FIELDS MEDAL WINNERS
1986 - 2002

Fields Medal - History & Background

FIELDS MEDAL WINNERS IN 2002

Vladimir Voevodsky - Russia - Vladimir Voevodsky (1966- 2017) was awarded the Fields Medal in 2002 for his work on motivic cohomology and homotopy theory of algebraic varieties. He developed a new cohomology theory for algebraic geometry, proving the Milnor conjecture and making significant progress on the Bloch-Kato conjecture. Voevodsky’s innovative use of homotopy-theoretic methods transformed the field, providing deep connections between algebraic geometry, topology and number theory.

Laurent Lafforgue - France - Laurent Lafforgue (1966- Present) was awarded the Fields Medal in 2002 for his work on Langlands program, specifically for proving Langlands correspondence for function fields. His achievement provided a major advance in number theory and representation theory by establishing a deep connection between automorphic forms and Galois representations. His work extended Drinfeld's results and had important implications for modern mathematics, significantly in advancing the Langlands conjectures.

FIELDS MEDAL WINNERS IN 1998

Curtis T. McMullen - USA - Curtis T. McMullen (1958 - Present) was awarded the Fields Medal in 1998 for his great contributions to complex dynamics, hyperbolic geometry and Teichmüller theory. He provided deep insights into the behavior of iterated rational maps, proved results on the renormalization of polynomials, and made significant advances in understanding Kleinian groups and Riemann surfaces.

Timothy Gowers - UK - Timothy Gowers (1963 - Present) was awarded the Fields Medal in 1998 for his deep contributions to functional analysis and additive combinatorics. He introduced new techniques to study Banach spaces, solving long-standing problems about their structure. Gower’s work in Szemerédi’s theorem and arithmetic progressions laid the foundation for modern additive combinatorics. His insights revolutionized the use of combinatorial methods in analysis, impacting number theory and theoretical computer science.

Maxim Kontsevich - Russia - Maxim Kontsevich (1964 - Present) was awarded the Fields Medal in 1998 for his work in mathematical physics, deformation quantization and algebraic geometry. He proved Witten’s conjecture on intersection theory, developed Kontsevich quantization in Poisson geometry, and introduced new invariants in low-dimensional topology. His deep insights connected physics and geometry, influencing quantum field theory, string theory and mirror symmetry, making crucial contributions to modern mathematical structures and their applications in physics.

Richard Borcherds - UK - Richard Borcherds (1959 - Present) was awarded the Fields Medal in 1998 for his work in algebra, Lie algebras, and mathematical physics. He proved the Moonshine Conjecture, revealing deep connections between monstrous symmetry groups and modular functions. Borcherd’s development of vertex algebras and contributions to Borcherds products transformed string theory and conformal field theory. His work bridged algebra, number theory and mathematical physics, thereby impacting these fields.

FIELDS MEDAL WINNERS IN 1994

Pierre-Louis Lions - France - Pierre-Louis Lions (1956 - Present) was awarded the Fields Medal in 1994 for his work in partial differential equations (PDEs), particularly in nonlinear equations. He made fundamental contributions to the theory of viscosity solutions, solving key problems in Hamilton-Jacobi equations. Lion’s work had significant applications in optimal control, fluid dynamics and mathematical physics, profoundly influencing the study of PDEs in diverse fields, including finance and engineering.

Jean Bourgain - Belgium - Jean Bourgain (1954 - 2018) was awarded the Fields Medal in 1994 for his contributions to analysis, combinatorics and mathematical physics. He made critical advances in Banach space geometry, ergodic theory, harmonic analysis and nonlinear partial differential equations. Bourgain has solved major problems in Fourier analysis, number theory and quantum chaos, introducing novel probabilistic and combinatorial methods that transformed modern analysis and its applications across multiple mathematical disciplines.

Efim Zelmanov - Russia - Efim Zelmanov (1955 - Present) was awarded the Fields Medal in 1994 for his outstanding work in mathematical structures, particularly in the theory of Lie algebras and algebraic groups. He solved the long-standing Kac-Moody conjecture by proving the solvability of certain Lie algebras. His work in infinite-dimensional Lie algebras and the non-linear theory of Lie groups significantly advanced algebraic and geometric methods, with profound implications for theoretical physics and other areas of mathematics.

Jean-Christophe Yoccoz- France - Jean-Christophe Yoccoz (1957 - 2016) was awarded the Fields Medal in 1994 for his deep contributions to dynamical systems, particularly the smoothness and stability of dynamical behaviors. He developed powerful tools for studying small divisors problems and proved key results on the linearization of analytic circle diffeomorphisms. Yoccoz’s work provided rigorous foundations for Kolmogorov-Arnold-Moser (KAM) theory and advanced the understanding of chaotic systems and stability in Hamiltonian dynamics.

FIELDS MEDAL WINNERS IN 1990

Shigefumi Mori - Japan - Shigefumi Mori (1951 - Present) was awarded the Fields Medal in 1990 for his pioneering work in algebraic geometry, particularly for proof of the Hartshorne Conjecture and the development of Minimal Model Program (MMP). His work established the foundation for birational geometry, classifying three-dimensional algebraic varieties and extending techniques from two dimensions. The MMP has become a central tool in higher-dimensional geometry, deeply influencing modern algebraic geometry and complex geometry.

Vladimir Drinfeld - Russia - Vladimir Drinfeld (1954 - Present) was awarded the Fields Medal in 1990 for his groundbreaking work in algebraic geometry, number theory and mathematical physics. He introduced Drinfeld modules, which revolutionized the theory of elliptic modules and function fields. His work on quantum groups laid the foundation for modern quantum algebra. Drinfeld also contributed to the Langlands program, particularly for function fields, significantly advancing representation theory and noncommutative geometry.

Edward Witten - USA - Edward Witten (1951 - Present) was awarded the Fields Medal in 1990 for his profound contributions to mathematical physics, particularly in applying quantum field theory to mathematics. His work on topological quantum field theory provided new insights into knot invariants, geometry and topology. He gave a physics-based proof of the Morse inequalities and introduced new perspectives on the Jones polynomial. Edward’s research has deeply influenced string theory, topology and geometric analysis.

Vaughan Jones - New Zealand - Vaughan Jones (1952 - 2020) was awarded the Fields Medal in 1990 for his discovery of the Jones polynomial, an invariant of knots and links in three-dimensional space. His work revolutionized knot theory and uncovered deep connections between low-dimensional topology, von Neumann algebras, and statistical mechanics. The Jones polynomial led to breakthroughs in quantum topology and played a key role in the development of topological quantum field theory and quantum computing.

FIELDS MEDAL WINNERS IN 1986

SIMON DONALDSON - UK - Simon Donaldson was awarded the Fields Medal in 1986 for his work on the topology of smooth four-manifolds. Using gauge theory and solutions to the Yang-Mills equations, he discovered exotic smooth structures on ℝ⁴, proving that smooth structures in four dimensions are far more intricate than in other dimensions. His work transformed differential geometry, with deep implications for mathematical physics, including connections to quantum field theory and string theory.

GERD FALTINGS - Germany - Gerd Faltings was awarded the Fields Medal in 1986 for proving the Mordell Conjecture, which states that algebraic curves of genus greater than one have only finitely many rational solutions. His work revolutionized arithmetic geometry, providing key insights into Diophantine equations and abelian varieties. Moreover, the techniques influenced modern number theory, including advances in the study of elliptic curves, which are crucial for cryptography and algebraic geometry.

MICHAEL FREEDMAN - USA - Michael Freedman was awarded the Fields Medal in 1986 for his work on the topology of 4-manifolds. He famously proved the four-dimensional Poincaré conjecture, a fundamental problem in mathematics concerning the characterization of the 4-dimensional sphere. His work resolved a major question in geometric topology and had deep implications for mathematical physics and quantum computing. Freedman’s insights revolutionized low-dimensional topology and shaped modern mathematics.

Fields Medal - History & Background
Fields Medal Winners 2006 - 2022
Fields Medal Winners 1986 - 2002
Fields Medal Winners 1936 - 1982