FIELDS MEDAL WINNERS
2006 - 2022

Fields Medal - History & Background

FIELDS MEDAL WINNERS IN 2022

Hugo Duminil-Copin - France - Hugo Duminil-Copin (1985 - Present) was awarded the Fields Medal in 2022 for his path breaking contributions to the Mathematical study of phase transitions in statistical Physics. He developed innovative techniques to solve long-standing problems in percolation theory and the Ising model. Hugo’s research primarily focused on understanding phase transitions in statistical physics, a complex area where materials change behavior depending on temperature or pressure.

June Huh - South Korea - June Huh (1983 - Present) was awarded the Fields Medal in 2022 for his transformative contributions to combinatorics, algebraic geometry and matroid theory. He solved longstanding problems, including Rota's Conjecture, by introducing deep connections between these fields. His work applied tools from Hodge theory and tropical geometry to combinatorial problems, revolutionizing the understanding of independent structures. Huh's groundbreaking research bridged abstract mathematical theories with concrete combinatorial applications, inspiring new directions in both pure and applied mathematics.

James Maynard - England - James Maynard (1987 - Present) was awarded the Fields Medal in 2022 for his exceptional contributions to analytic number theory, particularly in prime numbers. He developed innovative methods to study the gaps between primes, providing a simplified approach to bounded gaps and resolving longstanding conjectures, such as the existence of infinitely many primes missing specific digits. Maynard's techniques have significantly advanced our understanding of primes.

Maryna Viazovska - Ukraine - Maryna Viazovska (1984 - Present) was awarded the Fields Medal in 2022 for her contribution to solving the sphere-packing problem of 8 dimensions in 24 dimensions. Using modular forms and elegant mathematical techniques, she provided nearly perfect packing configurations, building on earlier work in 3 dimensions. Her methods not only resolved these long-standing problems but also opened new pathways in discrete geometry, harmonic analysis and mathematical physics.

FIELDS MEDAL WINNERS IN 2018

Caucher Birkar - Iran - Caucher Birkar (1978 - Present) was awarded the Fields Medal in 2018 for his contributions to algebraic geometry, particularly in advancing the minimal model program and the study of Fano varieties. His work resolved fundamental conjectures in birational geometry, including proving key results about the existence of minimal models and boundedness of Fano varieties. Birkar's achievements have profoundly shaped modern algebraic geometry and furthered its connections with other areas of mathematics.

Alessio Figalli - Italy - Alessio Figalli (1984 - Present) received the Fields Medal in 2018 for his work on the theory of optimal transport and its applications to partial differential equations, metric geometry and probability. His contributions include solving long-standing problems in the stability of functional inequalities and free boundary regularity in variational problems. Figalli's innovative techniques have influenced numerous fields, with applications ranging from physics to economics, showcasing the power of mathematical tools in understanding complex phenomena.

Peter Scholze - Germany - Peter Scholze (1987 - Present) was awarded the Fields Medal in 2018 for his deep contributions to arithmetic algebraic geometry and his development of the theory of perfectoid spaces. His innovative ideas have revolutionized p-adic geometry and provided new tools for addressing deep problems in number theory, including the Langlands program. Scholze's work combines elegance and power, bridging abstract mathematics with concrete applications, inspiring a new generation of mathematicians.

Akshay Venkatesh - Australia - Akshay Venkatesh (1981 - Present) earned the Fields Medal 2018 for his deep contributions to analytic number theory, algebraic topology and representation theory. His work illuminated the interactions between these fields, solving long-standing conjectures in the theory of automorphic forms and equidistribution problems. Venkatesh's insights into arithmetic and dynamics have profoundly advanced modern mathematics, offering innovative approaches to understanding the symmetries and structures underlying numbers and spaces.

FIELDS MEDAL WINNERS IN 2014

Artur Avila - Brazil - Artur Avila (1979 - Present) was awarded the Fields Medal in 2014 for his contributions to dynamical systems and mathematical physics. His work advanced the understanding of chaos and stability in various mathematical models, particularly in one-dimensional dynamics and the spectral theory of Schrödinger operators. Avila solved longstanding problems and bridged gaps between pure and applied mathematics, significantly influencing the study of dynamical systems.

Manjul Bhargava - India - Manjul Bhargava (1974 - Present) was awarded the Fields Medal in 2014 for his contributions to number theory, particularly in developing new methods to study quadratic forms and elliptic curves. His innovative approach to higher composition laws and the use of geometry revealed deep insights into classical problems, including counting rational points on algebraic varieties. Bhargava's work has significantly advanced the understanding of arithmetic structures and inspired future research in algebra and number theory.

Martin Hairer - Austria - Martin Hairer (1975 - Present) was awarded the Fields Medal in 2014 for his work on stochastic partial differential equations (SPDEs). He developed the theory of regularity structures, which provides a robust framework to solve equations previously considered unsolvable due to randomness and singularities. Hairer’s innovative techniques have profound applications in mathematical physics, probability and beyond, offering deep insights into the behavior of complex systems influenced by randomness.

Maryam Mirzakhani - Iran - Maryam Mirzakhani, (1977 - 2017) the first woman to win the Fields Medal was conferred this award in 2014 for her work on the dynamics and geometry of Riemann surfaces and their moduli spaces. Her innovative methods connected diverse fields, solving longstanding problems in geometry and topology. She made significant contributions to our understanding of the symmetry of curved surfaces, particularly in the study of moduli spaces and Riemann surfaces.

FIELDS MEDAL WINNERS IN 2010

Elon Lindenstrauss - Israel - Elon Lindenstrauss (1970 - Present) was awarded the Fields Medal in 2010 for his work in ergodic theory and its applications to number theory. His research, particularly on Littlewood conjecture and quantum unique ergodicity conjecture, provided deep insights into the distribution of mathematical objects in space. Elon’s use of entropy methods in dynamical systems led to major advancements in homogeneous dynamics and Diophantine approximation.

Ngo Bao Chau - Vietnam - Ngô Bảo Châu (1972 – Present) was awarded the Fields Medal in 2010 for his proof of Fundamental Lemma in the Langlands program, a central conjecture in number theory and representation theory. His work resolved a key problem in automorphic forms and arithmetic geometry, using deep insights from algebraic geometry. Chau’s proof had far-reaching implications, linking diverse areas of mathematics and advancing modern number theory significantly.

Stanislav Smirnov - Russia - Stanislav Smirnov (1970 - Present) was awarded the Fields Medal in 2010 for his work in statistical physics and probability theory. He proved the conformal invariance of percolation and the Ising model in two dimensions, confirming predictions from physics. Smirnov’s work provided a rigorous mathematical foundation for critical phenomena in statistical mechanics, linking probability theory, complex analysis and mathematical physics in novel ways.

Cedric Villani - France - Cédric Villani (1973 - Present) was awarded the Fields Medal in 2010 for his contributions to the theory of partial differential equations, particularly in mathematical physics and probability. His work on the Boltzmann equation and optimal transport theory provided deep insights into the behavior of gases and entropy dissipation. His groundbreaking results on nonlinear Landau damping and trend to equilibrium in kinetic theory had significant implications for statistical physics and fluid dynamics.

FIELDS MEDAL WINNERS IN 2006

Andrei Okounkov - Russia - Andrei Okounkov (1969 - Present) was awarded the Fields Medal in 2006 for his contributions to mathematical physics, representation theory and algebraic geometry. His work connected probability theory and statistical mechanics with algebraic geometry, particularly in the study of random surfaces and partitions. Andrei had developed probabilistic techniques to solve problems in enumerative geometry, linking them to quantum field theory and integrable systems, significantly advancing mathematical physics and combinatorial representation theory.

Grigori Perelman - Russia - Grigori Perelman (1966 - Present) was awarded the Fields Medal in 2006 for his proof of the Poincaré Conjecture, a century-old problem in topology. Using Richard S. Hamilton’s Ricci flow, he resolved the conjecture by demonstrating how three-dimensional spaces evolve under geometric deformation. His groundbreaking insights revolutionized geometric analysis. However, he declined the award, stating his disinterest in recognition and dissatisfaction with the mathematical community’s ethics.

Terence Tao - Australia - Terence Tao (1975 - Present) was awarded the Fields Medal in 2006 for his contributions to partial differential equations, additive number theory, harmonic analysis, and random matrices. His work on the Kakeya problem, arithmetic progressions in prime numbers (with Ben Green), and compressed sensing revolutionized multiple mathematical fields. Tao’s research had a profound impact on both pure and applied mathematics.

Wendelin Werner - France - Wendelin Werner (1968 - Present) was awarded the Fields Medal in 2006 for his pioneering work in probability theory, particularly in stochastic Loewner evolution (SLE) and its connections to two-dimensional critical phenomena in statistical physics. His research provided deep insights into the scaling limits of random processes, such as percolation and self-avoiding walks. Werner's work unified probability, complex analysis and mathematical physics, significantly advancing the understanding of conformal invariance in two-dimensional systems.

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