Breakthrough Prize in Mathematics

Dennis Gaitsgory won the Breakthrough Prize in Mathematics for his central role in the proof of the geometric Langlands conjecture.

Simon Brendle won the Breakthrough Prize in Mathematics for transformative contributions to differential geometry, including sharp geometric inequalities, many results on Ricci flow and mean curvature flow and the Lawson conjecture on minimal tori in the 3-sphere.

Daniel Spielman won the Breakthrough Prize in Mathematics for breakthrough contributions to theoretical computer science and mathematics, including to spectral graph theory, the Kadison-Singer problem, numerical linear algebra, optimization, and coding theory.

Takurō Mochizuki won the Breakthrough Prize in Mathematics for monumental work leading to a breakthrough in our understanding of the theory of bundles with flat connections over algebraic varieties, including the case of irregular singularities.

Martin Hairer won the Breakthrough Prize in Mathematics for transformative contributions to the theory of stochastic analysis, particularly the theory of regularity structures in stochastic partial differential equations.

Alex Eskin won the Breakthrough Prize in Mathematics for revolutionary discoveries in the dynamics and geometry of moduli spaces of Abelian differentials, including the proof of the 'magic wand theorem'.

Vincent Lafforgue won the Breakthrough Prize in Mathematics for ground breaking contributions to several areas of mathematics, in particular to the Langlands program in the function field case.

Christopher Hacon won the Breakthrough Prize in Mathematics for transformational contributions to birational algebraic geometry, especially to the minimal model program in all dimensions.

James McKernan won the Breakthrough Prize in Mathematics for transformational contributions to birational algebraic geometry, especially to the minimal model program in all dimensions.

Jean Bourgain won the Breakthrough Prize in Mathematics for multiple transformative contributions to analysis, combinatorics, partial differential equations, high-dimensional geometry and number theory.

Ian Agol won the Breakthrough Prize in Mathematics for spectacular contributions to low dimensional topology and geometric group theory, including work on the solutions of the tameness, virtually Haken and virtual fibering conjectures.

Simon Donaldson won the Breakthrough Prize in Mathematics for the new revolutionary invariants of 4-dimensional manifolds and for the study of the relation between stability in algebraic geometry and in global differential geometry, both for bundles and for Fano varieties.

Maxim Kontsevich won the Breakthrough Prize in Fundamental Physics For numerous contributions which have taken the fruitful interaction between modern theoretical physics and mathematics to new heights, including the development of homological mirror symmetry, and the study of wall-crossing phenomena.

Jacob Lurie won the Breakthrough Prize in Mathematics for his work on the foundations of higher category theory and derived algebraic geometry; for the classification of fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology.

Terence Tao won the Breakthrough Prize in Mathematics for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory.

Richard Taylor won the Breakthrough Prize in Mathematics for numerous breakthrough results in the theory of automorphic forms, including the Taniyama–Weil conjecture, the local Langlands conjecture for general linear groups, and the Sato–Tate conjecture.