Fields Medal

The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields.<ref name="Fields Institute About Us">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the Nobel Prize of Mathematics,<ref name=":0">Template:Cite journal</ref><ref name=":2">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name=":3">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria.<ref>Template:Cite journal</ref> According to the annual Academic Excellence Survey by ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> and in another reputation survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics.<ref>Template:Cite book</ref><ref>Template:Cite journal</ref>

The prize includes a monetary award which, since 2006, has been Template:CA$15,000.<ref name="BBC">Template:Cite news</ref><ref>"Israeli wins 'Nobel' of Mathematics" Template:Webarchive, The Jerusalem Post</ref> Fields was instrumental in establishing the award, designing the medal himself, and funding the monetary component, though he died before it was established and his plan was overseen by John Lighton Synge.<ref name="Fields Institute About Us" />

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. In 2014, the Iranian mathematician Maryam Mirzakhani became the first female Fields Medalist.<ref name="Farsnews">Template:Cite news</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref>Template:Cite news</ref> In total, 64 people have been awarded the Fields Medal.

The most recent group of Fields Medalists received their awards on 5 July 2022 in an online event which was live-streamed from Helsinki, Finland. It was originally meant to be held in Saint Petersburg, Russia, but was moved following the 2022 Russian invasion of Ukraine.

Conditions of the award

The Fields Medal has for a long time been regarded as the most prestigious award in the field of mathematics and is often described as the Nobel Prize of Mathematics.<ref name=":0" /><ref name=":2" /><ref name=":3" /> Unlike the Nobel Prize, the Fields Medal is only awarded every four years. The Fields Medal also has an age limit: a recipient must be under age 40 on 1 January of the year in which the medal is awarded. The under-40 rule is based on Fields's 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."<ref>Template:Harvnb</ref> Moreover, an individual can only be awarded one Fields Medal; winners are ineligible to be awarded future medals.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

First awarded in 1936, 64 people have won the medal as of 2022.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> With the exception of two PhD holders in physics (Edward Witten and Martin Hairer),<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> only people with a PhD in mathematics have won the medal.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

List of Fields medalists

In certain years, the Fields medalists have been officially cited for particular mathematical achievements, while in other years such specificities have not been given. However, in every year that the medal has been awarded, noted mathematicians have lectured at the International Congress of Mathematicians on each medalist's body of work. In the following table, official citations are quoted when possible (namely for the years 1958, 1998, and every year since 2006). For the other years through 1986, summaries of the ICM lectures, as written by Donald Albers, Gerald L. Alexanderson, and Constance Reid, are quoted.<ref>Albers, Donald J.; Alexanderson, G. L.; Reid, Constance. International mathematical congresses. An illustrated history 1893–1986. Rev. ed. including ICM 1986. Springer-Verlag, New York, 1986</ref> In the remaining years (1990, 1994, and 2002), part of the text of the ICM lecture itself has been quoted. The upcoming awarding of the Fields Medal at the 2026 International Congress of the International Mathematical Union is planned to take place in Philadelphia.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Year	ICM location	Medalists<ref name=IMU>{{#invoke:citation/CS1|citation		CitationClass=web }}</ref>	Affiliation (when awarded)	Affiliation (current/last)	Reasons
1936	Oslo, Norway	File:Lars Ahlfors - MFO.jpg	Template:Sortname	University of Helsinki, Finland	Harvard University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Awarded medal for research on covering surfaces related to Riemann surfaces of inverse functions of entire and meromorphic functions. Opened up new fields of analysis."<ref name="36reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
		File:Portrait of Jesse Douglas in c. 1932.jpg	Template:Sortname	Massachusetts Institute of Technology, US	City College of New York, US<ref>Template:Cite encyclopedia</ref><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Did important work on the Plateau problem which is concerned with finding minimal surfaces connecting and determined by some fixed boundary."<ref name="36reasons" />
1950	Cambridge, US	File:LaurentSchwartz.jpg	Template:Sortname	University of Nancy, France	University of Paris VII, France<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>Template:Cite book</ref>	"Developed the theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics."<ref name="50reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
		File:Atle Selberg.jpg	Template:Sortname	Institute for Advanced Study, US	Institute for Advanced Study, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Developed generalizations of the sieve methods of Viggo Brun; achieved major results on zeros of the Riemann zeta function; gave an elementary proof of the prime number theorem (with P. Erdős), with a generalization to prime numbers in an arbitrary arithmetic progression."<ref name="50reasons" />
1954	Amsterdam, Netherlands	File:Kodaira Kunihiko.jpg	Template:Sortname	Princeton University, US, University of Tokyo, Japan and Institute for Advanced Study, US<ref name="mathunion.org">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	University of Tokyo, Japan<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Achieved major results in the theory of harmonic integrals and numerous applications to Kählerian and more specifically to algebraic varieties. He demonstrated, by sheaf cohomology, that such varieties are Hodge manifolds."<ref name="54reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
		File:Jean-Pierre Serre, Erlangen 1997.JPG	Template:Sortname	University of Nancy, France	Collège de France, France<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>Template:Cite encyclopedia</ref>	"Achieved major results on the homotopy groups of spheres, especially in his use of the method of spectral sequences. Reformulated and extended some of the main results of complex variable theory in terms of sheaves."<ref name="54reasons" />
1958	Edinburgh, UK		Template:Sortname	University College London, UK	Imperial College London, UK<ref>Template:Harvnb</ref>	"for solving a famous problem of number theory, namely, the determination of the exact exponent in the Thue-Siegel inequality"<ref name="hopf">H. Hopf. Proceedings of the International Congress of Mathematicians 1958. Template:Webarchive Report of the Inaugural Session. p. liv</ref>
		File:René Thom.jpeg	Template:Sortname	University of Strasbourg, France	Institut des Hautes Études Scientifiques, France<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"for creating the theory of 'Cobordisme' which has, within the few years of its existence, led to the most penetrating insight into the topology of differentiable manifolds."<ref name="hopf" />
1962	Stockholm, Sweden	File:Lars Hörmander.jpg	Template:Sortname	Stockholm University, Sweden	Lund University, Sweden<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Worked in partial differential equations. Specifically, contributed to the general theory of linear differential operators. The questions go back to one of Hilbert's problems at the 1900 congress."<ref name="62reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
		File:John Milnor, 1993 Oct (portioned).jpg	Template:Sortname	Princeton University, US	Stony Brook University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology."<ref name="62reasons" />
1966	Moscow, USSR	File:Atiyah-Hirzebruch crop.jpeg	Template:Sortname	University of Oxford, UK	University of Edinburgh, UK<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Did joint work with Hirzebruch in K-theory; proved jointly with Singer the index theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the 'Lefschetz formula'."<ref name="66reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
			Template:Sortname	Stanford University, US	Stanford University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Used technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. The latter problem was the first of Hilbert's problems of the 1900 Congress."<ref name="66reasons" />
		File:Alexander Grothendieck.jpg	Template:Sortname	Institut des Hautes Études Scientifiques, France	Centre National de la Recherche Scientifique, France<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Built on work of Weil and Zariski and effected fundamental advances in algebraic geometry. He introduced the idea of K-theory (the Grothendieck groups and rings). Revolutionized homological algebra in his celebrated ‘Tôhoku paper’."<ref name="66reasons" />
		File:Stephen Smale2.jpg	Template:Sortname	University of California, Berkeley, US	City University of Hong Kong, Hong Kong<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Worked in differential topology where he proved the generalized Poincaré conjecture in dimension <math>n \geq 5</math>: Every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. Introduced the method of handle-bodies to solve this and related problems."<ref name="66reasons" />
1970	Nice, France	File:Alan Baker.jpg	Template:Sortname	University of Cambridge, UK	Trinity College, Cambridge, UK<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Generalized the Gelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified."<ref name="70reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
		File:Hironaka heisuke 1976.jpg	Template:Sortname	Harvard University, US	Kyoto University, Japan<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Generalized work of Zariski who had proved for dimension ≤ 3 the theorem concerning the resolution of singularities on an algebraic variety. Hironaka proved the results in any dimension."<ref name="70reasons" />
			Template:Sortname	Moscow State University, USSR	Steklov Mathematical Institute, Russia Moscow State University, Russia University of Maryland-College Park, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Made important advances in topology, the most well-known being his proof of the topological invariance of the Pontryagin classes of the differentiable manifold. His work included a study of the cohomology and homotopy of Thom spaces."<ref name="70reasons" />
		File:John Griggs Thompson (cropped).jpg	Template:Sortname	University of Cambridge, UK	University of Cambridge, UK University of Florida, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Proved jointly with W. Feit that all non-cyclic finite simple groups have even order. The extension of this work by Thompson determined the minimal simple finite groups, that is, the simple finite groups whose proper subgroups are solvable."<ref name="70reasons" />
1974	Vancouver, Canada	File:Enrico Bombieri.jpg	Template:Sortname	University of Pisa, Italy	Institute for Advanced Study, US<ref>Template:Cite book</ref>	"Major contributions in the primes, in univalent functions and the local Bieberbach conjecture, in theory of functions of several complex variables, and in theory of partial differential equations and minimal surfaces – in particular, to the solution of Bernstein's problem in higher dimensions."<ref name="74reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
		File:Mumford2.jpg	Template:Sortname	Harvard University, US	Brown University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Contributed to problems of the existence and structure of varieties of moduli, varieties whose points parametrize isomorphism classes of some type of geometric object. Also made several important contributions to the theory of algebraic surfaces."<ref name="74reasons" />
1978	Helsinki, Finland	File:Pierre Deligne (2005) (cropped).jpg	Template:Sortname	Institut des Hautes Études Scientifiques, France	Institute for Advanced Study, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Gave solution of the three Weil conjectures concerning generalizations of the Riemann hypothesis to finite fields. His work did much to unify algebraic geometry and algebraic number theory."<ref name="78reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
		File:Charles Fefferman.jpg	Template:Sortname	Princeton University, US	Princeton University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results."<ref name="78reasons" />
		File:Grigory Margulis 1978 (portioned).jpg	Template:Sortname	Moscow State University, USSR	Yale University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Provided innovative analysis of the structure of Lie groups. His work belongs to combinatorics, differential geometry, ergodic theory, dynamical systems, and Lie groups."<ref name="78reasons" />
		File:DQuillen.jpg	Template:Sortname	Massachusetts Institute of Technology, US	University of Oxford, UK<ref>Template:Cite journal</ref>	"The prime architect of the higher algebraic K-theory, a new tool that successfully employed geometric and topological methods and ideas to formulate and solve major problems in algebra, particularly ring theory and module theory."<ref name="78reasons" />
1982	Warsaw, Poland	File:Alain Connes.jpg	Template:Sortname	Institut des Hautes Études Scientifiques, France	Institut des Hautes Études Scientifiques, France Collège de France, France Ohio State University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Contributed to the theory of operator algebras, particularly the general classification and structure theorem of factors of type III, classification of automorphisms of the hyperfinite factor, classification of injective factors, and applications of the theory of C*-algebras to foliations and differential geometry in general."<ref name="82reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
		File:William Thurston.jpg	Template:Sortname	Princeton University, US	Cornell University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Revolutionized study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry. Contributed idea that a very large class of closed 3-manifolds carry a hyperbolic structure."<ref name="82reasons" />
		File:Shing-Tung Yau at Harvard.jpg	Template:Sortname	Institute for Advanced Study, US	Tsinghua University, China<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Made contributions in differential equations, also to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge–Ampère equations."<ref name="82reasons" />
1986	Berkeley, US	File:Simon Donaldson.jpg	Template:Sortname	University of Oxford, UK	Imperial College London, UK<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref> Stony Brook University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Received medal primarily for his work on topology of four-manifolds, especially for showing that there is a differential structure on euclidian four-space which is different from the usual structure."<ref name="86reasons">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref name="IMU Fields Medal 1986">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
		File:Gerd Faltings MFO.jpg	Template:Sortname	Princeton University, US	Max Planck Institute for Mathematics, Germany<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Using methods of arithmetic algebraic geometry, he received medal primarily for his proof of the Mordell Conjecture."<ref name="86reasons" />
		File:Michael Freedman, circa 1970s (re-scanned C; headshot).jpg	Template:Sortname	University of California, San Diego, US	Microsoft Station Q, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Developed new methods for topological analysis of four-manifolds. One of his results is a proof of the four-dimensional Poincaré Conjecture."<ref name="86reasons" />
1990	Kyoto, Japan		Template:Sortname	B Verkin Institute for Low Temperature Physics and Engineering, USSR<ref>Template:Cite encyclopedia</ref>	University of Chicago, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Drinfeld's main preoccupation in the last decade [are] Langlands' program and quantum groups. In both domains, Drinfeld's work constituted a decisive breakthrough and prompted a wealth of research."<ref>Yuri Ivanovich Manin. On the mathematical work of Vladimir Drinfeld. Proceedings of the International Congress of Mathematicians 1990. Volume I Template:Webarchive pp. 3–7</ref>
		File:Vaughan Jones p1190550.jpg	Template:Sortname	University of California, Berkeley, US	University of California, Berkeley, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref> Vanderbilt University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Jones discovered an astonishing relationship between von Neumann algebras and geometric topology. As a result, he found a new polynomial invariant for knots and links in 3-space."<ref>Joan S. Birman. The work of Vaughan F. R. Jones. Proceedings of the International Congress of Mathematicians 1990. Volume I Template:Webarchive pp. 9–18</ref>
		File:Shigefumi Mori.jpg	Template:Sortname	Kyoto University, Japan	Kyoto University, Japan<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"The most profound and exciting development in algebraic geometry during the last decade or so was [...] Mori's Program in connection with the classification problems of algebraic varieties of dimension three." "Early in 1979, Mori brought to algebraic geometry a completely new excitement, that was his proof of Hartshorne's conjecture."<ref>Heisuke Hironaka. On the work of Shigefumi Mori. Proceedings of the International Congress of Mathematicians 1990. Volume I Template:Webarchive pp. 19–25</ref>
		File:Edward Witten at Harvard.jpg	Template:Sortname	Institute for Advanced Study, US	Institute for Advanced Study, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	citation	CitationClass=web }}</ref>
1994	Zürich, Switzerland	File:Jean Bourgain (vertical crop).jpg	Template:Sortname	Institut des Hautes Études Scientifiques, France	Institute for Advanced Study, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Bourgain's work touches on several central topics of mathematical analysis: the geometry of Banach spaces, convexity in high dimensions, harmonic analysis, ergodic theory, and finally, nonlinear partial differential equations from mathematical physics."<ref>Luis Caffarelli. The work of Jean Bourgain. Proceedings of the International Congress of Mathematicians 1994. Volume I Template:Webarchive pp. 3–5</ref>
		File:Pierre-Louis Lions par Philippe Binant.jpg	Template:Sortname	University of Paris 9, France	Collège de France, France École polytechnique, France<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"His contributions cover a variety of areas, from probability theory to partial differential equations (PDEs). Within the PDE area he has done several beautiful things in nonlinear equations. The choice of his problems have always been motivated by applications."<ref>S. R. S. Varadhan. The work of Pierre-Louis Lions. Proceedings of the International Congress of Mathematicians 1994. Volume I Template:Webarchive pp. 6–10</ref>
		File:Jean-Christophe Yoccoz.jpg	Template:Sortname	Paris-Sud 11 University, France	Collège de France, France<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Yoccoz obtained a very enlightening proof of Bruno's theorem, and he was able to prove the converse [...] Palis and Yoccoz obtained a complete system of C∞ conjugation invariants for Morse-Smale diffeomorphisms."<ref>Adrien Douady. Presentation de Jean-Christophe Yoccoz. Proceedings of the International Congress of Mathematicians 1994. Volume I Template:Webarchive pp. 11–16</ref>
		File:EfimIZelmanov.jpg	Template:Sortname	University of Wisconsin-Madison University of Chicago, US	Steklov Mathematical Institute, Russia, University of California, San Diego, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For the solution of the restricted Burnside problem."<ref>Walter Feit. On the Work of Efim Zelmanov. Proceedings of the International Congress of Mathematicians 1994. Volume I Template:Webarchive pp. 17–24</ref>
1998	Berlin, Germany	File:Richard Borcherds.jpg	Template:Sortname	University of California, Berkeley, US University of Cambridge, UK	University of California, Berkeley, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex algebras and Borcherds' Lie algebras, the proof of the Conway–Norton moonshine conjecture and the discovery of a new class of automorphic infinite products."<ref name="1998cer">Opening ceremony. Proceedings of the International Congress of Mathematicians 1998. Volume I Template:Webarchive pp. 46–48</ref>
		File:Gowers timothy 2011.jpg	Template:Sortname	University of Cambridge, UK	University of Cambridge, UK<ref>Template:Cite encyclopedia</ref>	"For his contributions to functional analysis and combinatorics, developing a new vision of infinite-dimensional geometry, including the solution of two of Banach's problems and the discovery of the so called Gowers' dichotomy: every infinite dimensional Banach space contains either a subspace with many symmetries (technically, with an unconditional basis) or a subspace every operator on which is Fredholm of index zero."<ref name="1998cer" />
		File:Maxim Kontsevich 1994 (headshot).jpg	Template:Sortname	Institut des Hautes Études Scientifiques, France Rutgers University, US	Institut des Hautes Études Scientifiques, France Rutgers University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his contributions to algebraic geometry, topology, and mathematical physics, including the proof of Witten's conjecture of intersection numbers in moduli spaces of stable curves, construction of the universal Vassiliev invariant of knots, and formal quantization of Poisson manifolds."<ref name="1998cer" />
		File:Curtis T. McMullen, 1994 Aug-Sept (re-scanned, headshot).jpg	Template:Sortname	Harvard University, US	Harvard University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his contributions to the theory of holomorphic dynamics and geometrization of three-manifolds, including proofs of Bers' conjecture on the density of cusp points in the boundary of the Teichmüller space, and Kra's theta-function conjecture."<ref name="1998cer" />
2002	Beijing, China	File:Laurent Lafforgue.png	Template:Sortname	Institut des Hautes Études Scientifiques, France	Institut des Hautes Études Scientifiques, France<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups GLr (r≥1) over function fields of positive characteristic."<ref>Gérard Laumon. The work of Laurent Lafforgue. Proceedings of the International Congress of Mathematicians 2002. Volume I Template:Webarchive pp. 91–97</ref>
		File:VladimirVoevodsky.jpg	Template:Sortname	Institute for Advanced Study, US	Institute for Advanced Study, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"He defined and developed motivic cohomology and the A1-homotopy theory, provided a framework for describing many new cohomology theories for algebraic varieties; he proved the Milnor conjectures on the K-theory of fields."<ref>Christophe Soulé. The work of Vladimir Voevodsky. Proceedings of the International Congress of Mathematicians 2002. Volume I Template:Webarchive pp. 99–103</ref>
2006	Madrid, Spain	File:Andrei Okounkov 1999 (re-scanned, portioned).jpg	Template:Sortname	Princeton University, US	Columbia University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref> University of California, Berkeley, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his contributions bridging probability, representation theory and algebraic geometry."<ref name="2006cer">Opening ceremony. Proceedings of the International Congress of Mathematicians 2006. Volume I Template:Webarchive p. 36</ref>
		File:Grigori Perelman, 1993 (re-scanned) (cropped).jpg	Template:Sortname (declined)	None	St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences, Russia<ref>Template:Cite encyclopedia</ref>	"For his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow."<ref name="2006cer" />
		File:Terence Tao.jpg	Template:Sortname	University of California, Los Angeles, US	University of California, Los Angeles, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory."<ref name="2006cer" />
		File:Wendelin Werner.jpg	Template:Sortname	Paris-Sud 11 University, France	ETH Zurich, Switzerland<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory."<ref name="2006cer" />
2010	Hyderabad, India	File:Elon Lindenstrauss MFO.jpg	Template:Sortname	Hebrew University of Jerusalem, Israel Princeton University, US	Hebrew University of Jerusalem, Israel<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his results on measure rigidity in ergodic theory, and their applications to number theory."<ref name="2010cer">Opening ceremony. Proceedings of the International Congress of Mathematicians 2010. Volume I Template:Webarchive p. 23</ref>
		File:Ngo Bau Chau MFO.jpg	Ngô Bảo Châu	Paris-Sud 11 University, France Institute for Advanced Study, US	University of Chicago, US Institute for Advanced Study, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods."<ref name="2010cer" />
		File:Stanislav Smirnov2005 2.JPG	Template:Sortname	University of Geneva, Switzerland	University of Geneva, Switzerland St. Petersburg State University, Russia<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For the proof of conformal invariance of percolation and the planar Ising model in statistical physics."<ref name="2010cer" />
		File:Cedric Villani at his office 2015 n2 (cropped).jpg	Template:Sortname	École Normale Supérieure de Lyon, France Institut Henri Poincaré, France	Lyon University, France Institut Henri Poincaré, France<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation."<ref name="2010cer" />
2014	Seoul, South Korea	File:Artur Ávila crop.jpg	Template:Sortname	University of Paris VII, France CNRS, France Instituto Nacional de Matemática Pura e Aplicada, Brazil	University of Zurich, Switzerland Instituto Nacional de Matemática Pura e Aplicada, Brazil	"For his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle."<ref name="2014cer">Opening ceremony. Proceedings of the International Congress of Mathematicians 2014. Volume I Template:Webarchive p. 23</ref>
		File:Manjul Bhargava.jpg	Template:Sortname	Princeton University, US	Princeton University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves."<ref name="2014cer" />
		File:Professor Martin Hairer FRS.jpg	Template:Sortname	University of Warwick, UK	École Polytechnique Fédérale de Lausanne, Switzerland Imperial College London, UK	"For his outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations."<ref name="2014cer" />
		File:Maryam-mirzakhani (cropped).jpg	Template:Sortname	Stanford University, US	Stanford University, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces."<ref name="2014cer" />
2018	Rio de Janeiro, Brazil	File:Birkar (cropped01).jpg	Template:Sortname	University of Cambridge, UK	University of Cambridge, UK	"For the proof of the boundedness of Fano varieties and for contributions to the minimal model program."<ref name="2018cer">Opening ceremonies. Proceedings of the International Congress of Mathematicians 2018. Volume I Template:Webarchive pp. 13–16</ref>
		File:Alessio Figalli (cropped).jpg	Template:Sortname	Swiss Federal Institute of Technology Zurich, Switzerland	Swiss Federal Institute of Technology Zurich, Switzerland	"For contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability."<ref name="2018cer" />
		File:Peter Scholze (cropped).jpg	Template:Sortname	University of Bonn, Germany	University of Bonn, Germany	"For having transformed arithmetic algebraic geometry over p-adic fields."<ref name="2018cer" />
		File:Akshay Venkatesh 2014 (cropped).jpg	Template:Sortname	Stanford University, US	Institute for Advanced Study, US<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	"For his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects."<ref name="2018cer" />
2022	Helsinki, FinlandTemplate:Efn	File:Hugo Duminil-Copin in Oberwolfach (cropped).jpg	Template:Sortname	Institut des Hautes Études Scientifiques, France University of Geneva, Switzerland <ref name="unige.ch">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Institut des Hautes Études Scientifiques, France University of Geneva, Switzerland <ref name="unige.ch"/>	citation	CitationClass=web }}</ref>
		File:June Huh - ICM 2018.jpg	Template:Sortname	Princeton University, US	Princeton University, US	"For bringing the ideas of Hodge theory to combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture."<ref name="2022fields" />
		File:James Maynard MFO 2013.jpg	Template:Sortname	University of Oxford, UK	University of Oxford, UK	"For contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation."<ref name="2022fields" />
		File:Maryna Vazovska MFO 2013 crop.jpg	Template:Sortname	École Polytechnique Fédérale de Lausanne, Switzerland	École Polytechnique Fédérale de Lausanne, Switzerland	"For the proof that the <math>E_8</math> lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems in Fourier analysis."<ref name="2022fields" /><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>

Landmarks

The medal was first awarded in 1936 to the Finnish mathematician Lars Ahlfors and the 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.

In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27.<ref>Template:Cite journal</ref> He retains this distinction.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

In 1966, Alexander Grothendieck boycotted the ICM, held in Moscow, to protest against Soviet military actions taking place in Eastern Europe.<ref>Template:Cite journal</ref> Léon Motchane, founder and director of the Institut des Hautes Études Scientifiques, attended and accepted Grothendieck's Fields Medal on his behalf.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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."<ref>Margulis biography Template:Webarchive, School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 27 August 2006.</ref>

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 on 13 December 1981. The awards were announced at the ninth General Assembly of the IMU earlier in the year and awarded at the 1983 Warsaw congress.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

In 1990, Edward Witten became the first physicist to win the award.<ref name="National Science Foundation">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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.<ref>Wiles, Andrew John Template:Webarchive, Encyclopædia Britannica. Retrieved 27 August 2006.</ref> 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.<ref>Fields Medal Prize Winners (1998), 2002 International Congress of Mathematicians. Retrieved 27 August 2006. Template:Webarchive</ref><ref>Template:Cite journal</ref>

In 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal<ref name="BBC" /> and did not attend the congress.<ref>Template:Cite magazine</ref>

In 2014, Maryam Mirzakhani became the first Iranian as well as the first woman to win the Fields Medal, and Artur Avila became the first South American and Manjul Bhargava became the first person of Indian origin to do so.<ref name="CF">Template:Cite book</ref><ref>Template:Cite news</ref>

In 2022, Maryna Viazovska became the first Ukrainian to win the Fields Medal, and June Huh became the first person of Korean ancestry to do so.<ref name="DZH">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name="The Korea Times 2022">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Medal

File:FieldsMedalBack.jpg

The reverse of the Fields Medal

The medal was designed by Canadian sculptor R. Tait McKenzie.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> It is made of 14KT gold, has a diameter of 63.5mm, and weighs 169g.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

• On the obverse is Archimedes and a quote attributed to 1st century AD poet Manilius, which reads in Latin: {{#invoke:Lang|lang}} ("To surpass one's understanding and master the world").<ref>Template:Cite journal</ref><ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> The year number 1933 is written in Roman numerals and contains an error (MCNXXXIII rather than MCMXXXIII).<ref>Template:Cite book</ref> In capital Greek letters the word Ἀρχιμηδους, or "of Archimedes," is inscribed.

• On the reverse is the inscription:

{{#invoke:Lang|lang}}

Translation: "Mathematicians gathered from the entire world have awarded [understood but not written: '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 Cylinder, behind an olive 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 Template:Frac.)

The rim bears the name of the prizewinner.<ref name="Fields Institute for Research in Mathematical Sciences 2015">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Female recipients

The Fields Medal has had two female recipients, Maryam Mirzakhani from Iran in 2014, and Maryna Viazovska from Ukraine in 2022.<ref name="CF" /><ref name="DZH" />

In popular culture

The Fields Medal gained some recognition in popular culture due to references in the 1997 film, Good Will Hunting. In the movie, Gerald Lambeau (Stellan Skarsgård) is an MIT professor who won the award prior to the events of the story. Throughout the film, references made to the award are meant to convey its prestige in the field.<ref>Template:Cite news</ref>

See also

• Abel Prize
• Kyoto Prize
• List of prizes known as the Nobel or the highest honors of a field
• List of mathematics awards
• Nevanlinna Prize
• Rolf Schock Prizes
• Turing Award
• Wolf Prize in Mathematics

Further reading

• Template:Cite book
• Template:Cite book
• Template:Cite journal.

External links

• Template:Official website
• Overview at britannica.com