Fields Medal

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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" (but different at least for the age restriction).

The prize comes with a monetary award, which since 2006 has been C$ 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 a larger monetary prizes, comparable to the Nobel.

Fields medalists

Year	ICM location	Medalists	Institution	Nationality
1936	Oslo	Lars Ahlfors Jesse Douglas	University of Helsinki Massachusetts Institute of Technology
1950	Cambridge	Laurent Schwartz Atle Selberg	University of Nancy Institute for Advanced Study
1954	Amsterdam	Kunihiko Kodaira Jean-Pierre Serre	University of Tokyo and Princeton University University of Nancy
1958	Edinburgh	Klaus Roth René Thom	University College London University of Strasbourg
1962	Stockholm	Lars Hörmander John Milnor	University of Stockholm Princeton 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	None (Stateless)
1970	Nice	Alan Baker Heisuke Hironaka Sergei Novikov John G. Thompson	University of Cambridge Harvard University Moscow State University University of Cambridge
1974	Vancouver	Enrico Bombieri David Mumford	University of Pisa Harvard 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
1982	Warsaw	Alain Connes William Thurston Shing-Tung Yau	Institut des Hautes Études Scientifiques Princeton University Institute for Advanced Study
1986	Berkeley	Simon Donaldson Gerd Faltings Michael Freedman	University of Oxford Princeton University University of California, San Diego
1990	Kyoto	Vladimir Drinfeld Vaughan F. R. Jones Shigefumi Mori Edward Witten	B.Verkin Institute, Kharkov 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
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
2002	Beijing	Laurent Lafforgue Vladimir Voevodsky	Institut des Hautes Études Scientifiques and Paris-Sud 11 University 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
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
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
2018	Rio de Janeiro	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


United States	13
France	11
Soviet Union (3) / Russia (6)	9
United Kingdom	6
Japan	3
Belgium	2
West Germany (1) / Germany (0)	1
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
(None)	1

Number of Fields Medallists by working institutions

At the time of award, the Fields medalists were working in the following institutions:


Princeton University	8
University of Paris	7
Institute for Advanced Study	5
Institut des Hautes Études Scientifiques	5
University of Cambridge	4
Harvard University	3
University of Oxford	2
Massachusetts Institute of Technology	2
University of California, Berkeley	2
University of Nancy	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
B.Verkin Institute, Kharkov	1
Kyoto University	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").

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 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.

References

"2006 Fields Medals awarded" (PDF). Notices of the American Mathematical Society. 53 (9). American Mathematical Society: 1037–1044. October 2006.
"Reclusive Russian turns down math world's highest honour". Canadian Broadcasting Corporation. 22 August 2006. Retrieved 26 August 2006.
^ "Maths genius turns down top prize". BBC. 22 August 2006. Retrieved 22 August 2006.
Israeli wins 'Nobel' of Mathematics, JPost.com
^ "About Us: The Fields Medal". The Fields Institute, University of Toronto. Retrieved 21 August 2010.
"International Mathematical Union (IMU): 2014". Mathunion.org. Retrieved 14 August 2014.
jobs. "Iranian is first woman to nab highest prize in maths : Nature News & Comment". Nature.com. doi:10.1038/nature.2014.15686. Retrieved 14 August 2014.
Chang, Kenneth (12 March 2007). "Journeys to the Distant Fields of Prime". The New York Times.
McKinnon Riehm & Hoffman 2011, p. 183
On 1 April 2014 at 15:32 UTC, 8,000,000 Swedish kronor was worth $1,360,970 Canadian according to the OANDA currency converter.
"The Nobel Prize Amounts". Nobelprize.org. Nobel Foundation. Retrieved 13 August 2014.
"List of Fields Medallists". International Mathematical Union (IMU). 8 May 2008. Retrieved 25 March 2009.
http://www.mathunion.org/ICM/ICM1954.1/ICM1954.1.ocr.pdf
http://www.mathunion.org/ICM/ICM1954.1/ICM1954.1.ocr.pdf
http://www.mathunion.org/ICM/ICM1954.1/ICM1954.1.ocr.pdf
"Fazendo as contas para o futuro — Ciência Hoje" (in Template:Pt icon). Cienciahoje.uol.com.br. 25 February 2014. Retrieved 14 August 2014.{{cite web}}: CS1 maint: unrecognized language (link)
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.
"This Mathematical Month - August". American Mathematical Society.
Margulis biography, School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 27 August 2006.
Wiles, Andrew John, Encyclopædia Britannica. Retrieved 27 August 2006.
Fields Medal Prize Winners (1998), 2002 International Congress of Mathematicians. Retrieved 27 August 2006.
Notices of the AMS, November 1998. Vol. 45, No. 10, p. 1359.
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. (dead link). Archived version dated 14 December 2006; accessed 14 August 2014
"Infoplease.com". Infoplease.com. Retrieved 14 August 2014.
Including, after separation, Université Paris-Sud (4), Université Paris-Dauphine (1), Université Denis Diderot (1), Université Pierre et Marie Curie (1).
"Fields Institute - The Fields Medal". Fields.utoronto.ca. 9 August 1932. Retrieved 21 August 2010.
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

External links

Official website

v t e Fields Medalists
1936 Ahlfors Douglas 1950 Schwartz Selberg 1954 Kodaira Serre 1958 Roth Thom 1962 Hörmander Milnor 1966 Atiyah Cohen Grothendieck Smale 1970 Baker Hironaka Novikov Thompson 1974 Bombieri Mumford 1978 Deligne Fefferman Margulis Quillen 1982 Connes Thurston Yau 1986 Donaldson Faltings Freedman 1990 Drinfeld Jones Mori Witten 1994 Bourgain Lions Yoccoz Zelmanov 1998 Borcherds Gowers Kontsevich McMullen 2002 Lafforgue Voevodsky 2006 Okounkov Perelman Tao Werner 2010 Lindenstrauss Ngô Smirnov Villani 2014 Avila Bhargava Hairer Mirzakhani 2018 Birkar Figalli Scholze Venkatesh 2022 Duminil-Copin Huh Maynard Viazovska
Category Mathematics portal

Fields Medalists