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Fields Medal | |
---|---|

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 |

Last awarded | 2010 |

Official website | www.mathunion.org/general/prizes/fields/details |

This article is about the prize in mathematics. For the material, see Field's metal.

Fields Medal | |
---|---|

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 |

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 Mathematicians (ICM), 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 2006 is $15,000 (in Canadian dollars, roughly US $13,500^{[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]}

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.

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]}

United States | 12 | |

France | 10 | |

Soviet Union (3) / Russia (6) | 9 | |

United Kingdom | 6 | |

Japan | 3 | |

Belgium | 2 | |

West Germany (1) / Germany (0) | 1 | |

Australia | 1 | |

British Hong Kong | 1 | |

Finland | 1 | |

Israel | 1 | |

Italy | 1 | |

Norway | 1 | |

New Zealand | 1 | |

Sweden | 1 | |

Vietnam | 1 | |

(None) | 1 |

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

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]}

- 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.

- Abel Prize
- Chern Medal
- Kyoto Prize
- List of prizes, medals, and awards in mathematics
- Nevanlinna Prize
- Nobel Prize
- Rolf Schock Prizes
- Turing Award
- Wolf Prize in Mathematics

**^**"2006 Fields Medals awarded" (PDF).*Notices of the American Mathematical Society*(American Mathematical Society)**53**(9): 1037–1044. October 2006.**^**"Reclusive Russian turns down math world's highest honour". Canadian Broadcasting Corporation. 22 August 2006. Retrieved 26 August 2006.**^**On 2014-04-01 at 15:27 UTC, the OANDA currency converter gives $14,574.90 U.S.- ^
^{a}^{b}"Maths genius turns down top prize". BBC. 22 August 2006. Retrieved 22 August 2006. **^**Israeli wins 'Nobel' of Mathematics, JPost.com- ^
^{a}^{b}"About Us: The Fields Medal". The Fields Institute, University of Toronto. Retrieved 21 August 2010. **^**The Erdos Number Project http://www.oakland.edu/enp/erdpaths**^**Chang, Kenneth (12 March 2007). "Journeys to the Distant Fields of Prime".*The New York Times*.**^**McKinnon Riehm & Hoffman 2011, p. 183.**^**On 2014-04-01 at 15:32 UTC, the OANDA currency converter gives $1,360,970 Canadian.**^**"The Nobel Prize Amounts". Retrieved 2012-07-24.**^**"List of Fields Medallists". International Mathematical Union (IMU). 8 May 2008. Retrieved 25 March 2009.**^**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.**^**Infoplease.com**^**Y compris, après séparation, Université Paris-Sud (3) et Université Paris-Dauphine (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

- 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..

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