| Year | ICM location | Medalists[21] | Affiliation
(when awarded) | Affiliation
(current/last) | Reasons |
|---|
| 1936 | Oslo, Norway |  | Lars Ahlfors | University of Helsinki, Finland | Harvard University, US[22][23] | "Awarded medal for research on covering surfaces related toRiemann surfaces ofinverse functions of entire andmeromorphic functions. Opened up new fields of analysis."[24] |
 | Jesse Douglas | Massachusetts Institute of Technology, US | City College of New York, US[25][26] | "Did important work on thePlateau problem which is concerned with findingminimal surfaces connecting and determined by some fixed boundary."[24] |
| 1950 | Cambridge, US |  | Laurent Schwartz | University of Nancy, France | University of Paris VII, France[27][28] | "Developed thetheory of distributions, a new notion of generalized function motivated by theDirac delta-function of theoretical physics."[29] |
 | Atle Selberg | Institute for Advanced Study, US | Institute for Advanced Study, US[30] | "Developed generalizations of thesieve methods of Viggo Brun; achieved major results on zeros of theRiemann zeta function; gave an elementary proof of theprime number theorem (with P. Erdős), with a generalization to prime numbers in an arbitrary arithmetic progression."[29] |
| 1954 | Amsterdam, Netherlands |  | Kunihiko Kodaira | Princeton University, US,University of Tokyo, Japan andInstitute for Advanced Study, US[31] | University of Tokyo, Japan[32] | "Achieved major results in the theory of harmonic integrals and numerous applications to Kählerian and more specifically toalgebraic varieties. He demonstrated, bysheaf cohomology, that such varieties areHodge manifolds."[33] |
 | Jean-Pierre Serre | University of Nancy, France | Collège de France, France[34][35] | "Achieved major results on thehomotopy groups of spheres, especially in his use of the method ofspectral sequences. Reformulated and extended some of the main results of complex variable theory in terms ofsheaves."[33] |
| 1958 | Edinburgh, UK | | Klaus Roth | University College London, UK | Imperial College London, UK[36] | "for solving a famous problem of number theory, namely, the determination of the exact exponent in the Thue-Siegel inequality"[37] |
 | René Thom | University of Strasbourg, France | Institut des Hautes Études Scientifiques, France[38] | "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."[37] |
| 1962 | Stockholm, Sweden |  | Lars Hörmander | Stockholm University, Sweden | Lund University, Sweden[39] | "Worked inpartial differential equations. Specifically, contributed to the general theory of linear differential operators. The questions go back to one ofHilbert's problems at the 1900 congress."[40] |
 | John Milnor | Princeton University, US | Stony Brook University, US[41] | "Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field ofdifferential topology."[40] |
| 1966 | Moscow, USSR |  | Michael Atiyah | University of Oxford, UK | University of Edinburgh, UK[42] | "Did joint work with Hirzebruch inK-theory; proved jointly with Singer theindex theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the 'Lefschetz formula'."[43] |
 | Paul Cohen | Stanford University, US | Stanford University, US[44] | "Used technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalizedcontinuum hypothesis. The latter problem was the first of Hilbert's problems of the 1900 Congress."[43] |
 | Alexander Grothendieck | Institut des Hautes Études Scientifiques, France | Centre National de la Recherche Scientifique, France[45] | "Built on work of Weil and Zariski and effected fundamental advances inalgebraic geometry. He introduced the idea of K-theory (the Grothendieck groups and rings). Revolutionizedhomological algebra in his celebrated ‘Tôhoku paper’."[43] |
 | Stephen Smale | University of California, Berkeley, US | City University of Hong Kong, Hong Kong[46] | "Worked in differential topology where he proved thegeneralized Poincaré conjecture in dimension : Every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. Introduced the method ofhandle-bodies to solve this and related problems."[43] |
| 1970 | Nice, France |  | Alan Baker | University of Cambridge, UK | Trinity College, Cambridge, UK[47] | "Generalized theGelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified."[48] |
 | Heisuke Hironaka | Harvard University, US | Kyoto University, Japan[49][50] | "Generalized work of Zariski who had proved for dimension ≤ 3 the theorem concerning theresolution of singularities on analgebraic variety. Hironaka proved the results in any dimension."[48] |
| Sergei Novikov | Moscow State University, USSR | Steklov Mathematical Institute, Russia Moscow State University, RussiaUniversity of Maryland-College Park, US[51][52] | "Made important advances in topology, the most well-known being his proof of the topological invariance of thePontryagin classes of the differentiable manifold. His work included a study of the cohomology and homotopy ofThom spaces."[48] |
 | John G. Thompson | University of Cambridge, UK | University of Cambridge, UK University of Florida, US[53] | "Proved jointly withW. Feit thatall 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."[48] |
| 1974 | Vancouver, Canada |  | Enrico Bombieri | University of Pisa, Italy | Institute for Advanced Study, US[54] | "Major contributions in the primes, inunivalent functions and the localBieberbach conjecture, in theory of functions of several complex variables, and in theory of partial differential equations and minimal surfaces – in particular, to the solution ofBernstein's problem in higher dimensions."[55] |
 | David Mumford | Harvard University, US | Brown University, US[56] | "Contributed to problems of the existence and structure ofvarieties of moduli, varieties whose points parametrize isomorphism classes of some type of geometric object. Also made several important contributions to the theory ofalgebraic surfaces."[55] |
| 1978 | Helsinki, Finland |  | Pierre Deligne | Institut des Hautes Études Scientifiques, France | Institute for Advanced Study, US[57] | "Gave solution of the threeWeil conjectures concerning generalizations of theRiemann hypothesis to finite fields. His work did much to unify algebraic geometry and algebraic number theory."[58] |
 | Charles Fefferman | Princeton University, US | Princeton University, US[59] | "Contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results."[58] |
 | Grigory Margulis | Moscow State University, USSR | Yale University, US[60] | "Provided innovative analysis of the structure ofLie groups. His work belongs to combinatorics, differential geometry, ergodic theory, dynamical systems, and Lie groups."[58] |
 | Daniel Quillen | Massachusetts Institute of Technology, US | University of Oxford, UK[61] | "The prime architect of the higheralgebraic 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."[58] |
| 1982 | Warsaw, Poland |  | Alain Connes | Institut des Hautes Études Scientifiques, France | Institut des Hautes Études Scientifiques, France Collège de France, FranceOhio State University, US[62] | "Contributed to the theory ofoperator 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 ofC*-algebras to foliations and differential geometry in general."[63] |
 | William Thurston | Princeton University, US | Cornell University, US[64] | "Revolutionized study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry. Contributed idea that a very large class of closed3-manifolds carry a hyperbolic structure."[63] |
 | Shing-Tung Yau | Institute for Advanced Study, US | Tsinghua University, China[65] | "Made contributions in differential equations, also to theCalabi conjecture in algebraic geometry, to thepositive mass conjecture of general relativity theory, and to real and complexMonge–Ampère equations."[63] |
| 1986 | Berkeley, US |  | Simon Donaldson | University of Oxford, UK | Imperial College London, UK[66]Stony Brook University, US[67] | "Received medal primarily for his work on topology offour-manifolds, especially for showing that there is a differential structure on euclidian four-space which isdifferent from the usual structure."[68][69] |
 | Gerd Faltings | Princeton University, US | Max Planck Institute for Mathematics, Germany[70] | "Using methods of arithmetic algebraic geometry, he received medal primarily for his proof of theMordell Conjecture."[68] |
 | Michael Freedman | University of California, San Diego, US | Microsoft Station Q, US[71] | "Developed new methods for topological analysis offour-manifolds. One of his results is a proof of thefour-dimensional Poincaré Conjecture."[68] |
| 1990 | Kyoto, Japan | | Vladimir Drinfeld | B Verkin Institute for Low Temperature Physics and Engineering, USSR[72] | University of Chicago, US[73] | "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."[74] |
 | Vaughan Jones | University of California, Berkeley, US | University of California, Berkeley, US[75] Vanderbilt University, US[76] | "Jones discovered an astonishing relationship betweenvon Neumann algebras and geometric topology. As a result, he found a new polynomial invariant for knots and links in 3-space."[77] |
 | Shigefumi Mori | Kyoto University, Japan | Kyoto University, Japan[78] | "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."[79] |
 | Edward Witten | Institute for Advanced Study, US | Institute for Advanced Study, US[80] | "Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems."[81] |
| 1994 | Zürich, Switzerland |  | Jean Bourgain | Institut des Hautes Études Scientifiques, France | Institute for Advanced Study, US[82] | "Bourgain's work touches on several central topics of mathematical analysis: the geometry ofBanach spaces, convexity in high dimensions, harmonic analysis, ergodic theory, and finally, nonlinear partial differential equations from mathematical physics."[83] |
 | Pierre-Louis Lions | University of Paris 9, France | Collège de France, France École polytechnique, France[84] | "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."[85] |
 | Jean-Christophe Yoccoz | Paris-Sud 11 University, France | Collège de France, France[86] | "Yoccoz obtained a very enlightening proof ofBruno'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."[87] |
 | Efim Zelmanov | University of Wisconsin-MadisonUniversity of Chicago, US | Steklov Mathematical Institute, Russia, University of California, San Diego, US[88] | "For the solution of the restrictedBurnside problem."[89] |
| 1998 | Berlin, Germany |  | Richard Borcherds | University of California, Berkeley, US University of Cambridge, UK | University of California, Berkeley, US[90] | "For his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex algebras and Borcherds' Lie algebras, theproof of the Conway–Norton moonshine conjecture and the discovery of a new class of automorphic infinite products."[91] |
 | Timothy Gowers | University of Cambridge, UK | University of Cambridge, UK[92] | "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."[91] |
 | Maxim Kontsevich | Institut des Hautes Études Scientifiques, France Rutgers University, US | Institut des Hautes Études Scientifiques, France Rutgers University, US[93] | "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."[91] |
 | Curtis T. McMullen | Harvard University, US | Harvard University, US[94] | "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."[91] |
| 2002 | Beijing, China |  | Laurent Lafforgue | Institut des Hautes Études Scientifiques, France | Institut des Hautes Études Scientifiques, France[95] | "Laurent Lafforgue has been awarded the Fields Medal for his proof of theLanglands correspondence for the full linear groups GLr (r≥1) over function fields of positive characteristic."[96] |
 | Vladimir Voevodsky | Institute for Advanced Study, US | Institute for Advanced Study, US[97] | "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 theMilnor conjectures on the K-theory of fields."[98] |
| 2006 | Madrid, Spain |  | Andrei Okounkov | Princeton University, US | Columbia University, US[99] University of California, Berkeley, US[100] | "For his contributions bridging probability, representation theory and algebraic geometry."[101] |
 | Grigori Perelman(declined) | None | St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences, Russia[102] | "For his contributions to geometry and his revolutionary insights into the analytical and geometric structure of theRicci flow."[101] |
 | Terence Tao | University of California, Los Angeles, US | University of California, Los Angeles, US[103] | "For his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory."[101] |
 | Wendelin Werner | Paris-Sud 11 University, France | ETH Zurich, Switzerland[104] | "For his contributions to the development ofstochastic Loewner evolution, the geometry of two-dimensionalBrownian motion, andconformal field theory."[101] |
| 2010 | Hyderabad, India |  | Elon Lindenstrauss | Hebrew University of Jerusalem, Israel Princeton University, US | Hebrew University of Jerusalem, Israel[105] | "For his results on measure rigidity inergodic theory, and their applications to number theory."[106] |
 | Ngô Bảo Châu | Paris-Sud 11 University, France Institute for Advanced Study, US | University of Chicago, US Institute for Advanced Study, US[107] | "For his proof of theFundamental Lemma in the theory ofautomorphic forms through the introduction of new algebro-geometric methods."[106] |
 | Stanislav Smirnov | University of Geneva, Switzerland | University of Geneva, Switzerland St. Petersburg State University, Russia[108] | "For the proof of conformal invariance of percolation and the planarIsing model in statistical physics."[106] |
 | Cédric Villani | École Normale Supérieure de Lyon, France Institut Henri Poincaré, France | Lyon University, France Institut Henri Poincaré, France[109] | "For his proofs of nonlinearLandau damping and convergence to equilibrium for theBoltzmann equation."[106] |
| 2014 | Seoul, South Korea |  | Artur Avila | University of Paris VII, France CNRS, FranceInstituto 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."[110] |
 | Manjul Bhargava | Princeton University, US | Princeton University, US[111][112][113] | "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 ofelliptic curves."[110] |
 | Martin Hairer | University of Warwick, UK | 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."[110] |
 | Maryam Mirzakhani | Stanford University, US | Stanford University, US[114][115] | "For her outstanding contributions to the dynamics and geometry ofRiemann surfaces and their moduli spaces."[110] |
| 2018 | Rio de Janeiro, Brazil |  | Caucher Birkar | University of Cambridge, UK | University of Cambridge, UK | "For the proof of the boundedness ofFano varieties and for contributions to theminimal model program."[116] |
 | Alessio Figalli | Swiss Federal Institute of Technology Zurich, Switzerland | Swiss Federal Institute of Technology Zurich, Switzerland | "For contributions to the theory ofoptimal transport and its applications inpartial differential equations,metric geometry andprobability."[116] |
 | Peter Scholze | University of Bonn, Germany | University of Bonn, Germany | "For having transformed arithmetic algebraic geometry overp-adic fields."[116] |
 | Akshay Venkatesh | Stanford University, US | Institute for Advanced Study, US[117] | "For his synthesis ofanalytic number theory,homogeneous dynamics,topology, andrepresentation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects."[116] |
| 2022 | Helsinki, Finland[a] |  | Hugo Duminil-Copin | Institut des Hautes Études Scientifiques, France University of Geneva, Switzerland[120] | Institut des Hautes Études Scientifiques, France University of Geneva, Switzerland[120] | "For solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four."[121] |
 | June Huh | Princeton University, US | Princeton University, US | "For bringing the ideas ofHodge theory to combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture formatroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture."[121] |
 | James Maynard | 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 inDiophantine approximation."[121] |
 | Maryna Viazovska | École Polytechnique Fédérale de Lausanne, Switzerland | École Polytechnique Fédérale de Lausanne, Switzerland | "For the proof that the lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems inFourier analysis."[121][122] |
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