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Fields Medal Winners

2006		• 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. *See related AccessScience content:* Geometry \| Topology
		• Andrei Okounkov For his contributions bridging probability, representation theory, and algebraic geometry. *See related AccessScience content:* Algebraic geometry \| Group theory \| Probability
		• Terence Tao For his contributions to partial differential equations, combinatorics, harmonic analysis, and additive number theory. *See related AccessScience content:* Combinatorial theory \| Differential equation \| Fourier series and transforms \| Number theory
		• Wendelin Werner For his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory. *See related AccessScience content:* Brownian movement \| Conformal mapping \| Stochastic process
2002		• 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 *See related AccessScience content:* Group theory \| Number theory
		• Vladimir Voevodsky for developing a new cohomology theory for algebraic varieties, which represents an important advance in number theory and algebraic geometry *See related AccessScience content:* Algebraic geometry \| Number theory
1998		• Richard E. Borcherds for his work in the fileds of algebra and geometry, especially his proof of the "Moonshine conjecture"
		• W. Timothy Gowers for work on Banach space theory and combinatorics *See related AccessScience content:* Combinatorial theory
		• Maxim Kontsevich for his work in mathematical physics, algebraic geometry, and topology *See related AccessScience content:* Algebraic geometry \| Mathematical physics \| Topology
		• Curtis T. McMullen for his work in geometry and complex dynamics *See related AccessScience content:* Chaos
1994		• 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 *See related AccessScience content:* Differential equation \| Mathematical physics
		• Pierre-Louis Lions for important contributions to the theory of nonlinear partial differential equations *See related AccessScience content:* Differential equation
		• Jean-Christophe Yoccoz for his work on the theory of dynamical systems *See related AccessScience content:* Group theory
		• Efim Zelmanov for his work as an algebraist and in group theory; in particular, for solving the restricted Burnside problem, on eofthe fundamental questions in group theory
1990		• Vladimir Drinfeld for his work on quantum groups and in number theory *See related AccessScience content:* Number theory
		• 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 *See related AccessScience content:* Topology
		• Shigefumi Mori for his work in algebraic geometry and the classification of algebraic varieties *See related AccessScience content:* Algebraic geometry
		• Edward Witten for fundamental contributions to areas of mathematical physics such as quantum field theory *See related AccessScience content:* Mathematical physics \| Quantum field theory \| Superstring theory
1986		• Simon Donaldson for his fundamental findings in four-dimensional geometry *See related AccessScience content:* Topology
		• Gerd Faltings for his proof of the Mordell conjecture using arithmetic algebraic geometry *See related AccessScience content:* Algebraic geometry
		• Michael Freedman for his work in topological analysis, in particular the proof of the Poincaré conjecture for four-dimensional topological manifolds *See related AccessScience content:* Manifold (mathematics) \| Topology
1982		• Alain Connes for fundamental contributions, including his work on the theory and application of operator algebras
		• 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 *See related AccessScience content:* Topology
		• Shing-Tung Yau for contributions in areas such as partial differential equaitons, algebraic geometry, and general relativity theory *See related AccessScience content:* Algebraic geometry \| Differential equation \| Relativity
1978		• Pierre Deligne for his contributions to algebraic geometry and algebraic number theory *See related AccessScience content:* Algebraic geometry
		• Charles Fefferman for important advances in the study of multidimensional complex analysis *See related AccessScience content:* Complex numbers and complex variables
		• Gregori Margulis for contributions to numerous areas of mathematics, especially Lie groups *See related AccessScience content:* Lie group
		• Daniel Quillen for his work on higher algebraic K-theory and its use in solving major problems in algebraic theory
1974		• 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 surf *See related AccessScience content:* Complex numbers and complex variables \| Differential equation \| Minimal surfaces
		• David Mumford for his work on the theory of algebraic surfaces and on problems of the existence and structures of varieties of moduli *See related AccessScience content:* Algebraic geometry
1970		• 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 *See related AccessScience content:* Number theory
		• Heisuke Hironaka for his work on algebraic varieties *See related AccessScience content:* Algebraic geometry
		• 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 *See related AccessScience content:* Manifold (mathematics) \| Topology
		• John Thompson for his fundamental contributions to the study of finite groups *See related AccessScience content:* Group theory
1966		• Michael Atiyah for fundamental studies on the interaction between geometry and analysis and contributions to the development of powerful techniques such as K theory *See related AccessScience content:* Manifold (mathematics)
		• Paul Cohen for his fundamental contributions to the development of set theory *See related AccessScience content:* Set theory
		• Alex Grothendieck for fundamental advances in algebraic geometry and related fields of mathematics *See related AccessScience content:* Algebraic geometry
		• Stephen Smale for his work in differential geomtry with important results on topics such as the Morse theorem and the Poincaré conjecture *See related AccessScience content:* Differential geometry \| Topology
1962		• Lars Hörmander for his work in partial differential equations and the general theory of linear differential operators *See related AccessScience content:* Differential equation
		• John Milnor for pioneering contributions to the development of the new field of differential topology *See related AccessScience content:* Manifold (mathematics) \| Topology
1958		• Klaus Friedrich Roth solved the Thue-Siegel problem concerning the approximations of algebraic numbers by rational numbers *See related AccessScience content:* Number theory
		• 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 *See related AccessScience content:* Catastrophe theory \| Fiber bundle \| Mathematical biology
1954		• Kunihiko Kodaira for his work on the thoery and application of harmonic analysis
		• Jean-Pierre Serre for his work on the homotopy groups of spheres using methods of spectral sequences *See related AccessScience content:* Topology
1950		• Laurent Schwartz for his work on the development of the theory of distributions
		• 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
1936		• Jesse Douglas for solving the plateau problem *See related AccessScience content:* Minimal surfaces
		• Lars Ahlfors for his work on Riemann surfaces *See related AccessScience content:* Riemann surface

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