# Breakthrough Prize in Mathematics

The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013.
It is funded by Yuri Milner and 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

| Year | Laureate (birth/death) | Country | Rationale | Affiliation |
| 2015 | Simon Donaldson (b. 1957) | United Kingdom | "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 University Imperial College London |
| 2015 | Maxim Kontsevich (b. 1964) | Russia France | "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 |
| 2015 | Jacob Lurie (b. 1977) | United States | "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 |
| 2015 | Terence Tao (b. 1975) | Australia United States | "for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory." | University of California, Los Angeles |
| 2015 | Richard Taylor (b. 1962) | United Kingdom United States | "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) | United States | "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, Berkeley Institute for Advanced Study |
| 2017 | Jean Bourgain (1954–2018) | Belgium | "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) | United Kingdom United States | "for transformational contributions to birational algebraic geometry, especially to the minimal model program in all dimensions." | University of Utah |
| 2018 | James McKernan (b. 1964) | United Kingdom | "for transformational contributions to birational algebraic geometry, especially to the minimal model program in all dimensions." | University of California, San Diego |
| 2019 | Vincent Lafforgue (b. 1974) | France | "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 Scientifique Institut Fourier, Université Grenoble-Alpes |
| 2020 | Alex Eskin (b. 1965) | United States | "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 |
| 2020 | Maryam Mirzakhani (1977–2017) (posthumously awarded) | Iran United States | "for revolutionary discoveries in the dynamics and geometry of moduli spaces of Abelian differentials, including the proof of the 'magic wand theorem'." | Stanford University |
| 2021 | Martin Hairer (b. 1975) | Austria United Kingdom | "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) | Japan | "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) | United States | "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 University |
| 2024 | Simon Brendle (b. 1981) | Germany United States | "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 University |

## New Horizons in Mathematics Prize

The past laureates of the New Horizons in Mathematics prize are:
* 2016
** André Arroja Neves
** Larry Guth
** (prize was rejected by Peter Scholze)
* 2017
** Geordie Williamson
** Benjamin Elias
** Hugo Duminil-Copin
** Mohammed Abouzaid
* 2018
** Zhiwei Yun
** Wei Zhang
** Maryna Viazovska
** Aaron Naber
* 2019
** Chenyang Xu
** Karim Adiprasito
** June Huh
** Kaisa Matomäki
** Maksym Radziwill
* 2020
** Tim Austin
** Emmy Murphy
** Xinwen Zhu
* 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 Sebastian 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."

## Maryam Mirzakhani New Frontiers Prize

* 2021
** Nina Holden – "For work in random geometry, particularly on Liouville quantum gravity as a scaling limit of random triangulations."
** Urmila Mahadev – "For work that addresses the fundamental question of verifying the output of a quantum computation."
** Lisa Piccirillo – "For resolving the classic problem that the Conway knot is not smoothly slice."
* 2022
** Sarah Peluse – "For contributions to arithmetic combinatorics and analytic number theory, particularly with regards to polynomial patterns in dense sets."
** Hong Wang – "For advances on the restriction conjecture, the local smoothing conjecture, and related problems."
** Yilin Wang – "For innovative and far-reaching work on the Loewner energy of planar curves."
* 2023
** Maggie Miller – "For work on fibered ribbon knots and surfaces in 4-dimensional manifolds."
** Jinyoung Park – "For contributions to the resolution of several major conjectures on thresholds and selector processes."
** Vera Traub – "For advances in approximation results in classical combinatorial optimization problems, including the traveling salesman problem and network design."
* 2024
** Hannah Larson, University of California, Berkeley (PhD Stanford University 2022) – "For advances in Brill-Noether theory and the geometry of the moduli space of curves."
** Laura Monk, University of Bristol (PhD University of Strasbourg 2021) – "For advancing our understanding of random hyperbolic surfaces of large genus."
** Mayuko Yamashita, Kyoto University (PhD University of Tokyo 2022) – "For contributions to mathematical physics, index theory."