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 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" 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.

Fields Medalists

Year	ICM Location	Medalists
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, China
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
2006	Madrid, Spain	Andrei Okounkov, Russia, "for his contributions bridging probability, representation theory and algebraic geometry" Grigori Perelman, Russia — Medal declined, "for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow" Terence Tao, Australia, "for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory" Wendelin Werner, France, "for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory"

Landmarks

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 his own Fields Medal ceremony, held in Moscow, to protest Soviet military actions taking place in Eastern Europe.

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, 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 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. 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, credited with proving the Poincaré conjecture, refused his Fields Medal and did not attend the congress.

The medal

The medal was designed by Canadian sculptor R. Tait McKenzie.

• On the obverse is Archimedes and a quote attributed to him which reads in Latin: "Transire suum pectus mundoque potiri" (Rise above oneself and grasp the world).

• On the reverse is the inscription (in Latin):

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.

See also

• List of prizes, medals, and awards in mathematics

Notes

1. Fields Institute history
2. Margulis biography, School of Mathematics and Statistics, University of St Andrews, Scotland. Accessed 27 August 2006.
3. Wiles, Andrew John, Encyclopædia Britannica. Accessed 27 August 2006.
4. Fields Medal Prize Winners (1998), 2002 International Congress of Mathematicians. Accessed 27 August 2006.
5. Notices of the AMS, November 1998. Vol. 45, No. 10, p. 1359.
6. http://www.fields.utoronto.ca/aboutus/jcfields/fields_medal.html

External links

• Official site