The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians (ICM) of the International Mathematical Union (IMU), a convention which takes place every four years. The name of the award honors the Canadian mathematician John Charles Fields. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions to the field of mathematics.
The Fields Medal is regarded as one of the highest honors a mathematician can receive, according to the annual Academic Excellence Survey by ARWU, and has been described as the "Nobel Prize of Mathematics". In another reputation survey conducted by IREG in 2013–2014, the Fields Medal came closely after the Abel Prize, as the second most prestigious international award in mathematics.
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. In 2014, the Iranian mathematician Maryam Mirzakhani became the first female Fields Medalist. With the exception of two Ph.D. holders in physics (Edward Witten and Martin Hairer), only people with a Ph.D. in mathematics have won the medal. In total, 68 people have been awarded the Fields Medal . The most recent group of Fields Medalists received their awards on 23 July 2026, in Philadelphia.
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. The prize includes a monetary award which, since 2006, has been 15,000."Israeli wins 'Nobel' of Mathematics" , The Jerusalem Post
Conditions of the award The Fields Medal is widely regarded as one of the most prestigious awards in the field of mathematics and is often described as the "Nobel Prize of Mathematics". However, unlike the Nobel Prize, the Fields Medal is awarded once every four years and includes an age restriction: recipients must be under 40 years of age on 1 January of the year in which the medal is awarded.
The age limit reflects the intention of John Charles Fields that the award should not only recognize outstanding work already completed, but also encourage further achievement by the recipients and stimulate renewed effort among other mathematicians. In addition, an individual may receive the Fields Medal only once and is not eligible for future awards.
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 (ICM) 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.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 In the remaining years (1990, 1994, and 2002), part of the text of the ICM lecture itself has been quoted. The most recent awarding of the Fields Medal at the 2026 International Congress of the International Mathematical Union was in Philadelphia.
Year ICM locationMedalists Affiliation(when awarded) Affiliation(current/last) Reasons 1936 Oslo, Norway University of Helsinki, Finland Harvard University, US "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." Massachusetts Institute of Technology, US City College of New York, US "Did important work on the Plateau problem which is concerned with finding minimal surfaces connecting and determined by some fixed boundary." 1950 Cambridge, US University of Nancy, France University of Paris VII, France "Developed the theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics." Institute for Advanced Study, US "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." 1954 Amsterdam, Netherlands Princeton University, US Institute for Advanced Study, US University of Tokyo, Japan University of Tokyo, Japan "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." University of Nancy, France Collège de France, France "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." 1958 Edinburgh, UK Imperial College London, UK "for solving a famous problem of number theory, namely, the determination of the exact exponent in the Thue-Siegel inequality"H. Hopf. Proceedings of the International Congress of Mathematicians 1958. Report of the Inaugural Session. p. liv University of Strasbourg, France Institut des hautes études scientifiques, France "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." 1962 Stockholm, Sweden Stockholm University, Sweden Lund University, Sweden "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." Princeton University, US Stony Brook University, US "Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology" (see exotic sphere). 1966 Moscow, USSR University of Oxford, UK University of Edinburgh, UK "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'." Stanford University, US "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." Institut des hautes études scientifiques, France Centre National de la Recherche Scientifique, France "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'." University of California, Berkeley, US City University of Hong Kong, Hong Kong "Worked in differential topology where he proved the generalized Poincaré conjecture in dimension : 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." 1970 Nice, France University of Cambridge, UK Trinity College, Cambridge, UK "Generalized the Gelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified." Harvard University, US Kyoto University, Japan "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." Moscow State University, USSR Steklov Mathematical Institute, Russia Moscow State University, Russia University of Maryland-College Park, US "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." University of Cambridge, UK University of Cambridge, UK University of Florida, US "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." 1974 Vancouver, Canada University of Pisa, Italy Institute for Advanced Study, US "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." Harvard University, US Brown University, US "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." 1978 Helsinki, Finland Institut des hautes études scientifiques, France Institute for Advanced Study, US "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." Princeton University, US "Contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results." Moscow State University, USSR Yale University, US "Provided innovative analysis of the structure of Lie groups. His work belongs to combinatorics, differential geometry, ergodic theory, dynamical systems, and Lie groups." Massachusetts Institute of Technology, US University of Oxford, UK "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." 1982 Warsaw, Poland Institut des hautes études scientifiques, France Institut des hautes études scientifiques, France Collège de France, France