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 often viewed as the top honor a mathematician can receive. It comes with a monetary award, which in 2006 was C$15,000 (US$15,000 or €10,000). 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 periodically awarded since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions.
The Fields Medal is often described as the "Nobel Prize of Mathematics" for the prestige it carries, though in most other ways the relatively new Abel Prize is a more direct analogue. The comparison is not entirely accurate because the Fields Medal is awarded only every four years. The Medal also has an age limit: a recipient's 40th birthday must not occur before 1 January of the year in which the Fields Medal is awarded. As a result many great mathematicians have missed it by having done their best work (or having had their work recognized) too late in life. The 40-year 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.
|1936||Oslo, Norway||Lars Ahlfors, Finland
Jesse Douglas, USA
|1950||Cambridge, United States||Laurent Schwartz, France
Atle Selberg, Norway
|1954||Amsterdam, The Netherlands||Kunihiko Kodaira, Japan
Jean-Pierre Serre, France
|1958||Edinburgh, United Kingdom||Klaus Roth, UK
René Thom, France
|1962||Stockholm, Sweden||Lars Hörmander, Sweden
John Milnor, USA
|1966||Moscow, Soviet Union||Michael Atiyah, UK
Paul Joseph Cohen, USA
Alexander Grothendieck, France
Stephen Smale, USA
|1970||Nice, France||Alan Baker, UK
Heisuke Hironaka, Japan
Sergei Novikov, Soviet Union
John G. Thompson, USA
|1974||Vancouver, Canada||Enrico Bombieri, Italy
David Mumford, UK
|1978||Helsinki, Finland||Pierre Deligne, Belgium
Charles Fefferman, USA
Grigory Margulis, Soviet Union
Daniel Quillen, USA
|1982||Warsaw, Poland||Alain Connes, France
William Thurston, USA
Shing-Tung Yau, USA
|1986||Berkeley, United States||Simon Donaldson, UK
Gerd Faltings, Germany
Michael Freedman, USA
|1990||Kyoto, Japan||Vladimir Drinfel'd, Soviet Union
Vaughan F. R. Jones, New Zealand
Shigefumi Mori, Japan
Edward Witten, USA
|1994||Zürich, Switzerland||Jean Bourgain, Belgium
Pierre-Louis Lions, France
Jean-Christophe Yoccoz, France
Efim Zelmanov, Russia
|1998||Berlin, Germany||Richard Borcherds, UK
Timothy Gowers, UK
Maxim Kontsevich, Russia
Curtis T. McMullen, USA
|2002||Beijing, China||Laurent Lafforgue, France
Vladimir Voevodsky, Russia
In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27. He still retains this distinction.
In 1978, Grigory 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.
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 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. 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.
EX TOTO ORBE
OB SCRIPTA INSIGNIA
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.
The rim bears the name of the prizewinner.
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The Fields Medal is a prize given to two, three, or four people who study math who are not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years.
The Canadian mathematician John Charles Fields was the first to propose this medal and it was first awarded in 1936. It has been regularly awarded since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions.
Because of its prestige, the Fields Medal is often described as the "Nobel Prize of mathematics,", but the comparison is not so good. First, it is awarded not only to recognize the valuable contributions of a mathematician but also to encourage him or her to continue his work. The Fields Medals have generally been awarded for a mathematician's whole work, rather than for a particular result.
Another difference is that the Fields Medal is awarded every four years, and its recipients cannot be over the age of 40. Also, the money awarded with the medal is much lower than the US$1.3 million given with each Nobel prize.