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52-716: The Fields Medals , the IMU Abacus Medal (known before 2022 as 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

104-512: A hall of fame ". German mathematicians Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s. The University of Chicago , which had opened in 1892, organized an International Mathematical Congress at the Chicago World's Fair in 1893, where Felix Klein participated as the official German representative. The first official International Congress of Mathematicians

156-544: A chance at last to meet a mathematician whom I know only through his work and for whom I have the greatest respect and admiration." In 1982, the congress was due to be held in Warsaw but had to be rescheduled to the next year, because of martial law introduced in Poland on 13 December 1981. The awards were announced at the ninth General Assembly of the IMU earlier in the year and awarded at

208-483: A gift for languages, but he is only interested in the scientific and mathematical aspect of languages: he should become a mathematician." In 1934, he was admitted at the École Normale Supérieure, and in 1937 he obtained the agrégation (with rank 2). As a man of Trotskyist affinities and Jewish descent, life was difficult for Schwartz during World War II . He had to hide and change his identity to avoid being deported after Nazi Germany overran France. He worked for

260-503: A lecture where he claimed that Georg 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. During

312-569: A mathematician can receive, and has been described as the Nobel Prize of Mathematics , although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by ARWU , the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013–14,

364-480: Is made of 14KT gold, has a diameter of 63.5mm, and weighs 169g. Translation: "Mathematicians gathered from the entire world have awarded [understood but not written: 'this prize'] for outstanding writings." In the background, there is the representation of Archimedes' tomb , with the carving illustrating his theorem On the Sphere and Cylinder , behind an olive branch. (This is the mathematical result of which Archimedes

416-447: Is often described as the Nobel Prize of Mathematics . Unlike the Nobel Prize, the Fields Medal is only awarded every four years. The Fields Medal also has an age limit: a recipient must be under age 40 on 1 January of the year in which the medal is awarded. The under-40 rule is based on Fields's desire that "while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on

468-626: The French Academy of Sciences , and was promoted to full membership in 1975. In 1950 at the International Congress of Mathematicians , Schwartz was a plenary speaker and was awarded the Fields Medal for his work on distributions . He was the first French mathematician to receive the Fields medal. Because of his sympathy for Trotskyism , Schwartz encountered serious problems trying to enter

520-559: The Manifesto of the 121 about the Algerian war , a gesture not appreciated by Polytechnique's military administration. However, Schwartz had a lasting influence on mathematics at the École polytechnique, having reorganized both teaching and research there. In 1965 he established the Centre de mathématiques Laurent-Schwartz (CMLS) as its first director. In 1973 he was elected corresponding member of

572-533: The United States to receive the medal; however, he was ultimately successful. The theory of distributions clarified the (then) mysteries of the Dirac delta function and Heaviside step function . It helps to extend the theory of Fourier transforms and is now of critical importance to the theory of partial differential equations . Throughout his life, Schwartz actively worked to promote science and bring it closer to

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624-535: The University of Strasbourg (which had been relocated to Clermont-Ferrand because of the war) under the name of Laurent-Marie Sélimartin (his thesis "Étude des sommes d'exponentielles réelles" being however published in 1943 under his real name in the Publications de l'Institut de Mathématique de l'Université de Clermont-Ferrand, volume 959 of Hermann's Actualités scientifiques et industrielles), while Marie-Hélène used

676-814: The Wayback Machine 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

728-449: The theory of distributions , which gives a well-defined meaning to objects such as the Dirac delta function . He was awarded the Fields Medal in 1950 for his work on the theory of distributions. For several years he taught at the École polytechnique . Laurent Schwartz came from a Jewish family of Alsatian origin, with a strong scientific background: his father was a well-known surgeon , his uncle Robert Debré (who contributed to

780-575: 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. In the aftermath of World War I, at

832-565: 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. As a result of the exclusion rule and the protests it generated, the 1920 and the 1924 ICMs were considerably smaller than

884-497: The 1983 Warsaw congress. In 1990, Edward Witten became the first physicist to win the award. In 1998, at the ICM, Andrew Wiles was presented by the chair of the Fields Medal Committee, Yuri I. Manin , with the first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem . Don Zagier referred to the plaque as a "quantized Fields Medal". Accounts of this award frequently make reference that at

936-560: The 1990 ICM in Kyoto, by Karen Uhlenbeck . 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 Archived 2014-12-29 at

988-429: The 1997 film, Good Will Hunting . In the movie, Gerald Lambeau ( Stellan Skarsgård ) is an MIT professor who won the award prior to the events of the story. Throughout the film, references made to the award are meant to convey its prestige in the field. Laurent Schwartz Laurent-Moïse Schwartz ( French: [lɔʁɑ̃ mɔiz ʃvaʁts] ; 5 March 1915 – 4 July 2002) was a French mathematician . He pioneered

1040-477: The Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics. The prize includes a monetary award which, since 2006, has been CA$ 15,000. Fields was instrumental in establishing the award, designing the medal himself, and funding the monetary component, though he died before it was established and his plan was overseen by John Lighton Synge . The medal

1092-468: The Fields Medal. The most recent group of Fields Medalists received their awards on 5 July 2022 in an online event which was live-streamed from Helsinki, Finland. It was originally meant to be held in Saint Petersburg , Russia, but was moved following the 2022 Russian invasion of Ukraine . The Fields Medal has for a long time been regarded as the most prestigious award in the field of mathematics and

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1144-515: 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 . The first woman to give an ICM plenary lecture, at the 1932 congress in Zürich, was Emmy Noether . The second ICM plenary talk by a woman was delivered 58 years later, at

1196-733: The ICM, held in Moscow, to protest Soviet military actions taking place in Eastern Europe. Léon Motchane , founder and director of the Institut des Hautes Études Scientifiques , attended and accepted Grothendieck's Fields Medal on his behalf. In 1970, Sergei Novikov , because of restrictions placed on him by the Soviet government, was unable to travel to the congress in Nice to receive his medal. In 1978, Grigory Margulis , because of restrictions placed on him by

1248-620: 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. 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. Another, related, point of contention

1300-528: The IMU. Fields Medal 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 name of the award honours the Canadian mathematician John Charles Fields . The Fields Medal is regarded as one of the highest honors

1352-543: The IRC's instructions, in 1920 the Union Mathematique Internationale (UMI) was created. 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

1404-399: 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,

1456-459: The Soviet government, was unable to travel to the congress in Helsinki to receive his medal. The award was accepted on his behalf by Jacques Tits , who said in his address: "I cannot but express my deep disappointment—no doubt shared by many people here—in the absence of Margulis from this ceremony. In view of the symbolic meaning of this city of Helsinki, I had indeed grounds to hope that I would have

1508-521: The UMI. 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 Zürich a decision to dissolve the UMI was made, largely in opposition to IRC's pressure on the UMI. At the 1950 ICM the participants voted to reconstitute the International Mathematical Union (IMU), which

1560-516: The US. Only four were women: Iginia Massarini, Vera Schiff  [ ru ] , Charlotte Scott , and Charlotte Wedell . 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. At the 1904 ICM Gyula Kőnig delivered

1612-537: 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. 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

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1664-442: The creation of UNICEF ) was a famous pediatrician , and his great-uncle-in-law, Jacques Hadamard , was a famous mathematician. During his training at Lycée Louis-le-Grand to enter the École Normale Supérieure , he fell in love with Marie-Hélène Lévy , daughter of the probabilist Paul Lévy who was then teaching at the École polytechnique . They married in 1938. Later they had two children, Marc-André and Claudine. Marie-Hélène

1716-418: The first Iranian as well as the first woman to win the Fields Medal, and Artur Avila became the first South American and Manjul Bhargava became the first person of Indian origin to do so. In 2022, Maryna Viazovska became the first Ukrainian to win the Fields Medal, and June Huh became the first person of Korean ancestry to do so. The medal was designed by Canadian sculptor R. Tait McKenzie . It

1768-558: The general audience. Schwartz said: "What are mathematics helpful for? Mathematics are helpful for physics. Physics helps us make fridges. Fridges are made to contain spiny lobsters, and spiny lobsters help mathematicians who eat them and have hence better abilities to do mathematics, which are helpful for physics, which helps us make fridges which..." His mother, who was passionate about natural science, passed on her taste for entomology to Laurent. His personal collection of 20,000 Lepidoptera specimens, collected during his various travels

1820-583: 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

1872-436: The medal. In certain years, the Fields medalists have been officially cited for particular mathematical achievements, while in other years such specificities have not been given. However, in every year that the medal has been awarded, noted mathematicians have lectured at the International Congress of Mathematicians on each medalist's body of work. In the following table, official citations are quoted when possible (namely for

1924-554: The name Lengé instead of Lévy. Unlike other mathematicians at Clermont-Ferrand such as Feldbau , the couple managed to escape the Nazis. Schwartz taught mainly at École Polytechnique , from 1958 to 1980. At the end of the war, he spent one year in Grenoble (1944), then in 1945 joined the University of Nancy on the advice of Jean Delsarte and Jean Dieudonné , where he spent seven years. He

1976-453: 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”. As a consequence of this controversy, from the 1932 Zürich congress onward, the ICMs are not numbered. For the 1950 ICM in Cambridge, Massachusetts, Laurent Schwartz , one of

2028-451: The part of the recipients and a stimulus to renewed effort on the part of others." Moreover, an individual can only be awarded one Fields Medal; winners are ineligible to be awarded future medals. First awarded in 1936, 64 people have won the medal as of 2022. With the exception of two PhD holders in physics ( Edward Witten and Martin Hairer ), only people with a PhD in mathematics have won

2080-609: 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

2132-483: The time of the award Wiles was over the age limit for the Fields medal. Although Wiles was slightly over the age limit in 1994, he was thought to be a favorite to win the medal; however, a gap (later resolved by Taylor and Wiles) in the proof was found in 1993. In 2006, Grigori Perelman , who proved the Poincaré conjecture , refused his Fields Medal and did not attend the congress. In 2014, Maryam Mirzakhani became

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2184-1319: The years 1958, 1998, and every year since 2006). For the other years through 1986, summaries of the ICM lectures, as written by Donald Albers, Gerald L. Alexanderson , and Constance Reid , are quoted. In the remaining years (1990, 1994, and 2002), part of the text of the ICM lecture itself has been quoted. The upcoming Fields Medal ceremony is scheduled for 2026, taking place in Philadelphia , US. Moscow State University , Russia University of Maryland-College Park , US University of Florida , US Collège de France , France Ohio State University , US Vanderbilt University , US École polytechnique , France University of California, San Diego , US University of Cambridge , UK Rutgers University , US Rutgers University , US University of California, Berkeley , US Princeton University , US Institute for Advanced Study , US Institute for Advanced Study, US St. Petersburg State University , Russia Institut Henri Poincaré , France Institut Henri Poincaré , France CNRS , France Instituto Nacional de Matemática Pura e Aplicada , Brazil Instituto Nacional de Matemática Pura e Aplicada , Brazil University of Geneva , Switzerland University of Geneva , Switzerland The medal

2236-656: Was bequeathed to the Muséum national d'histoire naturelle , the Science Museum of Lyon , the Museum of Toulouse and the Museo de Historia Natural Alcide d'Orbigny in Cochabamba (Bolivia). Several species discovered by Schwartz bear his name. Apart from his scientific work, Schwartz was a well-known outspoken intellectual . As a young socialist influenced by Leon Trotsky , Schwartz opposed

2288-432: Was both an influential researcher and teacher, with students such as Bernard Malgrange , Jacques-Louis Lions , François Bruhat and Alexander Grothendieck . He joined the science faculty of the University of Paris in 1952. In 1958 he became a teacher at the École polytechnique after having at first refused this position. From 1961 to 1963 the École polytechnique suspended his right to teach, because of his having signed

2340-467: Was first awarded in 1936 to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas , and it has been awarded every four years since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions. In 2014, the Iranian mathematician Maryam Mirzakhani became the first female Fields Medalist. In total, 64 people have been awarded

2392-552: Was first awarded in 1936 to the Finnish mathematician Lars Ahlfors and the American mathematician Jesse Douglas , and it has been awarded every four years since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions. In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27. He retains this distinction. In 1966, Alexander Grothendieck boycotted

2444-462: 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 Zürich. 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

2496-492: Was gifted in mathematics as well, as she contributed to the geometry of singular analytic spaces and taught at the University of Lille . Angelo Guerraggio describes "Mathematics, politics and butterflies" as Schwartz's "three great loves". According to his teachers, Schwartz was an exceptional student. He was particularly gifted in Latin, Greek and mathematics. One of his teachers told his parents: "Beware, some will say your son has

2548-505: Was held in Zürich in August 1897. The organizers included such prominent mathematicians as Luigi Cremona , Felix Klein , Gösta Mittag-Leffler , Andrey Markov , and others. The congress was attended by 208 mathematicians from 16 countries, including more than 100 from Switzerland or Germany, around 20 from each of France, Italy, and Austria-Hungary , 13 from the Russian Empire and 7 from

2600-434: Was reportedly most proud: Given a sphere and a circumscribed cylinder of the same height and diameter, the ratio between their volumes is equal to 2 ⁄ 3 .) The rim bears the name of the prizewinner. The Fields Medal has had two female recipients, Maryam Mirzakhani from Iran in 2014, and Maryna Viazovska from Ukraine in 2022. The Fields Medal gained some recognition in popular culture due to references in

2652-459: 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 returned to more normal levels. However, even after 1957, tensions between ICM organizers and the Soviet side persisted. Soviet mathematicians invited to attend

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2704-471: 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. 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

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