The obverse of the Fields Medal
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 40year 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
JeanPierre 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
ShingTung 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
PierreLouis Lions, France
JeanChristophe 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 twodimensional Brownian
motion, and conformal field
theory" 
Landmarks
In 1954,
JeanPierre 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 firstever 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
Notes
 Fields Institute history
 Margulis biography, School of Mathematics and
Statistics, University of St Andrews, Scotland. Accessed 27 August
2006.
 Wiles, Andrew John, Encyclopædia Britannica. Accessed
27 August 2006.
 Fields Medal Prize Winners (1998), 2002 International
Congress of Mathematicians. Accessed 27 August 2006.
 Notices of the AMS, November 1998. Vol. 45, No.
10, p. 1359.

http://www.fields.utoronto.ca/aboutus/jcfields/fields_medal.html
External links