Fields Medal Winners

Alain Connes (French: [alɛ̃ kɔn]; born 1 April 1947) is a French mathematician. He teaches at the Collège de France, IHÉS, Ohio State University, and Vanderbilt University. He served as an Invited Professor at the Conservatoire national des arts et métiers in 2000.

Alan Baker (19 August 1939 – 4 February 2018) was an English mathematician. He studied effective methods in number theory. These methods came from transcendental number theory.

Alexander Grothendieck (; German: [ˈɡroːtn̩diːk]; French: [ɡʁɔtɛndik]; 28 March 1928 – 13 November 2014) became the main figure in modern algebraic geometry. His work expanded the field. It added commutative algebra, homological algebra, sheaf theory, and category theory to its bases. His "relative" view made big jumps in pure mathematics. Many call him the greatest mathematician of the 20th century. Grothendieck was born in Germany and grew up there.

Andrei Yuryevich Okounkov (Russian: Андре́й Ю́рьевич Окунько́в, Andrej Okun'kov) (born July 26, 1969) is a Russian mathematician. He studies representation theory and its use in algebraic geometry, mathematical physics, probability theory, and special functions. He is a professor at Columbia University. He supervises the HSE International Laboratory of Representation Theory and Mathematical Physics. In 2006, he won the Fields Medal for linking probability, representation theory, and algebraic geometry.

Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician. He worked on analytic number theory. He also studied the theory of automorphic forms. He connected these forms to spectral theory. He won the Fields Medal in 1950.

Charles Louis Fefferman (born April 18, 1949) is an American mathematician. He works at Princeton University. His main research area is mathematical analysis.

Curtis Tracy McMullen (born May 21, 1958) is an American mathematician. He holds the Cabot Professor of Mathematics at Harvard University. He won the Fields Medal in 1998 for his work on complex dynamics, hyperbolic geometry, and Teichmüller theory.

Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) is an American mathematician. From 1984 to 2006, he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. He created higher algebraic K-theory. For this work, he won the Cole Prize in 1975 and the Fields Medal in 1978.

David Bryant Mumford, born June 11, 1937, is an American mathematician. He earned distinction in algebraic geometry and vision and pattern theory research. He won the Fields Medal and received a MacArthur Fellowship. In 2010, the National Medal of Science went to him. David Mumford currently serves as a University Professor Emeritus in the Division of Applied Mathematics at Brown University.

Edward Witten, born August 26, 1951, is an American theoretical physicist. He teaches mathematical physics at the Institute for Advanced Study in Princeton, New Jersey. Witten researches string theory, quantum gravity, and supersymmetric quantum field theories, among other mathematical physics areas. Witten's work greatly affected pure mathematics. In 1990, he became the first physicist awarded a Fields Medal by the International Mathematical Union. This honor recognized his 1981 proof of the positive energy theorem in general relativity.

Efim Isaakovich Zelmanov, born September 7, 1955, in Khabarovsk, Russia, is a Russian-American mathematician. He studied combinatorial problems in nonassociative algebra and group theory. Zelmanov solved the restricted Burnside problem. He won a Fields Medal at the International Congress of Mathematicians in Zürich in 1994. Zelmanov came from a Jewish family in Khabarovsk, Soviet Union (now Russia). He started at Novosibirsk State University in 1972 at age 17. He earned his doctoral degree at Novosibirsk State University.

Enrico Bombieri, born November 26, 1940, in Milan, is an Italian mathematician. He studies analytic number theory, Diophantine geometry, complex analysis, and group theory. Bombieri won a Fields Medal in 1974. Bombieri is Professor Emeritus in the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey.

Gerd Faltings, born July 28, 1954, is a German mathematician. He studies arithmetic geometry.

Grigori Yakovlevich Perelman, born June 13, 1966, is a Russian mathematician. He contributed to Riemannian geometry and geometric topology. Perelman proved the soul conjecture in 1994. In 2003, he proved Thurston's geometrization conjecture. The proof confirmed in 2006 solved the Poincaré conjecture affirmatively. In August 2006, Perelman received the Fields Medal for his geometry contributions and revolutionary insights into analysis and geometry.

Gregori Aleksandrovich Margulis (Russian: Григо́рий Алекса́ндрович Маргу́лис, first name often Gregory, Grigori or Grigory; born February 24, 1946) is a Russian-American mathematician. He studied lattices in Lie groups and introduced ergodic theory methods into diophantine approximation. Margulis received a Fields Medal in 1978 and a Wolf Prize in Mathematics in 2005, making him the seventh mathematician with both awards. In 1991, he joined Yale University's faculty as the Erastus L. De Forest Professor of Mathematics.

Heisuke Hironaka (広中 平祐, Hironaka Heisuke, born April 9, 1931) is a Japanese mathematician. Hironaka entered Kyoto University in 1949. After finishing his undergraduate work at Kyoto University, he earned his Ph.D. in 1960 from Harvard, guided by Oscar Zariski. Hironaka won the Fields Medal in 1970. He proved in 1964 that singularities of algebraic varieties admit resolutions in characteristic zero. This means any algebraic variety can become birationally equivalent to a variety with no singularities.

Jean, Baron Bourgain (French: [buʁɡɛ̃]; February 28, 1954 – December 22, 2018) was a Belgian mathematician. Bourgain taught at the University of Illinois, Urbana-Champaign. From 1985 to 1995, he served as a professor at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France. He worked at the Institute for Advanced Study in Princeton, New Jersey from 1994 until 2018. Bourgain edited the Annals of Mathematics. From 2012 to 2014, UC Berkeley appointed him a visiting scholar.

Jean-Christophe Yoccoz (May 29, 1957 – September 3, 2016) was a French mathematician. Yoccoz won the Fields Medal in 1994 for his work on dynamical systems.

Jean-Pierre Serre (French: [sɛʁ]; born September 15, 1926) is a French mathematician. Serre made contributions to algebraic topology, algebraic geometry, and algebraic number theory. Serre won the Fields Medal in 1954 and the first Abel Prize in 2003.

Jesse Douglas (July 3, 1897 – September 7, 1965) was an American mathematician and Fields Medalist. Douglas is known for finding the general solution to the Problem of Plateau.

John Griggs Thompson (born October 13, 1932) is a mathematician at the University of Florida. Thompson worked in the field of finite groups. Thompson won the Fields Medal in 1970, the Wolf Prize in 1992, and the 2008 Abel Prize.

John Willard Milnor (born February 20, 1931) is an American mathematician. Milnor studied differential topology, K-theory, and dynamical systems. Milnor is a distinguished professor at Stony Brook University. Milnor is one of the four mathematicians who won the Fields Medal, the Wolf Prize, and the Abel Prize, alongside Pierre Deligne, Jean-Pierre Serre, and John G. Thompson.

Klaus Friedrich Roth (October 29, 1925 – November 10, 2015) was a German-born British mathematician. He won the Fields Medal for proving Roth's theorem on the Diophantine approximation of algebraic numbers. Roth moved to England in 1933 to escape the Nazis. He studied at Cambridge and University College London, earning his doctorate in 1950. Roth taught at University College London until 1966. He then took a chair at Imperial College London. He retired in 1988. Roth made major contributions to the theory of progress beyond his work on Diophantine approximation.

Kunihiko Kodaira (小平 邦彦, Kodaira Kunihiko, March 16, 1915 – July 26, 1997) was a Japanese mathematician. He made distinguished work in algebraic geometry and the theory of complex manifolds. Kodaira founded the Japanese school of algebraic geometers. He received a Fields Medal in 1954. He became the first Japanese national to get this honor.

Lars Valerian Ahlfors (April 18, 1907 – October 11, 1996) was a Finnish mathematician. He is remembered for his work in Riemann surfaces and his text on complex analysis.

Lars Valter Hörmander (January 24, 1931 – November 25, 2012) was a Swedish mathematician. He became "the foremost contributor to the modern theory of linear partial differential equations." In 1962, he received the Fields Medal. The Wolf Prize came in 1988. The Leroy P. Steele Prize was awarded in 2006. His book, *Analysis of Linear Partial Differential Operators I–IV*, is a standard work on linear partial differential operators. Hörmander finished his Ph.D. in 1955 at Lund University. Hörmander then worked at Stockholm University, Stanford University, and the Institute

Laurent Lafforgue (French: [lafɔʁɡ]; born November 6, 1966) is a French mathematician. He made outstanding contributions to Langlands' program in number theory and analysis. Lafforgue proved the Langlands conjectures for the automorphism group of a function field. Lafforgue's main contribution to solving this problem was constructing compactifications of certain moduli stacks of shtukas. This proof took more than six years of focused work. In 2002, at the 24th International Congress of Mathematicians in Beijing, China, he received the Fi

Laurent-Moïse Schwartz (French: [ʃvaʁts]; March 5, 1915 – July 4, 2002) was a French mathematician. He pioneered the theory of distributions. This theory gives a clear meaning to objects like the Dirac delta function. Schwartz won the Fields Medal in 1950 for his work on the theory of distributions. He taught at the École polytechnique for several years.

Maxim Lvovich Kontsevich (Russian: Макси́м Льво́вич Конце́вич; born August 25, 1964) is a Russian and French mathematician. He teaches at the Institut des Hautes Études Scientifiques and holds a distinguished professorship at the University of Miami. Kontsevich won the Henri Poincaré Prize in 1997. He earned the Fields Medal in 1998. The Crafoord Prize came in 2008. The Shaw Prize and Fundamental Physics Prize arrived in 2012. He received the Breakthrough Prize in Mathematics in 2014.

Sir Michael Francis Atiyah (April 22, 1929 – January 11, 2019) was a British-Lebanese mathematician specializing in geometry. Atiyah grew up in Sudan and Egypt. He spent most of his academic career in the United Kingdom at Oxford and Cambridge. He also worked in the United States at the Institute for Advanced Study. Atiyah served as President of the Royal Society from 1990 to 1995. He founded the Isaac Newton Institute from 1990 to 1996. He was master of Trinity College, Cambridge (1990–1997). He served as chancellor of the University of Leicester (1995–2005). He was also President of the Royal Society of Edinburgh.

Michael Hartley Freedman (born April 21, 1951) is an American mathematician at Microsoft Station Q, a research group at the University of California, Santa Barbara. In 1986, he won a Fields Medal for his work on the 4-dimensional Generalized Poincaré conjecture. Freedman and Robion Kirby proved an exotic R4 manifold exists.

Ngô Bảo Châu (Vietnamese: [ŋo ɓa᷉ːʊ̯ cəʊ̯], born June 28, 1972) is a Vietnamese-French mathematician at the University of Chicago. He is known for proving the fundamental lemma for automorphic forms proposed by Robert Langlands and Diana Shelstad. He is the first Vietnamese national to win the Fields Medal.

For other people named Paul Cohen, see Paul Cohen (disambiguation). Do not confuse him with Paul Cohn. Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician. He earned a Fields Medal for proving that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory.

Pierre René, Viscount Deligne (French: [dəliɲ]; born October 3, 1944) is a Belgian mathematician. He gained recognition for his work on the Weil conjectures, completing a proof in 1973. Deligne won the 2013 Abel Prize, the 2008 Wolf Prize, the 1988 Crafoord Prize, and the 1978 Fields Medal.

Pierre-Louis Lions (French: [ljɔ̃ːs]; born August 11, 1956) is a French mathematician. He received the 1994 Fields Medal.

René Frédéric Thom (French: [ʁəne tɔm]; September 2, 1923 – October 25, 2002) was a French mathematician. Thom built his reputation as a topologist, moving into singularity theory. He became world-famous among academics and the public for his work founding catastrophe theory (later developed by Erik Christopher Zeeman). He received the Fields Medal in 1958.

Richard Ewen Borcherds (born November 29, 1959) is a British-American mathematician. He works in quantum field theory. Borcherds earned the Fields Medal in 1998 for his work in lattices, number theory, group theory, and infinite-dimensional algebras.

Sergei Petrovich Novikov (Serguei; born March 20, 1938) is a Soviet and Russian mathematician. He studies algebraic topology and soliton theory. Novikov won the Fields Medal in 1970.

Shigefumi Mori (森 重文; born February 23, 1951) is a Japanese mathematician. Mori works in algebraic geometry, focusing on the classification of three-folds.

Shing-Tung Yau (Chinese: 丘成桐; pinyin: Qiū Chéngtóng; Cantonese Yale: Yāu Sìngtùng), born April 4, 1949, is a Chinese-born mathematician who became a naturalized American citizen. He won the Fields Medal in 1982. Today, Yau holds the William Caspar Graustein Professor of Mathematics position at Harvard University. Yau's research focuses mostly on differential geometry, specifically geometric analysis. His work affects both physics and mathematics. Yau works at the meeting point of geometry and theoretical physics. His proof of the positive energy theorem in general relativity showed sixty.

Sir Simon Kirwan Donaldson (born August 20, 1957) is an English mathematician. He studies the topology of smooth four-dimensional manifolds and Donaldson–Thomas theory. Donaldson is a permanent member of the Simons Center for Geometry and Physics at Stony Brook University and a Professor in Pure Mathematics at Imperial College London.

Stanislav Konstantinovich Smirnov (Станисла́в Константи́нович Cмирно́в; born September 3, 1970) is a Russian mathematician. He works at the University of Geneva. Smirnov received the Fields Medal in 2010. His research covers complex analysis, dynamical systems, and probability theory.

Stephen Smale (born July 15, 1930) is an American mathematician. He researches topology, dynamical systems, and mathematical economics. Smale won the Fields Medal in 1966. Smale spent over thirty years on the mathematics faculty at the University of California, Berkeley (1960–1961 and 1964–1995).

Terence Chi-Shen Tao (born July 17, 1975) is an Australian-American mathematician. Tao studies various math areas. He focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing, and analytic number theory. As of 2015, Tao holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Tao won the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He is the second ethnic Chinese person to win the Fields medal.

Sir William Timothy Gowers, born November 20, 1963, is a British mathematician. He serves as a Royal Society Research Professor at the University of Cambridge's Department of Pure Mathematics and Mathematical Statistics. He also holds the Rouse Ball chair and is a Fellow of Trinity College, Cambridge. In 1998, he earned the Fields Medal for research linking functional analysis and combinatorics.

Sir Vaughan Frederick Randal Jones, born December 31, 1952, is a New Zealand mathematician. He studied von Neumann algebras and knot polynomials. He won the Fields Medal in 1990. Jones wore a New Zealand rugby jersey during his Fields Medal acceptance speech in Kyoto.

Vladimir Gershonovich Drinfeld (Ukrainian: Володи́мир Ге́ршонович Дрінфельд; Russian: Влади́мир Ге́ршонович Дри́нфельд), born February 14, 1954, is a Soviet-American mathematician. He works at the University of Chicago. Drinfeld linked algebraic geometry over finite fields with number theory. This work used elliptic modules and the geometric Langlands correspondence, focusing on automorphic forms. Drinfeld introduced the quantum group concept; Michio Jimbo discovered it at the same time.

Vladimir Alexandrovich Voevodsky, born June 4, 1966, and died September 30, 2017, was a Russian-American mathematician. His work developed homotopy theory for algebraic varieties. He formulated motivic cohomology. Voevodsky received the Fields Medal in 2002. He also proved the Milnor conjecture and motivic Bloch-Kato conjectures. He established univalent foundations of mathematics and homotopy type theory.

Wendelin Werner was born September 23, 1968, in Germany. He is a French mathematician studying random processes. This includes self-avoiding random walks, Brownian motion, Schramm–Loewner evolution, and related probability theory and mathematical physics theories. In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain, Werner earned the Fields Medal. The award recognized his work on stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory. Werner is a professor at ETH Zürich.

William Paul Thurston, who lived from October 30, 1946, to August 21, 2012, was an American mathematician. He pioneered low-dimensional topology. In 1982, he won the Fields Medal for his work on 3-manifolds. From 2003 until his death, Thurston taught mathematics and computer science at Cornell University.