Fields Medal

Not to be confused with Field's metal.

Fields Medal
The obverse of the Fields Medal
Description	Outstanding contributions in mathematics attributed to young scientists
Country	Varies
Presented by	International Mathematical Union (IMU)
Reward(s)	C$15,000
First awarded	1936 (1936)
Last awarded	2014
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. 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 2006 has been $15,000 (in Canadian dollars). The colloquial name is in honour of Canadian mathematician John Charles Fields. Fields was instrumental in establishing the award, designing the medal itself, and funding the monetary component.

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.

In 2014 Maryam Mirzakhani became the first woman as well as the first Iranian, and Artur Avila became the first mathematician from Latin America to be awarded a Fields Medal.

Conditions of the award

The Fields Medal is often described as the "Nobel Prize of Mathematics" and for a long time was regarded as the most prestigious award in the field of mathematics. However, in contrast to the Nobel Prize, the Fields Medal is awarded only every four years. The Fields Medal also has an age limit: a recipient must be under age 40 until 1 January of the year in which the medal is awarded. The under 40 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 8,000,000 Swedish kronor (roughly 1,400,000 Canadian dollars) given with each Nobel prize as of 2014. Other major awards in mathematics, such as the Abel Prize and the Chern Medal, have larger monetary prizes, comparable to the Nobel.

Fields medalists

Year	ICM location	Medalists	Institution (At the time of receiving the medal)	Birthplace	Current/Last residency	Current/Last Institution
1936	Oslo	Lars Ahlfors Jesse Douglas	University of Helsinki Massachusetts Institute of Technology		United States United States	Harvard University City College of New York
1950	Cambridge	Laurent Schwartz Atle Selberg	University of Nancy Institute for Advanced Study		France United States	Université de Paris VII Institute for Advanced Study
1954	Amsterdam	Kunihiko Kodaira Jean-Pierre Serre	Institute for Advanced Study and Princeton University University of Nancy		Japan France	University of Tokyo Collège de France
1958	Edinburgh	Klaus Roth René Thom	University College London University of Strasbourg		United Kingdom France	Imperial College London Institut des Hautes Études Scientifiques
1962	Stockholm	Lars Hörmander John Milnor	University of Stockholm Princeton University		Sweden United States	Lund University Stony Brook University
1966	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 Stateless United States	University of Edinburgh Stanford University Institut des Hautes Études Scientifiques City University of Hong Kong
1970	Nice	Alan Baker Heisuke Hironaka Sergei Novikov John G. Thompson	University of Cambridge Harvard University Moscow State University University of Cambridge		United Kingdom Japan Russia United States	University of Cambridge Kyoto University Steklov Mathematical Institute University of Florida
1974	Vancouver	Enrico Bombieri David Mumford	University of Pisa Harvard University		United States United States	Institute for Advanced Study Brown University
1978	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 United States United States	Institute for Advanced Study Princeton University Yale University University of Oxford
1982	Warsaw	Alain Connes William Thurston Shing-Tung Yau	Institut des Hautes Études Scientifiques Princeton University Institute for Advanced Study		France United States United States	Institut des Hautes Études Scientifiques Cornell University Harvard University
1986	Berkeley	Simon Donaldson Gerd Faltings Michael Freedman	University of Oxford Princeton University University of California, San Diego		United Kingdom Germany United States	Imperial College London Max Planck Institute for Mathematics Microsoft Station Q
1990	Kyoto	Vladimir Drinfeld Vaughan F. R. Jones Shigefumi Mori Edward Witten	University of Kharkiv University of California, Berkeley Kyoto University Institute for Advanced Study		United States United States Japan United States	University of Chicago University of California, Berkeley Kyoto University Institute for Advanced Study
1994	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 and United States France France United States	Institute for Advanced Study Collège de France Collège de France University of California, San Diego
1998	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 States and United Kingdom United Kingdom France United States	University of California, Berkeley University of Cambridge Institut des Hautes Études Scientifiques and Rutgers University Harvard University
2002	Beijing	Laurent Lafforgue Vladimir Voevodsky	Institut des Hautes Études Scientifiques Institute for Advanced Study		France United States	Institut des Hautes Études Scientifiques Institute for Advanced Study
2006	Madrid	Andrei Okounkov Grigori Perelman Terence Tao Wendelin Werner	Princeton University None (Saint Petersburg) University of California, Los Angeles Paris-Sud 11 University		United States Russia United States France	University of Chicago None University of California, Los Angeles ETH Zurich
2010	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 and United States Switzerland France	Hebrew University Paris-Sud 11 University and University of Chicago and Vietnam Institute for Advanced Study University of Geneva Lyon University and Institut Henri Poincaré
2014	Seoul	Artur Avila Manjul Bhargava Martin Hairer Maryam Mirzakhani	Instituto Nacional de Matemática Pura e Aplicada, CNRS and Paris Diderot University Princeton University University of Warwick Stanford University		Brazil and France United States United Kingdom United States	Paris Diderot University and Instituto Nacional de Matemática Pura e Aplicada Princeton University University of Warwick Stanford University
2018	Rio de Janeiro	n/a	n/a	n/a	n/a	n/a

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 the ICM, held in Moscow, to protest Soviet military actions taking place in Eastern Europe. Léon Motchane, founder and director of the Institut des Hautes Études Scientifiques attended and accepted Grothendieck's Fields Medal on his behalf.

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."

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. 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, who proved the Poincaré conjecture, refused his Fields Medal and did not attend the congress. Ironically, this attracted the public attention he was trying to avoid.

In 2014, Artur Avila was the first Brazilian and Latin American awarded the Fields Medal. The same year, Maryam Mirzakhani became the first woman to win this award, as well as the first Iranian person to do so.

Number of Fields Medallists by country of origin

United States	12
Soviet Union	9
France	8
United Kingdom	5
West Germany (2) / Germany (2)	4
Japan	3
Belgium	2
Austria	1
Australia	1
Brazil	1
British Hong Kong	1
Canada	1
Finland	1
Iran	1
Israel	1
Italy	1
Norway	1
New Zealand	1
Sweden	1
Vietnam	1

Number of Fields Medallists by working institutions

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

Princeton University	8
University of Paris	7
Institute for Advanced Study	6
Institut des Hautes Études Scientifiques	5
University of Cambridge	4
Harvard University	4
University of Oxford	3
Massachusetts Institute of Technology	2
University of California, Berkeley	2
Free University of Brussels	2
Moscow State University	2
Stanford University	2
University College London	2
University of Warwick	1
École Normale Supérieure de Lyon	1
Hebrew University of Jerusalem	1
University of California, Los Angeles	1
University of California, San Diego	1
University of Geneva	1
University of Kharkiv	1
Kyoto University	1
University of Nancy	1
University of Pisa	1
Rutgers University	1
University of Stockholm	1
University of Strasbourg	1
University of Wisconsin	1
Instituto de Matemática Pura e Aplicada	1

The medal

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

• 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").

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

• Kyoto Prize
• List of prizes, medals, and awards in mathematics
• Nevanlinna Prize
• Rolf Schock Prizes
• Turing Award
• Wolf Prize in Mathematics

Further reading

• 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. {{cite book}}: Invalid |ref=harv (help)
• 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

• Official website