: Hermann Bleuler, Heinrich Burkhardt, Luigi Cremona, Gustave Dumas, Jérôme Franel, Carl Friedrich Geiser, Alfred George Greenhill, Albin Herzog, George William Hill, Adolf Hurwitz, Felix Klein, Andrey Markov, Franz Mertens, Hermann Minkowski, Gösta Mittag-Leffler, Gabriel Oltramare, Henri Poincaré, Johann Jakob Rebstein, Ferdinand Rudio, Karl von der Mühll , and Heinrich Friedrich Weber. (See: Rudio, F., ed. (1898).*Verhandlungen des ersten Internationalen Kongresses in Zürich vom 9. bis 11. August 1897*. BG Teubner. p. 6.) - ↑ Curbera (2009), p. 16.
- ↑ Scott, Charlotte Angas (1900). "The International Congress of Mathematicians in Paris" (PDF).
*Bull. Amer. Math. Soc*.**7**(2): 57–79. doi:10.1090/s0002-9904-1900-00768-3. - 1 2 3 4 5 6 7 G. Curbera. ICM through history. Newsletter of the European Mathematical Society, no. 63, March 2007, pp. 16-21. Accessed December 23, 2009.
- ↑ Vladimir Maz'ya, Tatyana Shaposhnikova. Jacques Hadamard: a universal mathematician. American Mathematical Society, 1999. ISBN 0-8218-1923-2; p. 271
- ↑ Michèle Audin,
*Correspondance entre Henri Cartan et André Weil (1928-1991)*, Documents Mathématiques**6**, Société Mathématique de France, 2011, p. 259-313 - 1 2 Guillermo Curbera.
*Mathematicians of the World, Unite!: The International Congress of Mathematicians: A Human Endeavor*AK Peters, 2009. ISBN 1-56881-330-9; pp. 95-96 - ↑ Sylvia Wiegand. Report on the Berlin ICM. AWM Newsletter, 28(6), November–December 1998, pp. 3-8
- 1 2 Guillermo Curbera.
*Mathematicians of the World, Unite!: The International Congress of Mathematicians: A Human Endeavor*AK Peters, 2009. ISBN 1-56881-330-9; pp 149-150. - 1 2 3 Olli Lehto. Mathematics without borders: a history of the International Mathematical Union. Springer-Verlag, 1998. ISBN 0-387-98358-9; pp. 205-206

- Guillermo Curbera.
*Mathematicians of the World, Unite!: The International Congress of Mathematicians: A Human Endeavor*AK Peters, 2009. ISBN 1-56881-330-9 - Olli Lehto.
*Mathematics without borders: a history of the International Mathematical Union*Springer-Verlag, 1998. ISBN 0-387-98358-9 - Donald J. Albers, Gerald L. Alexanderson, Constance Reid.
*International Mathematical Congresses: An Illustrated History, 1893-1986*, Springer-Verlag, 1986. ISBN 0-387-96409-6 - Yousef Alavi, Peter Hilton and Jean Pedersen. "Let's Meet at the Congress"
*American Mathematical Monthly*, Vol. 93, No. 1 (Jan., 1986), pp. 3–8

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*International Mathematical Congress:*held in connection with the World's Columbian Exposition, Chicago- International Mathematical Union: Proceedings 1893-2014
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