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This article is about the prize in mathematics. For the material, see Field's metal.
Fields Medal
FieldsMedalFront.jpg
The obverse of the Fields Medal
Awarded for Outstanding contributions in mathematics
Country Varies
Presented by International Mathematical Union (IMU)
Reward C$15,000
First awarded 1936 (1936)
Last awarded 2010
Official website www.mathunion.org/general/prizes/fields/details

The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, 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 (IMU), a meeting that takes place every four years. The Fields Medal is often viewed as the greatest honour a mathematician can receive.[1][2] The Fields Medal and the Abel Prize have often been described as the "mathematician's Nobel Prize".

The prize comes with a monetary award, which since 2014 is $15,000 (in Canadian dollars, roughly US $13,800[3]).[4][5] The colloquial name is in honour of Canadian mathematician John Charles Fields.[6] Fields was instrumental in establishing the award, designing the medal itself, and funding the monetary component.[6]

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. No woman has won a Fields Medal. The average Erdős number of Fields Medalists is 3.21, with a standard deviation of 0.87 and a median of 3.[7]

Conditions of the award[edit]

The Fields Medal is often described as the "Nobel Prize of Mathematics" for being traditionally regarded as the most prestigious award in the field of mathematics;[8] however, in contrast to the actual Nobel Prize, 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 some 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.[9]

The monetary award is much lower than the 8,000,000 Swedish kronor (roughly $1,400,000 in Canadian dollars)[10] given with each Nobel prize as of 2012.[11] Other major awards in mathematics, such as the Abel Prize and the Chern Medal, have a large monetary prize like a Nobel.

Fields medalists[edit]

Year ICM location Medalists[12] Institution Nationality
1936 Norway Oslo Lars Ahlfors
Jesse Douglas
University of Helsinki
Massachusetts Institute of Technology
Finland
United States
1950 United States Cambridge Laurent Schwartz
Atle Selberg
University of Nancy
Institute for Advanced Study
France
Norway
1954 Netherlands Amsterdam Kunihiko Kodaira
Jean-Pierre Serre
Institute for Advanced Study
Centre National de la Recherche Scientifique
Japan
France
1958 United Kingdom Edinburgh Klaus Roth
René Thom
Imperial College London
University of Strasbourg
United Kingdom
France
1962 Sweden Stockholm Lars Hörmander
John Milnor
University of Stockholm
Princeton University
Sweden
United States
1966 Soviet Union Moscow Michael Atiyah
Paul Joseph Cohen
Alexander Grothendieck
Stephen Smale
University of Oxford
Stanford University
Institut des Hautes Études Scientifiques
University of California, Berkeley
United Kingdom
United States
None (Stateless)
United States
1970 France Nice Alan Baker
Heisuke Hironaka
Sergei Novikov
John G. Thompson
University of Cambridge
Harvard University
Moscow State University
University of Cambridge
United Kingdom
Japan
Soviet Union
United States
1974 Canada Vancouver Enrico Bombieri
David Mumford
University of Pisa
Harvard University
Italy
United States
1978 Finland Helsinki Pierre Deligne
Charles Fefferman
Grigory Margulis
Daniel Quillen
Institut des Hautes Études Scientifiques
Princeton University
Moscow State University
Massachusetts Institute of Technology
Belgium
United States
Soviet Union
United States
1982 Poland Warsaw Alain Connes
William Thurston
Shing-Tung Yau
Institut des Hautes Études Scientifiques
Princeton University
Institute for Advanced Study
France
United States
British Hong Kong
1986 United States Berkeley Simon Donaldson
Gerd Faltings
Michael Freedman
University of Oxford
Princeton University
University of California, San Diego
United Kingdom
West Germany
United States
1990 Japan Kyoto Vladimir Drinfeld
Vaughan F. R. Jones
Shigefumi Mori
Edward Witten
University of Kharkiv
University of California, Berkeley
Kyoto University
Institute for Advanced Study
Soviet Union
New Zealand
Japan
United States
1994 Switzerland Zurich Jean Bourgain
Pierre-Louis Lions
Jean-Christophe Yoccoz
Efim Zelmanov
Institut des Hautes Études Scientifiques
Paris Dauphine University
Paris-Sud 11 University
University of California, San Diego
Belgium
France
France
Russia
1998 Germany Berlin Richard Borcherds
Timothy Gowers
Maxim Kontsevich
Curtis T. McMullen
University of California, Berkeley and University of Cambridge
University of Cambridge
Institut des Hautes Études Scientifiques and Rutgers University
Harvard University
United Kingdom
United Kingdom
Russia
United States
2002 China Beijing Laurent Lafforgue
Vladimir Voevodsky
Institut des Hautes Études Scientifiques
Institute for Advanced Study
France
Russia
2006 Spain Madrid Andrei Okounkov
Grigori Perelman
Terence Tao
Wendelin Werner
Princeton University
None (Saint Petersburg)
University of California, Los Angeles
Paris-Sud 11 University
Russia
Russia
Australia
France
2010 India Hyderabad Elon Lindenstrauss
Ngô Bảo Châu
Stanislav Smirnov
Cédric Villani
Hebrew University of Jerusalem and Princeton University
Paris-Sud 11 University and Institute for Advanced Study
University of Geneva
École Normale Supérieure de Lyon and Institut Henri Poincaré
Israel
Vietnam France
Russia
France
2014 South Korea Seoul TBD

Landmarks[edit]

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.[13] Léon Motchane, founder and director of the Institut des Hautes Études Scientifiques attended and accepted Grothendieck's Fields Medal on his behalf.[14]

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."[15]

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 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.[16] 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.[17][18]

In 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal[4] and did not attend the congress.[19]

Number of Fields Medallists by country[edit]

 United States 12 Jesse Douglas, 1936John Milnor, 1962Paul Cohen, 1966Stephen Smale, 1966John G. Thompson, 1970David Mumford, 1974Charles Fefferman, 1978Daniel Quillen, 1978William Thurston, 1982Michael Freedman, 1986Edward Witten, 1990Curtis T. McMullen, 1998
 France 10 Laurent Schwartz, 1950Jean-Pierre Serre, 1954René Thom, 1958Alain Connes, 1982Pierre-Louis Lions, 1994Jean-Christophe Yoccoz, 1994Laurent Lafforgue, 2002Wendelin Werner, 2006Ngô Bảo Châu, 2010 (also Vietnam)Cédric Villani, 2010
 Soviet Union (3) /  Russia (6) 9 Sergei Novikov, 1970Grigory Margulis, 1978Vladimir Drinfeld, 1990Efim Zelmanov, 1994Maxim Kontsevich, 1998Vladimir Voevodsky, 2002Andrei Okounkov, 2006Grigori Perelman, 2006Stanislav Smirnov, 2010
 United Kingdom 6 Klaus Roth, 1958Michael Atiyah, 1966Alan Baker, 1970Simon Donaldson, 1986Richard Borcherds, 1998Timothy Gowers, 1998
 Japan 3 Kunihiko Kodaira, 1954Heisuke Hironaka, 1970Shigefumi Mori, 1990
 Belgium 2 Pierre Deligne, 1978Jean Bourgain, 1994
 West Germany (1) /  Germany (0) 1 Gerd Faltings, 1986
 Australia 1 Terence Tao, 2006
 British Hong Kong 1 Shing-Tung Yau, 1982
 Finland 1 Lars Ahlfors, 1936
 Israel 1 Elon Lindenstrauss, 2010
 Italy 1 Enrico Bombieri, 1974
 Norway 1 Atle Selberg, 1950
 New Zealand 1 Vaughan F. R. Jones, 1990
 Sweden 1 Lars Hörmander, 1962
 Vietnam 1 Ngô Bảo Châu, 2010 (also France)
(None) 1 Alexander Grothendieck, 1966


Number of Fields Medallists by working institutions[edit]

Upon appointment, the Fields medalists were working in the following institutions:[20]

Princeton University 7 Médaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNG
University of Paris[21] 7 Médaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNG
Institute for Advanced Study 6 Médaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNG
Institut des Hautes Études Scientifiques 5 Médaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNG
University of Cambridge 4 Médaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNG
Harvard University 4 Médaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNG
University of Oxford 3 Médaille Fields miniature.PNGMédaille Fields miniature.PNGMédaille Fields miniature.PNG
Massachusetts Institute of Technology 2 Médaille Fields miniature.PNGMédaille Fields miniature.PNG
University of California, Berkeley 2 Médaille Fields miniature.PNGMédaille Fields miniature.PNG
Free University of Brussels 2 Médaille Fields miniature.PNGMédaille Fields miniature.PNG
Moscow State University 2 Médaille Fields miniature.PNGMédaille Fields miniature.PNG
Stanford University 2 Médaille Fields miniature.PNGMédaille Fields miniature.PNG
Imperial College London 2 Médaille Fields miniature.PNGMédaille Fields miniature.PNG
École Normale Supérieure de Lyon 1 Médaille Fields miniature.PNG
Hebrew University of Jerusalem 1 Médaille Fields miniature.PNG
University of California, Los Angeles 1 Médaille Fields miniature.PNG
University of California, San Diego 1 Médaille Fields miniature.PNG
University of Geneva 1 Médaille Fields miniature.PNG
University of Kharkiv 1 Médaille Fields miniature.PNG
Kyoto University 1 Médaille Fields miniature.PNG
University of Nancy 1 Médaille Fields miniature.PNG
University of Pisa 1 Médaille Fields miniature.PNG
Rutgers University 1 Médaille Fields miniature.PNG
University of Stockholm 1 Médaille Fields miniature.PNG
University of Strasbourg 1 Médaille Fields miniature.PNG
University of Wisconsin 1 Médaille Fields miniature.PNG


The medal[edit]

The medal was designed by Canadian sculptor R. Tait McKenzie.[22]

  • On the obverse is Archimedes and a quote attributed to Marcus Manilius which reads in Latin: "Transire suum pectus mundoque potiri" (Rise above oneself and grasp the world). The date is written in Roman numerals and contains an error ("MCNXXXIII" rather than "MCMXXXIII").[23]
The reverse of the Fields Medal
  • On the reverse is the inscription (in Latin):
CONGREGATI
EX TOTO ORBE
MATHEMATICI
OB SCRIPTA INSIGNIA
TRIBUERE

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 2/3.)

The rim bears the name of the prizewinner.

See also[edit]


References[edit]

  1. ^ "2006 Fields Medals awarded" (PDF). Notices of the American Mathematical Society (American Mathematical Society) 53 (9): 1037–1044. October 2006. 
  2. ^ "Reclusive Russian turns down math world's highest honour". Canadian Broadcasting Corporation. 22 August 2006. Retrieved 26 August 2006. 
  3. ^ On 2014-04-01 at 15:27 UTC, the OANDA currency converter gives $14,574.90 U.S.
  4. ^ a b "Maths genius turns down top prize". BBC. 22 August 2006. Retrieved 22 August 2006. 
  5. ^ Israeli wins 'Nobel' of Mathematics, JPost.com
  6. ^ a b "About Us: The Fields Medal". The Fields Institute, University of Toronto. Retrieved 21 August 2010. 
  7. ^ The Erdos Number Project http://www.oakland.edu/enp/erdpaths
  8. ^ Chang, Kenneth (12 March 2007). "Journeys to the Distant Fields of Prime". The New York Times. 
  9. ^ McKinnon Riehm & Hoffman 2011, p. 183.
  10. ^ On 2014-04-01 at 15:32 UTC, the OANDA currency converter gives $1,360,970 Canadian.
  11. ^ "The Nobel Prize Amounts". Retrieved 2012-07-24. 
  12. ^ "List of Fields Medallists". International Mathematical Union (IMU). 8 May 2008. Retrieved 25 March 2009. 
  13. ^ Jackson, Allyn (October 2004). "As If Summoned from the Void: The Life of Alexandre Grothendieck" (PDF). Notices of the American Mathematical Society 51 (9): 1198. Retrieved 26 August 2006. 
  14. ^ "This Mathematical Month - August". American Mathematical Society. 
  15. ^ Margulis biography, School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 27 August 2006.
  16. ^ Wiles, Andrew John, Encyclopædia Britannica. Retrieved 27 August 2006.
  17. ^ Fields Medal Prize Winners (1998), 2002 International Congress of Mathematicians. Retrieved 27 August 2006.
  18. ^ Notices of the AMS, November 1998. Vol. 45, No. 10, p. 1359.
  19. ^ Nasar, Sylvia; Gruber, David (21 August 2006). "Manifold Destiny: A legendary problem and the battle over who solved it.". The New Yorker. Retrieved 24 August 2006. 
  20. ^ Infoplease.com
  21. ^ Y compris, après séparation, Université Paris-Sud (3) et Université Paris-Dauphine (1).
  22. ^ "Fields Institute - The Fields Medal". Fields.utoronto.ca. 9 August 1932. Retrieved 21 August 2010. 
  23. ^ EBERHARD KNOBLOCH Generality and Infinitely Small Quantities in Leibniz's Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves. In Infinitesimal Differences: Controversies between Leibniz and his Contemporaries. Edited by Ursula Goldenbaum and Douglas Jesseph. Walter de Gruyter, 2008

Further reading[edit]

  • McKinnon Riehm, Elaine; Hoffman, Frances (2011). Turbulent Times in Mathematics: The Life of J.C. Fields and the History of the Fields Medal. Providence, RI: American Mathematical Society. ISBN 0-8218-6914-0. 
  • Monastyrsky, Michael (1998). Modern Mathematics in the Light of the Fields Medal. Wellesley, MA: A. K. Peters. ISBN 1-56881-083-0. 
  • Tropp, Henry S. (1976). "The Origins and History of the Fields Medal". Historia Mathematica 3 (2): 167–181. doi:10.1016/0315-0860(76)90033-1. .

External links[edit]


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