Fields Medal
mathematics award
Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, award granted to between two and four mathematicians for outstanding or seminal research. The Fields Medal is often referred to as the mathematical equivalent of the Nobel Prize, but it is granted only every four years and is given, by tradition, to mathematicians under the age of 40, rather than to more senior scholars.
The Fields Medal originated from surplus funds raised by John Charles Fields (1863–1932), a professor of mathematics at the University of Toronto, as organizer and president of the 1924 International Congress of Mathematicians in Toronto. The Committee of the International Congress had $2,700 left after printing the conference proceedings and voted to set aside $2,500 for the establishment of two medals to be awarded at later congresses. Following an endowment from Fields’s estate, the proposed awards—contrary to his explicit request—became known as the Fields Medals. The first two Fields Medals were awarded in 1936. An anonymous donation allowed the number of prize medals to increase starting in 1966. Medalists also receive a small (currently $1,500) cash award. A related award, the Rolf Nevanlinna Prize, has also been presented at each International Congress of Mathematicians since 1982. It is awarded to one young mathematician for work dealing with the mathematical aspects of information science.
The International Mathematical Union’s executive committee appoints Fields Medal and Nevanlinna Prize committees, to which national committees may suggest candidates in writing to the secretary of the International Mathematical Union. The medals have been presented at each International Congress of Mathematicians since 1936. (See table.)
year
name
birthplace
primary research
*Because Poland was under martial law in 1982, the scheduled meeting of the International Congress of Mathematicians in Warsaw was postponed until 1983.
1936
Ahlfors, Lars
Helsinki, Finland
Riemann surfaces
1936
Douglas, Jesse
New York, New York, U.S.
Plateau problem
1950
Schwartz, Laurent
Paris, France
functional analysis
1950
Selberg, Atle
Langesund, Norway
number theory
1954
Kodaira Kunihiko
Tokyo, Japan
algebraic geometry
1954
Serre, Jean-Pierre
Bages, France
algebraic topology
1958
Roth, Klaus
Breslau, Germany
number theory
1958
Thom, René
Montbéliard, France
topology
1962
Hörmander, Lars
Mjällby, Sweden
partial differential equations
1962
Milnor, John
Orange, New Jersey, U.S.
differential topology
1966
Atiyah, Michael
London, England
topology
1966
Cohen, Paul
Long Branch, New Jersey, U.S.
set theory
1966
Grothendieck, Alexandre
Berlin, Germany
algebraic geometry
1966
Smale, Stephen
Flint, Michigan, U.S.
topology
1970
Baker, Alan
London, England
number theory
1970
Hironaka Heisuke
Yamaguchi prefecture, Japan
algebraic geometry
1970
Novikov, Sergey
Gorky, Russia, U.S.S.R.
topology
1970
Thompson, John
Ottawa, Kansas, U.S.
group theory
1974
Bombieri, Enrico
Milan, Italy
number theory
1974
Mumford, David
Worth, Sussex, England
algebraic geometry
1978
Deligne, Pierre
Brussels, Belgium
algebraic geometry
1978
Fefferman, Charles
Washington, D.C., U.S.
classical analysis
1978
Margulis, Gregori
Moscow, Russia, U.S.S.R.
Lie groups
1978
Quillen, Daniel
Orange, New Jersey, U.S.
algebraic K-theory
1983*
Connes, Alain
Darguignan, France
operator theory
1983*
Thurston, William
Washington, D.C., U.S.
topology
1983*
Yau, Shing-Tung
Shantou, China
differential geometry
1986
Donaldson, Simon
Cambridge, Cambridgeshire, England
topology
1986
Faltings, Gerd
Gelsenkirchen, West Germany
Mordell conjecture
1986
Freedman, Michael
Los Angeles, California, U.S.
Poincaré conjecture
1990
Drinfeld, Vladimir
Kharkov, Ukraine, U.S.S.R.
algebraic geometry
1990
Jones, Vaughan
Gisborne, New Zealand
knot theory
1990
Mori Shigefumi
Nagoya, Japan
algebraic geometry
1990
Witten, Edward
Baltimore, Maryland, U.S.
superstring theory
1994
Bourgain, Jean
Ostend, Belgium
analysis
1994
Lions, Pierre-Louis
Grasse, France
partial differential equations
1994
Yoccoz, Jean-Christophe
Paris, France
dynamical systems
1994
Zelmanov, Efim
Khabarovsk, Russia, U.S.S.R.
group theory
1998
Borcherds, Richard
Cape Town, South Africa
mathematical physics
1998
Gowers, William
Marlborough, Wiltshire, England
functional analysis
1998
Kontsevich, Maxim
Khimki, Russia, U.S.S.R.
mathematical physics
1998
McMullen, Curtis
Berkeley, California, U.S.
chaos theory
2002
Lafforgue, Laurent
Antony, France
number theory
2002
Voevodsky, Vladimir
Moscow, Russia, U.S.S.R.
algebraic geometry
2006
Okounkov, Andrei
Moscow, Russia, U.S.S.R.
mathematical physics
2006
Perelman, Grigori
U.S.S.R.
geometry
2006
Tao, Terence
Adelaide, Australia
partial differential equations
2006
Werner, Wendelin
Cologne, Germany
geometry
2010
Lindenstrauss, Elon
Jerusalem
ergodic theory
2010
Ngo Bao Chau
Hanoi, Vietnam
algebraic geometry
2010
Smirnov, Stanislav
Leningrad, Russia, U.S.S.R.
mathematical physics
2010
Villani, Cédric
Brive-la-Gaillarde, France
mathematical physics
2014
Avila, Artur
Rio de Janeiro, Brazil
dynamic systems theory
2014
Bhargava, Manjul
Hamilton, Ontario, Canada
geometry of numbers
2014
Hairer, Martin
Switzerland
stochastic partial differential equations
2014
Mirzakhani, Maryam
Tehrān, Iran
Riemann surfaces
2018
Birkar, Caucher
Marīvān, Iran
algebraic geometry
2018
Figalli, Alessio
Rome, Italy
optimal transport, calculus of variations
2018
Scholze, Peter
Dresden, Germany
arithmetic algebraic geometry
2018
Venkatesh, Akshay
New Delhi, India
number theory
2022
Duminil-Copin, Hugo
Châtenay-Malabry, France
statistical physics
2022
Huh, June
Stanford, California, U.S.
geometric combinatorics
2022
Maynard, James
Chelmsford, England
analytic number theory
2022
Viazovska, Maryna
Kyiv, Ukraine
sphere packing
The Fields Medal is a good indicator of current fertile areas of mathematical research, as the winners have generally made contributions that opened up whole fields or integrated technical ideas and tools from a wide variety of disciplines. A preponderance of winners worked in highly abstract and integrative fields such as algebraic geometry and algebraic topology. This is to some extent a reflection of the influence and power of the French consortium of mathematicians, writing since 1939 under the name of Nicolas Bourbaki, which in its multivolume Éléments de mathématiques has sought a modern, rigorous, and comprehensive treatment of all of mathematics and mathematical foundations. However, medals have also been awarded for work in more classical fields of mathematics and for mathematical physics, including a number for solutions to problems that David Hilbert enunciated at the International Congress of Mathematicians in Paris in 1900.
A marked clustering of Fields Medalists may be observed within a few research institutions. In particular, almost half of the medalists have held appointments at the Institute for Advanced Study, Princeton, N.J., U.S.
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