The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years. The Fields Medal is widely viewed as the top honor a mathematician can receive.^[1][2] It comes with a monetary award, which in 2006 was C$15,000 (US$13,400 or €10,550).^[3] Founded at the behest of Canadian mathematician John Charles Fields, the medal was first awarded in 1936, to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas and has been regularly awarded since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions.

Conditions of the award

The Fields Medal is often described as the "Nobel Prize of Mathematics," a reference to its prestige^[4]. The comparison is not entirely accurate because the Fields Medal is only awarded every four years. The Medal also has an age limit: a recipient's 40th birthday must not occur before January 1 of the year in which the Fields Medal is awarded. This 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.

The monetary award is much lower than the roughly US$1.5 million given with each Nobel prize. Finally, Fields Medals have generally been awarded for a body of work, rather than for a particular result; and instead of a direct citation there is a speech of congratulation.

Other major awards in mathematics, such as the Wolf Prize in Mathematics and the Abel Prize, recognise lifetime achievement, again making them different in kind from the Nobels, although the Abel has a large monetary prize like a Nobel. The Fields Medal has the prestige of the selection by the IMU, which represents the world mathematical community.

Fields Medalists

• 2006: Andrei Okounkov (Russia), Grigori Perelman (Russia) (declined), Terence Tao (Australia), Wendelin Werner (France)
• 2002: Laurent Lafforgue (France), Vladimir Voevodsky (Russia)
• 1998: Richard Ewen Borcherds (UK), William Timothy Gowers (UK), Maxim Kontsevich (Russia), Curtis T. McMullen (U.S.)
• 1994: Efim Isakovich Zelmanov (Russia), Pierre-Louis Lions (France), Jean Bourgain (Belgium), Jean-Christophe Yoccoz (France)
• 1990: Vladimir Drinfeld (USSR), Vaughan Frederick Randal Jones (New Zealand), Shigefumi Mori (Japan), Edward Witten (U.S.)
• 1986: Simon Donaldson (UK), Gerd Faltings (West Germany), Michael Freedman (U.S.)
• 1982: Alain Connes (France), William Thurston (U.S.), Shing-Tung Yau (China/U.S.)
• 1978: Pierre Deligne (Belgium), Charles Fefferman (U.S.), Grigory Margulis (USSR), Daniel Quillen (U.S.)
• 1974: Enrico Bombieri (Italy), David Mumford (U.S.)
• 1970: Alan Baker (UK), Heisuke Hironaka (Japan), Sergei Petrovich Novikov (USSR), John Griggs Thompson (U.S.)
• 1966: Michael Atiyah (UK), Paul Joseph Cohen (U.S.), Alexander Grothendieck (France), Stephen Smale (U.S.)
• 1962: Lars Hörmander (Sweden), John Milnor (U.S.)
• 1958: Klaus Roth (UK), René Thom (France)
• 1954: Kunihiko Kodaira (Japan), Jean-Pierre Serre (France)
• 1950: Laurent Schwartz (France), Atle Selberg (Norway)
• 1936: Lars Ahlfors (Finland), Jesse Douglas (U.S.)

Landmarks

In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at just over 28. He still retains this distinction.

In 1966, Alexander Grothendieck boycotted his own Fields Medal ceremony, held in Moscow, to protest Soviet military actions taking place in Eastern Europe.^[5]

In 1970, Sergei Petrovich Novikov, due to restrictions placed on him by the Soviet government, was unable to travel to the congress in Nice to receive his medal.

In 1978, Gregori Margulis, due to 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.^[6]

In 1982, the congress was due to be held in Warsaw but had to be rescheduled to the next year, due to political instability. The awards were announced at the ninth General Assembly of the IMU earlier in the year and awarded at the 1983 Warsaw congress.

In 1998, at the ICM, Andrew Wiles was presented by the chair of the Fields Medal Committee, Yuri 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 (e.g., see ^[7]). 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 Wiles) in the proof was found in 1993. ^{[8] [9]}

In 2006, Grigori Perelman, credited with proving the Poincaré conjecture, refused his Fields Medal^[3] and did not attend the congress. ^[10]

The medal

Realised by Canadian sculptor Robert Tait McKenzie.

• In the front, we can see Archimedes and some inscriptions.

• In the back, we can see the inscription (in Latin):

“

CONGREGATI EX TOTO ORBE MATHEMATICI OB SCRIPTA INSIGNIA TRIBUERE

”

Translation: "The mathematicians having congregated from the whole world awarded because of outstanding writings."

In the background, there is the representation of Archimedes' tomb, with the carving of his theorem on the Sphere and the Cylinder (a sphere and a circumscribed cylinder of the same height and diameter, the result of which he was most proud) behind a branch.

See also

• List of prizes, medals, and awards in mathematics

Notes

External links

• Official site

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