The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013.
It is supported by foundations co-founded by Julia and Yuri Milner, Mark Zuckerberg and others. The annual award comes with a cash gift of $3 million. The Breakthrough Prize Board also selects up to three laureates for the New Horizons in Mathematics Prize, which awards $100,000 to early-career researchers. Starting in 2021 (prizes announced in September 2020), the $50,000 Maryam Mirzakhani New Frontiers Prize is also awarded to a number of women mathematicians who have completed their PhDs within the past two years.
Motivation The founders of the prize have stated that they want to help scientists to be perceived as celebrities again, and to reverse a 50-year "downward trend". They hope that this may make "more young students aspire to be scientists".
Laureates YearPortraitLaureate(birth/death)CountryRationaleAffiliation 2015 Simon Donaldson(b. 1957) "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." Stony Brook UniversityImperial College London Maxim Kontsevich(b. 1964) "for work making a deep impact in a vast variety of mathematical disciplines, including algebraic geometry, deformation theory, symplectic topology, homological algebra and dynamical systems." Institut des Hautes Études Scientifiques Jacob Lurie(b. 1977) "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." Harvard University Terence Tao(b. 1975) "for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory." University of California, Los Angeles Richard Taylor(b. 1962) "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." Institute for Advanced Study 2016 Ian Agol(b. 1970) "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." University of California, BerkeleyInstitute for Advanced Study 2017 Jean Bourgain(1954–2018) "for multiple transformative contributions to analysis, combinatorics, partial differential equations, high-dimensional geometry and number theory." Institute for Advanced Study 2018 Christopher Hacon(b. 1970) "for transformational contributions to birational algebraic geometry, especially to the minimal model program in all dimensions." University of Utah James McKernan(b. 1964) University of California, San Diego 2019 Vincent Lafforgue(b. 1974) "for ground breaking contributions to several areas of mathematics, in particular to the Langlands program in the function field case." Centre National de la Recherche ScientifiqueInstitut Fourier, Université Grenoble-Alpes 2020 Alex Eskin(b. 1965) "for revolutionary discoveries in the dynamics and geometry of moduli spaces of Abelian differentials, including the proof of the 'magic wand theorem'." University of Chicago Maryam Mirzakhani(1977–2017)(posthumously awarded) Stanford University 2021 Martin Hairer(b. 1975) "for transformative contributions to the theory of stochastic analysis, particularly the theory of regularity structures in stochastic partial differential equations." Imperial College London 2022 Takurō Mochizuki(b. 1972) "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." Kyoto University 2023 Daniel Spielman(b. 1970) "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." Yale University2024Simon Brendle (b. 1981)"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."Columbia University2025Dennis Gaitsgory (b. 1973)"for his central role in the proof of the geometric Langlands conjecture."Max Planck Institute for Mathematics2026Frank Merle (b. 1962)"for breakthroughs in nonlinear evolution equations, with regards to their stability, singularity formation, or resolution into solitons."Laureate 2026CY Cergy Paris University and Institut des Hautes Études Scientifiques
New Horizons in Mathematics Prize The past laureates of the New Horizons in Mathematics prize are: 2016 André Arroja Neves – "For outstanding contributions to several areas of differential geometry, including work on scalar curvature, geometric flows, and his solution with Fernando Codá Marques of the 50-year-old Willmore Conjecture." Larry Guth – "For ingenious and surprising solutions to long standing open problems in symplectic geometry, Riemannian geometry, harmonic analysis, and combinatorial geometry." (prize was rejected by Peter Scholze) 2017 Geordie Williamson – "For pioneering work in geometric representation theory, including the development of Hodge theory for Soergel bimodules and the proof of the Kazhdan-Lusztig conjectures for general Coxeter groups." Benjamin Elias – "For pioneering work in geometric representation theory, including the development of Hodge theory for Soergel bimodules and the proof of the Kazhdan-Lusztig conjectures for general Coxeter groups." Hugo Duminil-Copin – "For brilliant solutions to multiple landmark problems in probability, particularly regarding critical phenomena for Ising-type models." Mohammed Abouzaid – "For distinguishing cotangent bundles of exotic spheres, constructing the wrapped Fukaya category with Paul Seidel, and other decisive contributions to symplectic topology and mirror symmetry." 2018 Zhiwei Yun – "For deep work on the global Gan-Gross-Prasad conjecture and the discovery of geometric interpretations for the higher derivatives of L-functions in the function field case." Wei Zhang – "For deep work on the global Gan-Gross-Prasad conjecture and the discovery of geometric interpretations for the higher derivatives of L-functions in the function field case." Maryna Viazovska – "For remarkable application of the theory of modular forms to the sphere packing problem in special dimensions." Aaron Naber – "For work in geometric analysis and Riemannian geometry, introducing powerful new techniques to solve outstanding problems, particularly for manifolds with Ricci curvature bounds." 2019 Chenyang Xu – "For major advances in the minimal model program and applications to the moduli of algebraic varieties." Karim Adiprasito – "For the development, with Eric Katz, of combinatorial Hodge theory leading to the resolution of the log-concavity conjecture of Rota." June Huh – "For the development, with Eric Katz, of combinatorial Hodge theory leading to the resolution of the log-concavity conjecture of Rota." Kaisa Matomäki – "For fundamental breakthroughs in the understanding of local correlations of values of multiplicative functions." Maksym Radziwill – "For fundamental breakthroughs in the understanding of local correlations of values of multiplicative functions." 2020 Tim Austin – "For multiple contributions to ergodic theory, most notably the solution of the weak Pinsker conjecture." Emmy Murphy – "For contributions to symplectic and contact geometry, in particular the introduction of notions of loose Legendrian submanifolds and, with Matthew Strom Borman and Yakov Eliashberg, overtwisted contact structures in higher dimensions." Xinwen Zhu – "For work in arithmetic algebraic geometry including applications to the theory of Shimura varieties and the Riemann-Hilbert problem for p-adic varieties." 2021 Bhargav Bhatt – "For outstanding work in commutative algebra and arithmetic algebraic geometry, particularly on the development of p-adic cohomology theories." Aleksandr Logunov – "For novel techniques to study solutions to elliptic equations, and their application to long-standing problems in nodal geometry." Song Sun – "For many groundbreaking contributions to complex differential geometry, including existence results for Kähler–Einstein metrics and connections with moduli questions and singularities." 2022 Aaron Brown and Sebastián Hurtado-Salazar – "For contributions to the proof of Zimmer's conjecture." Jack Thorne – "For transformative contributions to diverse areas of algebraic number theory, and in particular for the proof, in collaboration with James Newton, of the automorphy of all symmetric powers of a holomorphic modular newform." Jacob Tsimerman – "For outstanding work in analytic number theory and arithmetic geometry, including breakthroughs on the André–Oort and Griffiths conjecture 2023 Ana Caraiani – "For diverse transformative contributions to the Langlands program, and in particular for work with Peter Scholze on the Hodge-Tate period map for Shimura varieties and its applications." Ronen Eldan – "For the creation of the stochastic localization method, that has led to significant progress in several open problems in high-dimensional geometry and probability, including Jean Bourgain's slicing problem and the KLS conjecture." James Maynard – "For multiple contributions to analytic number theory, and in particular to the distribution of prime numbers." 2024 Roland Bauerschmidt, New York University – "For outstanding contributions to probability theory and the development of renormalisation group techniques." Michael Groechenig, University of Toronto – "For contributions to the theory of rigid local systems and applications of p-adic integration to mirror symmetry and the fundamental lemma." Angkana Rüland, University of Bonn – "For contributions to applied analysis, in particular the analysis of microstructure in solid-solid phase transitions and the theory of inverse problems." 2025 Ewain Gwynne, University of Chicago – "for his work in conformal probability, which studies probabilistic objects such as random curves and surfaces." John Pardon, Stony Brook University – "for his producing a number of important results in geometry and topology, particularly in the field of symplectic geometry and pseudo-holomorphic curve, which are certain types of smooth surfaces in manifolds." Sam Raskin, Yale University – "for his playing a significant role in the major recent progress on the geometric Langlands program, including the final proof of the geometric Langlands conjecture in characteristic zero." 2026 Otis Chodosh, Stanford University – "For contributions to differential geometry and the calculus of variations, including work on minimal surfaces and manifolds with positive scalar curvature." Hong Wang, Institut des Hautes Études Scientifiques and New York University – "For work in harmonic analysis, partial differential equations, and geometric measure theory, including the local smoothing conjecture, Furstenberg set conjecture, and the Kakeya conjecture." Vesselin Dimitrov, Caltech, and Yunqing Tang, University of California, Berkeley – "For work in Diophantine geometry, including the proof of the Atkin-Swinnerton-Dyer unbounded denominators conjecture and new irrationality results for special values of Dirichlet L-series (both joint with Frank Calegari)."
Maryam Mirzakhani New Frontiers Prize The Maryam Mirzakhani New Frontiers Prize, in honour of Iranian mathematician Maryam Mirzakhani, is presented to female mathematicians who have completed their PhDs within the previous two years. 2021