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The obverse of the Fields Medal

The Fields Medal 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, a meeting that takes place every four years. The Fields Medal is often viewed as the top honor a mathematician can receive.[1][2] It comes with a monetary award, which in 2006 was C$15,000 (US$15,000 or 10,000).[3] Founded at the behest of Canadian mathematician John Charles Fields,[4] the medal was first awarded in 1936, to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas, and has been periodically awarded since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions.

Contents

Conditions of the award

The Fields Medal is often described as the "Nobel Prize of Mathematics" for the prestige it carries,[5] though in most other ways the relatively new Abel Prize is a more direct analogue. The comparison is not entirely accurate because 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 many 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.

The monetary award is much lower than the roughly US$1.5 million given with each Nobel prize. Finally, Fields Medals have generally been awarded for a body of work, rather than for a particular result; and instead of a direct citation there is a speech of congratulation.

Other major awards in mathematics, such as the Wolf Prize in Mathematics and the Abel Prize, recognise lifetime achievement, again making them different in kind from the Nobels, although the Abel has a large monetary prize like a Nobel. The Fields Medal has the prestige of the selection by the IMU, which represents the world mathematical community.

Fields Medalists

Year ICM Location Medalists[6]
1936 Oslo, Norway Lars Ahlfors, Finland
Jesse Douglas, USA
1950 Cambridge, United States Laurent Schwartz, France
Atle Selberg, Norway
1954 Amsterdam, The Netherlands Kunihiko Kodaira, Japan
Jean-Pierre Serre, France
1958 Edinburgh, United Kingdom Klaus Roth, UK
René Thom, France
1962 Stockholm, Sweden Lars Hörmander, Sweden
John Milnor, USA
1966 Moscow, Soviet Union Michael Atiyah, UK
Paul Joseph Cohen, USA
Alexander Grothendieck, France
Stephen Smale, USA
1970 Nice, France Alan Baker, UK
Heisuke Hironaka, Japan
Sergei Novikov, Soviet Union
John G. Thompson, USA
1974 Vancouver, Canada Enrico Bombieri, Italy
David Mumford, UK
1978 Helsinki, Finland Pierre Deligne, Belgium
Charles Fefferman, USA
Grigory Margulis, Soviet Union
Daniel Quillen, USA
1982 Warsaw, Poland Alain Connes, France
William Thurston, USA
Shing-Tung Yau, USA
1986 Berkeley, United States Simon Donaldson, UK
Gerd Faltings, Germany
Michael Freedman, USA
1990 Kyoto, Japan Vladimir Drinfel'd, Soviet Union
Vaughan F. R. Jones, New Zealand
Shigefumi Mori, Japan
Edward Witten, USA
1994 Zürich, Switzerland Jean Bourgain, Belgium
Pierre-Louis Lions, France
Jean-Christophe Yoccoz, France
Efim Zelmanov, Russia
1998 Berlin, Germany Richard Borcherds, UK
Timothy Gowers, UK
Maxim Kontsevich, Russia
Curtis T. McMullen, USA
2002 Beijing, China Laurent Lafforgue, France
Vladimir Voevodsky, Russia
2006 Madrid, Spain

Andrei Okounkov, Russia,
Grigori Perelman, Russia — Medal declined,
Terence Tao, Australia,
Wendelin Werner, France

2010 Hyderabad, India

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 his own Fields Medal ceremony, held in Moscow, to protest Soviet military actions taking place in Eastern Europe.[7]

In 1970, Sergei Novikov, due to 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, due to 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.[8]

In 1982, the congress was due to be held in Warsaw but had to be rescheduled to the next year, due to political instability. 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.[9] 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.[10][11]

In 2006, Grigori Perelman, credited with proving the Poincaré conjecture, refused his Fields Medal[3] and did not attend the congress.[12]

The medal

The medal was designed by Canadian sculptor R. Tait McKenzie.[13]

  • 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).
FieldsMedalBack.jpg
  • On the reverse is the inscription (in Latin):
CONGREGATI

EX TOTO ORBE

MATHEMATICI

OB SCRIPTA INSIGNIA

TRIBUERE

Translation: "The mathematicians having congregated from the whole world awarded because of outstanding writings."

In the background, there is the representation of Archimedes' tomb, with the carving of his theorem on the sphere and the cylinder (a sphere and a circumscribed cylinder of the same height and diameter, the result of which he was most proud) behind a branch.

The rim bears the name of the prizewinner.

See also

References

  1. ^ "2006 Fields Medals awarded" (PDF). Notices of the American Mathematical Society (American Mathematical Society) 53 (9): 1037–1044. October 2006. http://www.ams.org/notices/200609/comm-prize-fields.pdf. 
  2. ^ "Reclusive Russian turns down math world's highest honour". Canadian Broadcasting Corporation (CBC). 22 August 2006. http://www.cbc.ca/technology/story/2006/08/22/math-fields.html. Retrieved 26 August 2006. 
  3. ^ a b "Maths genius turns down top prize". BBC. 22 August 2006. 
  4. ^ Fields Institute history
  5. ^ Kenneth Chang (12 March 2007). "Journeys to the Distant Fields of Prime". The New York Times. 
  6. ^ "List of Fields Medallists". International Mathematical Union (IMU). 8 May 2008. http://www.mathunion.org/general/prizes/fields/prizewinners. Retrieved 25 March 2009. 
  7. ^ Jackson, Allyn (10 2004). "As If Summoned from the Void: The Life of Alexandre Grothendieck" (PDF). Notices of the American Mathematical Society 51 (9): 1198. http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf. Retrieved 26 August 2006. 
  8. ^ Margulis biography, School of Mathematics and Statistics, University of St Andrews, Scotland. Accessed 27 August 2006.
  9. ^ Wiles, Andrew John, Encyclopædia Britannica. Accessed 27 August 2006.
  10. ^ Fields Medal Prize Winners (1998), 2002 International Congress of Mathematicians. Accessed 27 August 2006.
  11. ^ Notices of the AMS, November 1998. Vol. 45, No. 10, p. 1359.
  12. ^ Nasar, Sylvia; Gruber, David (21 August 2006). "Manifold Destiny: A legendary problem and the battle over who solved it.". The New Yorker. http://www.newyorker.com/fact/content/articles/060828fa_fact2. Retrieved 24 August 2006. 
  13. ^ http://www.fields.utoronto.ca/aboutus/jcfields/fields_medal.html

Further reading

  • Monastyrsky, Michael (1998), Modern Mathematics in the Light of the Fields Medal, Wellesley, MA: A. K. Peters, ISBN 1568810830 
  • 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

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Simple English

The Fields Medal is a prize given to two, three, or four people who study math who are not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years.

The Canadian mathematician John Charles Fields was the first to propose this medal and it was first awarded in 1936. It has been regularly awarded since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions.

Contents

Standing of the award

The Fields Medal is viewed, at least in the media, as the top honor a mathematician can receive.[1] It comes with a monetary award, which in 2006 was C$15,000 (US$13,400 or 10,550).[2]

Conditions of the award

Because of its prestige, the Fields Medal is often described as the "Nobel Prize of mathematics,", but the comparison is not so good. First, it is awarded not only to recognize the valuable contributions of a mathematician but also to encourage him or her to continue his work. The Fields Medals have generally been awarded for a mathematician's whole work, rather than for a particular result.

Another difference is that the Fields Medal is awarded every four years, and its recipients cannot be over the age of 40. Also, the money awarded with the medal is much lower than the US$1.3 million given with each Nobel prize.

Fields Medalists

  • 2006: Andrei Okounkov (Russia), Grigori Perelman (Russia) (declined award), Terence Tao (Australia), Wendelin Werner (France)
  • 2002: Laurent Lafforgue (France), Vladimir Voevodsky (Russia)
  • 1998: Richard Ewen Borcherds (UK), William Timothy Gowers (UK), Maxim Kontsevich (Russia), Curtis T. McMullen (U.S.)
  • 1994: Efim Isakovich Zelmanov (Russia), Pierre-Louis Lions (France), Jean Bourgain (Belgium), Jean-Christophe Yoccoz (France)
  • 1990: Vladimir Drinfeld (USSR), Vaughan Frederick Randal Jones (New Zealand), Shigefumi Mori (Japan), Edward Witten (U.S.)
  • 1986: Simon Donaldson (UK), Gerd Faltings (West Germany), Michael Freedman (U.S.)
  • 1982: Alain Connes (France), William Thurston (U.S.), Shing-Tung Yau (China)
  • 1978: Pierre Deligne (Belgium), Charles Fefferman (U.S.), Grigory Margulis (USSR), Daniel Quillen (U.S.)
  • 1974: Enrico Bombieri (Italy), David Mumford (U.S.)
  • 1970: Alan Baker (UK), Heisuke Hironaka (Japan), Sergei Petrovich Novikov (USSR), John Griggs Thompson (U.S.)
  • 1966: Michael Atiyah (UK), Paul Joseph Cohen (U.S.), Alexander Grothendieck (France), Stephen Smale (U.S.)
  • 1962: Lars Hörmander (Sweden), John Milnor (U.S.)
  • 1958: Klaus Roth (UK), René Thom (France)
  • 1954: Kunihiko Kodaira (Japan), Jean-Pierre Serre (France)
  • 1950: Laurent Schwartz (France), Atle Selberg (Norway)
  • 1936: Lars Ahlfors (Finland), Jesse Douglas (U.S.)

Footnotes

  1. "Reclusive Russian turns down math world's highest honour". Canadian Broadcasting Corporation (CBC). 2006-08-22. http://www.cbc.ca/technology/story/2006/08/22/math-fields.html. Retrieved 2006-08-26. 
  2. Woolls, Daniel (2006-08-22). "Russian refuses math's highest honor". Yahoo News. http://news.yahoo.com/s/ap/20060822/ap_on_re_eu/spain_math_genius_4. Retrieved 2006-08-26. 

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