The Field Medals were first proposed at the 1924 International Congress of Mathematicians in Toronto, where a resolution was adopted stating that at each subsequent conference, two gold medals should be awarded to recognize outstanding mathematical achievement. Professor J. C. Fields, a Canadian mathematician who was secretary of the 1924 Congress, later donated funds establishing the medals which were named in his honor. Consistent with Fields' wish that the awards recognize both existing work and the promise of future achievement, it was agreed to restrict the medals to mathematicians not over forty at the year of the Congress. In 1966 it was agreed that, in light of the great expansion of mathematical research, up to four medals could be awarded at each Congress.
The Fields Medal is the highest scientific award for mathematicians, and is presented every four years at the International Congress of Mathematicians, together with a prize of
Canadian
dollars. The first Fields Medal was awarded in 1936 at the World Congress in
Oslo. The Fields Medal is made of gold, and shows the head of Archimedes
(287-212 BC) together with a quotation attributed to him: "Transire suum pectus
mundoque potiri" ("Rise above oneself and grasp the world"). The reverse side
bears the inscription: "Congregati ex toto orbe mathematici ob scripta insignia
tribuere" ("the mathematicians assembled here from all over the world pay
tribute for outstanding work"). Nobel prizes were created in the will of the Swedish chemist and inventor of dynamite Alfred Nobel, but Nobel, who was an inventor and industrialist, did not create a prize in mathematics because he was not particularly interested in mathematics or theoretical science. In fact, his will speaks of prizes for those "inventions or discoveries" of greatest practical benefit to mankind. While it is commonly stated that Nobel decided against a Nobel prize in math because of anger over the romantic attentions of a famous mathematician (often claimed to be Gosta Mittag-Leffler) to a woman in his life, there is no historical evidence to support the story. Furthermore, Nobel was a lifelong bachelor, although he did have a Viennese woman named Sophie Hess as his mistress (Lopez-Ortiz).
The following table summarizes Fields Medals winners together with their institutions.
| year | winners |
| 1936 | Lars Valerian Ahlfors (Harvard University) |
| Jesse Douglas (Massachusetts Institute of Technology) | |
| 1950 | Laurent Schwartz (University of Nancy) |
| Atle Selberg (Institute for Advanced Study, Princeton) | |
| 1954 | Kunihiko Kodaira (Princeton University) |
| Jean-Pierre Serre (University of Paris) | |
| 1958 | Klaus Friedrich Roth (University of London) |
| René Thom (University of Strasbourg) | |
| 1962 | Lars V. Hörmander (University of Stockholm) |
| John Willard Milnor (Princeton University) | |
| 1966 | Michael Francis Atiyah (Oxford University) |
| Paul Joseph Cohen (Stanford University) | |
| Alexander Grothendieck (University of Paris) | |
| Stephen Smale (University of California, Berkeley) | |
| 1970 | Alan Baker (Cambridge University) |
| Heisuke Hironaka (Harvard University) | |
| Serge P. Novikov (Moscow University) | |
| John Griggs Thompson (Cambridge University) | |
| 1974 | Enrico Bombieri (University of Pisa) |
| David Bryant Mumford (Harvard University) | |
| 1978 | Pierre René Deligne (Institut des Hautes Études Scientifiques) |
| Charles Louis Fefferman (Princeton University) | |
| Gregori Alexandrovitch Margulis (Moscow University) | |
| Daniel G. Quillen (Massachusetts Institute of Technology) | |
| 1982 | Alain Connes (Institut des Hautes Études Scientifiques) |
| William P. Thurston (Princeton University) | |
| Shing-Tung Yau (Institute for Advanced Study, Princeton) | |
| 1986 | Simon Donaldson (Oxford University) |
| Gerd Faltings (Princeton University) | |
| Michael Freedman (University of California, San Diego) | |
| 1990 | Vladimir Drinfeld (Phys. Inst. Kharkov) |
| Vaughan Jones (University of California, Berkeley) | |
| Shigefumi Mori (University of Kyoto) | |
| Edward Witten (Institute for Advanced Study, Princeton) | |
| 1994 | Pierre-Louis Lions (Université de Paris-Dauphine) |
| Jean-Christophe Yoccoz (Université de Paris-Sud, Orsay, France) | |
| Jean Bourgain (Institute for Advanced Study, Princeton) | |
| Efim Zelmanov (University of Wisconsin) | |
| 1998 | Richard E. Borcherds (Cambridge University) |
| W. Timothy Gowers (Cambridge University) | |
| Maxim Kontsevich (IHES Bures-sur-Yvette) | |
| Curtis T. McMullen (Harvard University) | |
| 2002 | Laurent Lafforgue (Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France) |
| Vladimir Voevodsky (Institute for Advanced Study, Princeton) | |
| 2006 | Andrei Okounkov (Princeton University) |
| Grigori Perelman (Russia) [declined award] | |
| Terence Tao (University of California, Los Angeles) | |
| Wendelin Werner (Université de Paris-Sud, Orsay, France) | |
| 2010 | Elon Lindenstrauss (Hebrew University of Jerusalem) |
| Ngô Bao Châu (Institute for Advanced Study, Princeton) | |
| Stanislav Smirnov (Université de Genève, Switzerland) | |
| Cédric Villani Wolfram |
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