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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 Fields Medal is sometimes viewed as the highest honour a mathematician can receive.^{[1]}^{[2]} The Fields Medal and the Abel Prize have often been described as the "mathematician's Nobel Prize" (but different at least for the age restriction).
The prize comes with a monetary award, which since 2006 has been C$15,000 (in Canadian dollars).^{[3]}^{[4]} The colloquial name is in honour of Canadian mathematician John Charles Fields.^{[5]} Fields was instrumental in establishing the award, designing the medal itself, and funding the monetary component.^{[5]}
The medal 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 Maryam Mirzakhani became the first woman as well as the first Iranian, and Artur Avila became the first mathematician from Latin America to be awarded a Fields Medal.^{[6]}^{[7]}
The Fields Medal is often described as the "Nobel Prize of Mathematics" and for a long time was regarded as the most prestigious award in the field of mathematics.^{[8]} However, in contrast to the Nobel Prize, the Fields Medal is awarded only 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. This is similar to restrictions applicable to the Clark Medal in economics. The under-40 rule is based on Fields' 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 the part of the recipients and a stimulus to renewed effort on the part of others."^{[9]}
The monetary award is much lower than the 8,000,000 Swedish kronor (roughly 1,400,000 Canadian dollars)^{[10]} given with each Nobel prize as of 2014.^{[11]} Other major awards in mathematics, such as the Abel Prize and the Chern Medal, have larger monetary prizes, comparable to the Nobel.
University of Florida, US^{[35]}
Moscow State University, Russia
University of Maryland-College Park, US^{[36]}^{[37]}
Collège de France, France
Ohio State University, US^{[44]}
Vanderbilt University, US^{[54]}
École polytechnique, France^{[59]}
University of California, San Diego, US^{[61]}
University of Cambridge, UK
Rutgers University, US
Rutgers University, US^{[64]}
GLr (r≥1) over function fields."
Princeton University, US
Institute for Advanced Study, US
University of Chicago, US
Vietnam Institute for Advanced Study, Vietnam^{[73]}
St. Petersburg State University, Russia^{[74]}
Institut Henri Poincaré, France
Institut Henri Poincaré, France^{[75]}
CNRS, France
Instituto Nacional de Matemática Pura e Aplicada, Brazil
In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27. He still retains this distinction.
In 1966, Alexander Grothendieck boycotted the ICM, held in Moscow, to protest Soviet military actions taking place in Eastern Europe.^{[85]} Léon Motchane, founder and director of the Institut des Hautes Études Scientifiques attended and accepted Grothendieck's Fields Medal on his behalf.^{[86]}
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 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 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."^{[87]}
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 Dec 1981. The awards were announced at the ninth General Assembly of the IMU earlier in the year and awarded at the 1983 Warsaw congress.
In 1990, Edward Witten became the first and so far only physicist to win this 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 the time of the award Wiles was over the age limit for the Fields medal.^{[88]} 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.^{[89]}^{[90]}
In 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal^{[3]} and did not attend the congress.^{[91]}
In 2014, Maryam Mirzakhani became the first woman, Artur Avila the first South American and Manjul Bhargava the first person of Indian origins to win the Fields Medal.
The medal was designed by Canadian sculptor R. Tait McKenzie.^{[93]}
Translation: "Mathematicians gathered from the entire world have awarded [understood '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 the cylinder, behind a branch. (This is the mathematical result of which Archimedes 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 ⅔.)
The rim bears the name of the prizewinner.
Trinity College, Cambridge, St John's College, Cambridge, University of Oxford, United Kingdom, Darwin College, Cambridge
Princeton, New Jersey, New Jersey, Princeton University, United States, Albert Einstein
Brown University, Harvard University, Ivy League, Woodrow Wilson, Princeton Tigers
Stanford University, Google, California, University of California, Irvine, University of California, San Diego
University of Cambridge, United Kingdom, Oxford University Press, Colleges of the University of Oxford, Jesus College, Oxford
Nobel Prize in Physics, Fields Medal, Nobel Peace Prize, Physics, Anton Chekhov
Nobel Prize, Pulitzer Prize, Fields Medal, University of Chicago, American Historical Association
Fields Medal, Princeton University, String theory, Quantum gravity, Topology
Fields Medal, Norway, Princeton, New Jersey, United States, University of Oslo