Fields Medal Winners
Fields medal
Year | Awardee |
---|---|
2018 |
Awarded to: Caucher Birkar for the proof of the boundedness of Fano varieties and for contributions to the minimal model program. |
2018 |
Awarded to: Alessio Figalli for contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability. |
2018 |
Awarded to: Peter Scholze for transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, with application to Galois representations, and for the development of new cohomology theories. |
2018 |
Awarded to: Akshay Venkatesh 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. |
2014 |
Awarded to: Artur Avila 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. |
2014 |
Awarded to: Manjul Bhargava 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. |
2014 |
Awarded to: Martin Hairer 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. |
2014 |
Awarded to: Maryam Mirzakhani for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces. |
2010 |
Awarded to: Elon Lindenstrauss for his results on measure rigidity in ergodic theory, and their applications to number theory. |
2010 |
Awarded to: Ngô Báo Châ for his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebra-geometric methods. |
2010 |
Awarded to: Stanislav Smirnov for the proof of conformal invariance of percolation and the planar Ising model in statistical physics. |
2010 |
Awarded to: Cedric Villani for his work proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation. |
2006 |
Awarded to: Grigory Perelman for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow. His results provide a way of resolving two outstanding problems in topology: the Poincaré Conjecture and the Thurston Geometrization Conjecture. The mathematical community is in the process of checking his work to ensure that it is entirely correct and that the conjectures have been proved. |
2006 |
Awarded to: Andrei Okounkov for his contributions bridging probability, representation theory, and algebraic geometry. |
2006 |
Awarded to: Terence Tao for his contributions to partial differential equations, combinatorics, harmonic analysis, and additive number theory. |
2006 |
Awarded to: Wendelin Werner for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory. |
2002 |
Awarded to: Laurent Lafforgue for proving the global Langlands correspondence for function fields, a major advance toward the realization of the "Langlands Program," which deals with the deep connections between number theory, analysis, and group representation. |
2002 |
Awarded to: Vladimir Voevodsky for developing a new cohomology theory for algebraic varieties, which represents an important advance in number theory and algebraic geometry. |
1998 |
Awarded to: Richard E. Borcherds for his work in the fieds of algebra and geometry, especially his proof of the "Moonshine conjecture." |
1998 |
Awarded to: W. Timothy Gowers for work on Banach space theory and combinatorics. |
1998 |
Awarded to: Maxim Kontsevich for his work in mathematical physics, algebraic geometry, and topology. |
1998 |
Awarded to: Curtis T. McMullen for his work in geometry and complex dynamics. |
1994 |
Awarded to: Jean Bourgain for outstanding contributions in the fields of mathematical analysis including the geometry of Banach spaces, harmonic analysis, and nonlinear partial differential equations from mathematical physics. |
1994 |
Awarded to: Pierre-Louis Lions for important contributions to the theory of nonlinear partial differential equations. |
1994 |
Awarded to: Jean-Christophe Yoccoz for his work on the theory of dynamical systems. |
1994 |
Awarded to: Efim Zelmanov for his work as an algebraist and in group theory; in particular, for solving the restricted Burnside problem, one of the fundamental questions in group theory. See related AccessScience content: |
1990 |
Awarded to: Vladimir Drinfeld for his work on quantum groups and in number theory. |
1990 |
Awarded to: Vaughan Jones for his discovery of a new polynomial invariant for knots, which provided a connecting link for a wide varitety of topics in mathematics and physics. |
1990 |
Awarded to: Shigefumi Mori for his work in algebraic geometry and the classification of algebraic varieties. |
1990 |
Awarded to: Edward Witten for fundamental contributions to areas of mathematical physics such as quantum field theory. |
1986 |
Awarded to: Simon Donaldson for his fundamental findings in four-dimensional geometry. |
1986 |
Awarded to: Gerd Faltings for his proof of the Mordell conjecture using arithmetic algebraic geometry. |
1986 |
Awarded to: Michael Freedman for his work in topological analysis, in particular the proof of the Poincaré conjecture for four-dimensional topological manifolds. |
1982 |
Awarded to: Alain Connes for fundamental contributions, including his work on the theory and application of operator algebras. See related AccessScience content: |
1982 |
Awarded to: William Thurston for his advancement of the study of topology in two and three dimensions and contributions to the understanding of interrelationships between analysis, topology, and geometry. |
1982 |
Awarded to: Shing-Tung Yau for contributions in areas such as partial differential equations, algebraic geometry, and general relativity theory. |
1978 |
Awarded to: Pierre Deligne for his contributions to algebraic geometry and algebraic number theory. |
1978 |
Awarded to: Charles Fefferman for important advances in the study of multidimensional complex analysis. |
1978 |
Awarded to: Gregori Margulis for contributions to numerous areas of mathematics, especially Lie groups. |
1978 |
Awarded to: Daniel Quillen for his work on higher algebraic K-theory and its use in solving major problems in algebraic theory. |
1974 |
Awarded to: Enrico Bombieri for contributions to areas such as the study of prime numbers, the study of univalent functions and the local Bieberbach conjecture; the theory of functions of several complex variables; and to the theory of partial differential equations and minimal surfaces. |
1974 |
Awarded to: David Mumford for his work on the theory of algebraic surfaces and on problems of the existence and structures of varieties of moduli. |
1970 |
Awarded to: Alan Baker for generalizing the Gelfond-Schneider theorem, generating previously unidentified transcendental numbers, and showing how the theory could be used in the field of diophantine equations. |
1970 |
Awarded to: Heisuke Hironaka for his work on algebraic varieties. |
1970 |
Awarded to: Serge Novikov for his contributions in the field of differential topology; in 1965, he stated a conjecture now known as the Novikov conjecture, one of the most fundamental problems in topology. |
1970 |
Awarded to: John Thompson for his fundamental contributions to the study of finite groups. |
1966 |
Awarded to: Michael Atiyah for fundamental studies on the interaction between geometry and analysis and contributions to the development of powerful techniques such as K theory. |
1966 |
Awarded to: Paul Cohen for his fundamental contributions to the development of set theory. |
1966 |
Awarded to: Alex Grothendieck for fundamental advances in algebraic geometry and related fields of mathematics. |
1966 |
Awarded to: Stephen Smale for his work in differential geomtry with important results on topics such as the Morse theorem and the Poincaré conjecture. |
1962 |
Awarded to: Lars Hörmander for his work in partial differential equations and the general theory of linear differential operators. |
1962 |
Awarded to: John Milnor for pioneering contributions to the development of the new field of differential topology. |
1958 |
Awarded to: Klaus Friedrich Roth solved the Thue-Siegel problem concerning the approximations of algebraic numbers by rational numbers. |
1958 |
Awarded to: René Thom known for his work on catastrophe theory, the medal resulted from his work on cobordism theory, characteristics classes, and the Thom transversality theorem. |
1954 |
Awarded to: Kunihiko Kodaira for his work on the theory and application of harmonic analysis. |
1954 |
Awarded to: Jean-Pierre Serre for his work on the homotopy groups of spheres using methods of spectral sequences. |
1950 |
Awarded to: Laurent Schwartz for his work on the development of the theory of distributions. See related AccessScience content: |
1950 |
Awarded to: Atle Selberg for his work on the zeros of the Riemann zeta function (proof that a positive proportion of its zeros satisfy the Riemann hypothesis) as well as for generalizations of the sieve methods of Viggo Brun. See related AccessScience content: |
1936 |
Awarded to: Jesse Douglas for solving the plateau problem. |
1936 |
Awarded to: Lars Ahlfors for his work on Riemann surfaces. |
Year | Awarded to |
---|---|
2014 |
Awarded to: Artur Avila 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. |
2014 |
Awarded to: Manjul Bhargava 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. |
2014 |
Awarded to: Martin Hairer 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. |
2014 |
Awarded to: Maryam Mirzakhani for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces. |
2010 |
Awarded to: Elon Lindenstrauss for his results on measure rigidity in ergodic theory, and their applications to number theory. |
2010 |
Awarded to: Ngô Báo Châ for his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebra-geometric methods. |
2010 |
Awarded to: Stanislav Smirnov for the proof of conformal invariance of percolation and the planar Ising model in statistical physics. |
2010 |
Awarded to: Cedric Villani for his work proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation. |
2006 |
Awarded to: Grigory Perelman for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow. His results provide a way of resolving two outstanding problems in topology: the Poincaré Conjecture and the Thurston Geometrization Conjecture. The mathematical community is in the process of checking his work to ensure that it is entirely correct and that the conjectures have been proved. |
2006 |
Awarded to: Andrei Okounkov for his contributions bridging probability, representation theory, and algebraic geometry. |
2006 |
Awarded to: Terence Tao for his contributions to partial differential equations, combinatorics, harmonic analysis, and additive number theory. |
2006 |
Awarded to: Wendelin Werner for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory. |
2002 |
Awarded to: Laurent Lafforgue for proving the global Langlands correspondence for function fields, a major advance toward the realization of the "Langlands Program," which deals with the deep connections between number theory, analysis, and group representation. |
2002 |
Awarded to: Vladimir Voevodsky for developing a new cohomology theory for algebraic varieties, which represents an important advance in number theory and algebraic geometry. |
1998 |
Awarded to: Richard E. Borcherds for his work in the fieds of algebra and geometry, especially his proof of the "Moonshine conjecture." |
1998 |
Awarded to: W. Timothy Gowers for work on Banach space theory and combinatorics. |
1998 |
Awarded to: Maxim Kontsevich for his work in mathematical physics, algebraic geometry, and topology. |
1998 |
Awarded to: Curtis T. McMullen for his work in geometry and complex dynamics. |
1994 |
Awarded to: Jean Bourgain for outstanding contributions in the fields of mathematical analysis including the geometry of Banach spaces, harmonic analysis, and nonlinear partial differential equations from mathematical physics. |
1994 |
Awarded to: Pierre-Louis Lions for important contributions to the theory of nonlinear partial differential equations. |
1994 |
Awarded to: Jean-Christophe Yoccoz for his work on the theory of dynamical systems. |
1994 |
Awarded to: Efim Zelmanov for his work as an algebraist and in group theory; in particular, for solving the restricted Burnside problem, one of the fundamental questions in group theory. See related AccessScience content: |
1990 |
Awarded to: Vladimir Drinfeld for his work on quantum groups and in number theory. |
1990 |
Awarded to: Vaughan Jones for his discovery of a new polynomial invariant for knots, which provided a connecting link for a wide varitety of topics in mathematics and physics. |
1990 |
Awarded to: Shigefumi Mori for his work in algebraic geometry and the classification of algebraic varieties. |
1990 |
Awarded to: Edward Witten for fundamental contributions to areas of mathematical physics such as quantum field theory. |
1986 |
Awarded to: Simon Donaldson for his fundamental findings in four-dimensional geometry. |
1986 |
Awarded to: Gerd Faltings for his proof of the Mordell conjecture using arithmetic algebraic geometry. |
1986 |
Awarded to: Michael Freedman for his work in topological analysis, in particular the proof of the Poincaré conjecture for four-dimensional topological manifolds. |
1982 |
Awarded to: Alain Connes for fundamental contributions, including his work on the theory and application of operator algebras. See related AccessScience content: |
1982 |
Awarded to: William Thurston for his advancement of the study of topology in two and three dimensions and contributions to the understanding of interrelationships between analysis, topology, and geometry. |
1982 |
Awarded to: Shing-Tung Yau for contributions in areas such as partial differential equations, algebraic geometry, and general relativity theory. |
1978 |
Awarded to: Pierre Deligne for his contributions to algebraic geometry and algebraic number theory. |
1978 |
Awarded to: Charles Fefferman for important advances in the study of multidimensional complex analysis. |
1978 |
Awarded to: Gregori Margulis for contributions to numerous areas of mathematics, especially Lie groups. |
1978 |
Awarded to: Daniel Quillen for his work on higher algebraic K-theory and its use in solving major problems in algebraic theory. |
1974 |
Awarded to: Enrico Bombieri for contributions to areas such as the study of prime numbers, the study of univalent functions and the local Bieberbach conjecture; the theory of functions of several complex variables; and to the theory of partial differential equations and minimal surfaces. |
1974 |
Awarded to: David Mumford for his work on the theory of algebraic surfaces and on problems of the existence and structures of varieties of moduli. |
1970 |
Awarded to: Alan Baker for generalizing the Gelfond-Schneider theorem, generating previously unidentified transcendental numbers, and showing how the theory could be used in the field of diophantine equations. |
1970 |
Awarded to: Heisuke Hironaka for his work on algebraic varieties. |
1970 |
Awarded to: Serge Novikov for his contributions in the field of differential topology; in 1965, he stated a conjecture now known as the Novikov conjecture, one of the most fundamental problems in topology. |
1970 |
Awarded to: John Thompson for his fundamental contributions to the study of finite groups. |
1966 |
Awarded to: Michael Atiyah for fundamental studies on the interaction between geometry and analysis and contributions to the development of powerful techniques such as K theory. |
1966 |
Awarded to: Paul Cohen for his fundamental contributions to the development of set theory. |
1966 |
Awarded to: Alex Grothendieck for fundamental advances in algebraic geometry and related fields of mathematics. |
1966 |
Awarded to: Stephen Smale for his work in differential geomtry with important results on topics such as the Morse theorem and the Poincaré conjecture. |
1962 |
Awarded to: Lars Hörmander for his work in partial differential equations and the general theory of linear differential operators. |
1962 |
Awarded to: John Milnor for pioneering contributions to the development of the new field of differential topology. |
1958 |
Awarded to: Klaus Friedrich Roth solved the Thue-Siegel problem concerning the approximations of algebraic numbers by rational numbers. |
1958 |
Awarded to: René Thom known for his work on catastrophe theory, the medal resulted from his work on cobordism theory, characteristics classes, and the Thom transversality theorem. |
1954 |
Awarded to: Kunihiko Kodaira for his work on the theory and application of harmonic analysis. |
1954 |
Awarded to: Jean-Pierre Serre for his work on the homotopy groups of spheres using methods of spectral sequences. |
1950 |
Awarded to: Laurent Schwartz for his work on the development of the theory of distributions. See related AccessScience content: |
1950 |
Awarded to: Atle Selberg for his work on the zeros of the Riemann zeta function (proof that a positive proportion of its zeros satisfy the Riemann hypothesis) as well as for generalizations of the sieve methods of Viggo Brun. See related AccessScience content: |
1936 |
Awarded to: Jesse Douglas for solving the plateau problem. |
1936 |
Awarded to: Lars Ahlfors for his work on Riemann surfaces. |