The Fields Medal is a prize awarded to two, three, or four

, although there are several key differences, including frequency of award, number of awards, and age limits. According to the annual Academic Excellence Survey by mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
One of ...

s under 40 years of age at the International Congress
International is an adjective (also used as a noun) meaning "between nations".
International may also refer to:
Music
Albums
* ''International'' (Kevin Michael album), 2011
* ''International'' (New Order album), 2002
* ''International'' (The Three ...

of the International Mathematical Union
The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports t ...

(IMU), a meeting that takes place every four years.
The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the mathematician's Nobel Prize#REDIRECT Nobel Prize#REDIRECT Nobel Prize
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The ''Academic Ranking of World Universities'' (''ARWU''), also known as the Shanghai Ranking, is one of the annual publications of world university rankings. The league table was originally compiled and issued by Shanghai Jiao Tong University in 20 ...

, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize#REDIRECT Abel Prize
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as the second most prestigious international award in mathematics.
The prize comes with a monetary award which, since 2006, has been 15,000. The name of the award is in honour of Canadian
Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections exist and are collectively the source of ...

mathematician John Charles Fields
John Charles Fields, FRS, FRSC (May 14, 1863 – August 9, 1932) was a Canadian mathematician and the founder of the Fields Medal for outstanding achievement in mathematics.
Life and career
Born in Hamilton, Ontario, to a leather shop owner, ...

. Fields was instrumental in establishing the award, designing the medal himself, and funding the monetary component.
The medal was first awarded in 1936 to Finnish mathematician Lars Ahlfors
Lars Valerian Ahlfors (18 April 1907 – 11 October 1996) was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his text on complex analysis.
Background
Ahlfors was born in Helsinki, Finland. His mother, Sievä ...

and American mathematician Jesse Douglas
Jesse Douglas (3 July 1897 – 7 September 1965) was an American mathematician and Fields Medalist known for his general solution to Plateau's problem.
Life and career
He was born to a Jewish family in New York City, the son of Sarah (née ...

, 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, the Iranian mathematician Maryam Mirzakhani
Maryam Mirzakhani ( fa, مریم میرزاخانی, ; 03 May 1977 – 14 July 2017) was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, e ...

became the first female Fields Medalist. In all, sixty people have been awarded the Fields Medal.
The most recent group of Fields Medalists received their awards on 1 August 2018 at the opening ceremony of the IMU International Congress, held in Rio de Janeiro
Rio de Janeiro (; ;), or simply Rio, is the second-most populous city in Brazil and the sixth-most populous in the Americas. Rio de Janeiro is the capital of the state of Rio de Janeiro, Brazil's third-most populous state, after São Paulo and Mi ...

, Brazil. The medal belonging to one of the four joint winners, Caucher Birkar
Caucher Birkar ( ku, کۆچەر بیرکار/Koçer Bîrkar, lit=migrant mathematician; born Fereydoun Derakhshani ( fa, فریدون درخشانی); July 1978) is a UK-based Iranian Kurdish mathematician and a professor at the University of Cambrid ...

, was stolen shortly after the event. The ICM presented Birkar with a replacement medal a few days later.
Conditions of the award

The Fields Medal has for a long time been regarded as the most prestigious award in the field of mathematics and is often described as the Nobel Prize of Mathematics. Unlike theNobel Prize#REDIRECT Nobel Prize#REDIRECT Nobel Prize
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..., the Fields Medal is only awarded every four years. The Fields Medal also has an age limit: a recipient must be under age 40 on 1 January of the year in which the medal is awarded. The under-40 rule is based on Fields's 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." Moreover, an individual can only be awarded one Fields Medal; winners are ineligible to be awarded future medals. First awarded in 1936, 60 people have won the medal as of 2018. With the exception of one Ph.D. holder in physics (

Edward Witten
Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is currently the Charles Simonyi Professor in the School of Natural Sciences at the Institute for Advanced Study. Witten is a researcher in string theor ...

), only people with a Ph.D. in mathematics have won the medal.
Fields medalists

Landmarks

The medal was first awarded in 1936 to the Finnish mathematicianLars Ahlfors
Lars Valerian Ahlfors (18 April 1907 – 11 October 1996) was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his text on complex analysis.
Background
Ahlfors was born in Helsinki, Finland. His mother, Sievä ...

and the American mathematician Jesse Douglas
Jesse Douglas (3 July 1897 – 7 September 1965) was an American mathematician and Fields Medalist known for his general solution to Plateau's problem.
Life and career
He was born to a Jewish family in New York City, the son of Sarah (née ...

, 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 1954, Jean-Pierre Serre
Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaug ...

became the youngest winner of the Fields Medal, at 27. He retains this distinction.
In 1966, Alexander Grothendieck
Alexander Grothendieck (; ; ; 28 March 1928 – 13 November 2014) was a mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative ...

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 Scientifiquesthumbnail, IHÉS main building
The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French institute supporting advanced research in mathematics and theoretical physics. It is located in Bures- ...

, 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
Nice (, ; ; Nissard oc, Niça, classical norm, or ', nonstandard, ; it, Nizza ; el, Νίκαια; la, Nicaea) is the seventh most populous urban area in France and the capital of the Alpes-Maritimes department. The metropolitan area of Nice exte ...

to receive his medal.
In 1978, Grigory Margulis
Grigory Aleksandrovich Margulis (russian: Григо́рий Алекса́ндрович Маргу́лис, first name often given as Gregory, Grigori or Gregori; born February 24, 1946) is a Russian-American mathematician known for his work on ...

, because of restrictions placed on him by the Soviet government, was unable to travel to the congress in Helsinki
Helsinki ( or ; ; sv, Helsingfors, ; la, Helsingia) is the capital, primate and most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of Uusimaa in southern Finland, and has a population of ...

to receive his medal. The award was accepted on his behalf by Jacques Tits
Jacques Tits (; born 12 August 1930 in Uccle) is a Belgium-born French mathematician who works on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric.
Career
Tits was born ...

, 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
Warsaw ( ; pl, Warszawa ; see also other names) is the capital and largest city of Poland. The metropolis stands on the Vistula River in east-central Poland and its population is officially estimated at 1.8 million residents within a gre ...

but had to be rescheduled to the next year, because of martial law#REDIRECT Martial law#REDIRECT Martial law
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Edward Witten
Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is currently the Charles Simonyi Professor in the School of Natural Sciences at the Institute for Advanced Study. Witten is a researcher in string theor ...

became the first physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate cause ...

to win the award.
In 1998, at the ICM, Andrew Wiles
Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarde ...

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
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been kn ...

. 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 Richard Taylor (mathematician), 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.
In 2014, Maryam Mirzakhani
Maryam Mirzakhani ( fa, مریم میرزاخانی, ; 03 May 1977 – 14 July 2017) was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, e ...

became the first woman as well as the first Iranian to win the Fields Medal, and Artur Avila became the first South American and Manjul Bhargava became the first person of Indian people, Indian origin to do so.
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"). The date is written in Roman numerals and contains an error ("MCNXXXIII" rather than "MCMXXXIII"). In capital Greek letters the word ΑΡXIMHΔΟΥΣ, or "of Archimedes". * On the reverse is the inscription (in Latin): : : : : : Translation: "Mathematicians gathered from the entire world have awarded [understood but not written: 'this prize'] for outstanding writings." In the background, there is the representation of Archimedes' Archimedes#Biography, tomb, with the carving illustrating his theorem On the Sphere and Cylinder, behind an olive 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 .) The rim bears the name of the prizewinner.Female recipients

The Fields Medal, which was initiated in 1936 and is considered the most prestigious prize in mathematics, was only obtained for the first time by a woman,Maryam Mirzakhani
Maryam Mirzakhani ( fa, مریم میرزاخانی, ; 03 May 1977 – 14 July 2017) was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, e ...

from Iran, in 2014.
See also

*Abel Prize#REDIRECT Abel Prize
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* Kyoto Prize
* List of Fields Medal winners by university affiliation
* List of prizes known as the Nobel of a field or the highest honors of a field
* List of mathematics awards
* Nevanlinna Prize
* Rolf Schock Prizes
* Turing Award
* Wolf Prize in Mathematics
References

Further reading

* * * .External links

* {{Authority control Fields Medalists, Awards established in 1936 Awards with age limits Mathematics awards