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Breakthrough Prize in Mathematics

The Breakthrough Prize in Mathematics is an annual award presented to individuals for profound contributions to the field of mathematics, with a top prize of $3 million aimed at recognizing groundbreaking discoveries across its diverse branches.^[1] Established in 2014 as part of the broader Breakthrough Prizes initiative, it seeks to honor exceptional mathematicians, inspire future research, and highlight the importance of mathematics in advancing human knowledge.^[2] Founded by philanthropists including Yuri Milner, Sergey Brin, Anne Wojcicki, Mark Zuckerberg, and Priscilla Chan, the prize is funded through grants from foundations co-founded by Milner and his wife Julia, among others.^[1]^[3] In addition to the flagship Breakthrough Prize in Mathematics, the program includes the New Horizons in Mathematics Prize, which awards $100,000 to up to three early-career researchers for significant work already accomplished, fostering emerging talent in the field.^[1] Following the passing of mathematician Maryam Mirzakhani in 2017, a dedicated Maryam Mirzakhani New Frontiers Prize of $50,000 was introduced in 2019 to recognize up to three outstanding rising female mathematicians who have completed their PhDs within the past two years.^[4] These awards collectively emphasize both established achievements and underrepresented voices, with nominations open to the public and selections made by committees comprising previous laureates to ensure rigorous, peer-reviewed evaluation.^[5] Often dubbed the "Oscars of Science" for its prestige and substantial funding—totaling over $300 million distributed across all Breakthrough categories since inception—the Mathematics Prize has celebrated transformative work in areas such as algebraic geometry, number theory, and theoretical computer science.^[3] The inaugural 2014 ceremony awarded the prize to five mathematicians: Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Terence Tao, and Richard Taylor, marking a historic recognition of the field's global impact.^[2] By providing financial freedom for laureates to pursue ambitious projects, the prize not only rewards past innovations but also amplifies mathematics' role in interdisciplinary breakthroughs, from physics to artificial intelligence.^[1]

Background

Establishment and Founders

The Breakthrough Prize in Mathematics emerged as an extension of the broader Breakthrough Prize program, which was founded in 2012 by Russian-born philanthropist and investor Yuri Milner through the Breakthrough Prize Foundation to recognize transformative achievements in fundamental science. Milner, a physicist by training, co-founded the initiative alongside his wife Julia Milner, with initial sponsorship from prominent figures including Google co-founder Sergey Brin, Facebook founder Mark Zuckerberg and his wife Priscilla Chan, and 23andMe co-founder Anne Wojcicki. These supporters contributed through their personal foundations, establishing a model of private philanthropy aimed at elevating scientific recognition beyond traditional awards.^[6]^[7]^[3] The mathematics prize was specifically announced on December 13, 2013, during the second annual Breakthrough Prize ceremony in Mountain View, California, expanding the program's scope from its original emphasis on fundamental physics and life sciences. Milner, in collaboration with Zuckerberg, spearheaded this addition to address what they perceived as insufficient recognition for mathematical breakthroughs compared to other scientific fields. This move built on the foundation's growing momentum, with the mathematics category designed to parallel the structure of its counterparts while highlighting pure and applied mathematical innovations.^[7]^[2] The inaugural Breakthrough Prizes in Mathematics were awarded in June 2014 to five laureates—Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Terence Tao, and Richard Taylor—for their profound contributions to geometry, algebraic geometry, topology, harmonic analysis, and number theory, respectively. These awards were formally presented at the November 2014 ceremony, signifying the prize's official entry into the mathematical community and underscoring its integration into the Breakthrough ecosystem.^[2] Administered by the Breakthrough Prize Foundation in coordination with a dedicated board, the mathematics prize operates within the shared framework of the overall program, including nomination processes, selection committees, and annual ceremonies that celebrate multiple disciplines. This unified structure ensures consistent standards and visibility across the prizes while allowing field-specific adaptations.^[3]

Objectives and Significance

The Breakthrough Prize in Mathematics aims to recognize profound contributions to the field by honoring mathematicians whose work represents major advances across its diverse branches, thereby supporting their ongoing research and future endeavors.^[2] Established to elevate the public profile of mathematicians, the prize seeks to counter declining interest in STEM disciplines by showcasing the excitement and fundamental importance of mathematics to society and human progress.^[2] It emphasizes celebrating "breakthroughs" that significantly advance human knowledge, without restrictions on age, nationality, or institutional affiliation, allowing for broad recognition of transformative ideas.^[8] Inspired by the Nobel Prize but designed to surpass it in scope and visibility, the Breakthrough Prize offers awards of $3 million—more than double the Nobel's monetary value—to attract greater attention to mathematical achievements and inspire young students to pursue careers in the field.^[9] Founder Yuri Milner has stated that the initiative focuses on "raising public awareness" of science and mathematics, aiming to make laureates "household names" and promote these disciplines as prestigious and rewarding paths.^[9] This approach draws from the Nobel's prestige while addressing its limitations, such as the exclusion of mathematics, to foster a more inclusive celebration of scientific innovation.^[10] The prize's broader significance lies in its role in increasing media coverage of mathematical accomplishments, which helps communicate the subject's universal relevance as the "language of nature" underpinning physics, life sciences, and computation.^[8] By highlighting interdisciplinary connections—such as the application of mathematical tools in other sciences—it encourages collaborative work that bridges traditional boundaries and drives innovation across fields.^[2] Overall, the Breakthrough Prize contributes to a cultural shift, reinforcing mathematics' vital place in advancing knowledge and inspiring global engagement with STEM.^[9]

Prize Categories

Main Breakthrough Prize in Mathematics

The Main Breakthrough Prize in Mathematics is the flagship award within the Breakthrough Prize program, recognizing profound and transformative contributions to the field of mathematics. Established to honor groundbreaking achievements that advance mathematical understanding, it celebrates work that has a lasting impact across diverse areas, including pure mathematics such as geometry, number theory, and analysis, as well as applied domains.^[1]^[11] The prize carries a value of $3 million, which is awarded to the recipient or recipients for their exceptional accomplishments. In cases of collaborative efforts deemed exceptional by the selection committee, the award may be shared among multiple individuals for joint transformative work.^[1]^[11] Eligibility for the prize is open to mathematicians of any nationality and age worldwide, encompassing both recent breakthroughs and lifetime bodies of work that demonstrate significant influence on the discipline. The focus is on contributions that exhibit originality and depth, with an emphasis on developments that reshape mathematical paradigms, though the committee prioritizes more recent advancements while considering earlier achievements within a relevant timeframe.^[11]^[12] Since its inception in 2014, the prize has been conferred annually, typically to one primary laureate per cycle, though multiple recipients are possible in collaborative scenarios. This structure underscores its role as a premier accolade, complementing other categories in the program like the New Horizons and Maryam Mirzakhani New Frontiers Prizes by targeting established, high-impact innovations.^[1]^[11]

New Horizons in Mathematics Prize

The New Horizons in Mathematics Prize recognizes promising early-career researchers who have already produced important work in mathematics, aiming to support and highlight contributions with high potential for future impact.^[1] Established as part of the Breakthrough Prize program in 2015, the prize was first awarded in 2015 to nurture emerging talent across various mathematical fields, such as probability, geometry, and number theory.^[13] This award aligns with the broader objectives of the Breakthrough Prize in Mathematics to advance fundamental research by celebrating innovative achievements at different career stages.^[1] Eligibility for the prize is limited to early-career mathematicians who have held their PhD or equivalent degree for no more than 10 years at the time nominations close, though exceptions may be made in compelling cases; there are no age restrictions.^[11] Nominations must include biographical details, at least one letter of recommendation from a third party, and up to 10 citations from academic databases demonstrating the candidate's recent, promising work.^[11] The focus is on high-potential contributions that demonstrate originality and the likelihood of leading to major breakthroughs, rather than fully mature accomplishments.^[1] Each year, up to three recipients are selected, with an award value of $100,000 per laureate to support their ongoing research.^[1] This structure allows the prize to spotlight a diverse range of early-stage innovations, fostering the next generation of mathematical leaders without restricting to specific subdisciplines.^[11]

Maryam Mirzakhani New Frontiers Prize

The Maryam Mirzakhani New Frontiers Prize, valued at $50,000 per recipient, recognizes up to three outstanding women mathematicians early in their careers each year for exceptional contributions in any area of mathematics.^[1] This award provides financial support and visibility to emerging talent at a critical juncture, shortly after completing their doctoral training.^[4] Established by the Breakthrough Prize Foundation and announced on November 4, 2019, the prize is named in honor of Maryam Mirzakhani (1977–2017), the Iranian-American mathematician and Stanford University professor who became the first woman to receive the Fields Medal in 2014 for her groundbreaking work on the dynamics and geometry of Riemann surfaces and their moduli spaces.^[4]^[14] Mirzakhani's achievements highlighted the potential of women in mathematics, and the prize seeks to perpetuate her legacy by specifically supporting female mathematicians, thereby encouraging greater participation and equity in the field where women remain underrepresented.^[4]^[15] Eligibility is restricted to women who have completed their PhD within the previous two years, ensuring the award targets those at the very outset of their independent research careers.^[1] The first recipients were honored in 2021, marking the prize's debut as part of the broader Breakthrough Prize in Mathematics portfolio.^[1]

Selection Process

Nomination Procedure

The nomination process for the Breakthrough Prize in Mathematics is open to the public and designed to encourage broad participation from the global mathematical community. Anyone worldwide may submit a nomination for any of the mathematics prizes, with no restrictions based on nationality, institutional affiliation, or career stage. Self-nominations are explicitly prohibited, ensuring that endorsements come from independent sources.^[11] Nominations are accepted annually during a designated open period, which typically spans several months and is announced in advance on the official Breakthrough Prize website. For instance, nominations for the 2026 prizes were open from April 15, 2025, to July 11, 2025. Submissions must be made exclusively through the online nomination form available at breakthroughprize.org/Nominations, where nominators provide basic biographical details for both themselves and the nominee, a summary of the nominee's key contributions to mathematics, up to 10 relevant citations from an academic publishing database, and at least one third-party letter of recommendation supporting the nomination. For the Maryam Mirzakhani New Frontiers Prize specifically, the nominee's PhD thesis is also required as part of the submission.^[16]^[11] The process emphasizes accessibility and thoroughness to facilitate review by the Selection Committee, which evaluates all valid nominations after the deadline. Nominators are encouraged to highlight transformative achievements in mathematical research that align with the prize's focus on profound insights and advancements.^[11]

Selection Committee and Criteria

The Selection Committee for the Breakthrough Prize in Mathematics is composed exclusively of past recipients of the prize, ensuring a panel of distinguished mathematicians who have themselves made profound contributions to the field. As of 2025, the committee includes more than ten members, such as Ian Agol, Simon Brendle, Ingrid Daubechies, Simon Donaldson, Alex Eskin, Dennis Gaitsgory, Martin Hairer, Christopher Hacon, Maxim Kontsevich, Peter Scholze, Terence Tao, Richard Taylor, and Avi Wigderson.^[5]^[16] This structure, established since the prize's inception, invites previous laureates to serve and select future winners, fostering continuity and expertise in the evaluation process.^[11]^[3] The committee evaluates nominations based on the profundity, originality, and impact of the nominees' contributions to mathematics, with a particular emphasis on work accomplished within the preceding decade, though exceptional earlier achievements may also be considered.^[11] For the main Breakthrough Prize in Mathematics, selections prioritize transformative advancements that reshape mathematical understanding or applications. In contrast, the New Horizons in Mathematics Prize targets early-career researchers—typically those within ten years of their PhD—with criteria focusing on the importance of their existing work and its potential for future influence. Similarly, the Maryam Mirzakhani New Frontiers Prize assesses women mathematicians early in their careers (within two years post-PhD) on the basis of their doctoral theses, evaluating novelty, depth, and promise for ongoing impact.^[11]^[1] The decision-making process occurs confidentially, with the committee reviewing all valid nominations—submitted openly by the public without self-nominations—and selecting winners through deliberation among its members.^[11]^[17] While specific voting mechanics, such as majority vote, are not publicly detailed, the process is designed to be merit-driven, with no involvement from the prize's founders or sponsors to maintain independence and objectivity.^[3] Winners are announced annually in April, following the close of the nomination period.^[18]^[16]

Laureates

Main Prize Laureates

The Main Breakthrough Prize in Mathematics, established in 2014 and awarding $3 million to recipients for profound advances in the field, has honored mathematicians for transformative work across diverse areas.^[8] In 2014, the inaugural prizes were shared among five laureates: Simon Donaldson of Stony Brook University and Imperial College London for his pioneering contributions to gauge theory and four-dimensional manifolds, which revolutionized the understanding of smooth structures on manifolds; Maxim Kontsevich of the Institut des Hautes Études Scientifiques for his foundational work in algebraic geometry and topology, including homological mirror symmetry that bridges symplectic and algebraic geometry; Jacob Lurie of Harvard University for developing derived algebraic geometry, providing new foundations for algebraic geometry and its applications in mathematical physics; Terence Tao of the University of California, Los Angeles for his wide-ranging breakthroughs in harmonic analysis, partial differential equations, combinatorics, and number theory that have advanced analytic tools across mathematics; and Richard Taylor of the Institute for Advanced Study for his key contributions to the Langlands program, particularly in establishing deep connections between Galois representations and automorphic forms.^[2] The 2016 prize went to Ian Agol of the University of California, Berkeley for his groundbreaking work in low-dimensional topology and geometric group theory, notably his proof of the virtually Haken conjecture, which resolved a major problem about the structure of 3-manifolds and advanced the geometrization of 3-dimensional spaces.^[13] In 2017, Jean Bourgain of the Institute for Advanced Study received the award for his multiple transformative contributions to analysis, combinatorics, partial differential equations, and number theory, including innovative techniques that resolved longstanding problems in harmonic analysis and arithmetic combinatorics.^[19] The 2018 prize was awarded jointly to Christopher Hacon of the University of Utah and James McKernan of the University of California, San Diego for their joint contributions to birational geometry, particularly the proof of the minimal model program for varieties of log general type in three dimensions, which provided crucial tools for classifying algebraic varieties.^[20] Vincent Lafforgue of the Centre National de la Recherche Scientifique (CNRS) and Institut Fourier, Université Grenoble Alpes, won the 2019 prize for his groundbreaking contributions to the geometric Langlands correspondence in high dimensions and the theory of arithmetic groups, establishing profound links between representation theory and number theory. In 2020, the prize was awarded to Alex Eskin of the University of Chicago for his revolutionary work on the dynamics and geometry of moduli spaces of abelian differentials, including proofs of the Zipper Lemma and closing lemma that illuminated the structure of Teichmüller dynamics.^[21] The 2021 award went to Martin Hairer of Imperial College London for his transformative contributions to the theory of stochastic partial differential equations, developing the theory of regularity structures that enables the rigorous analysis of singular equations arising in physics and beyond.^[22] In 2022, Takurō Mochizuki of Kyoto University received the prize for his monumental contributions to p-adic non-abelian Hodge theory and its applications, particularly in advancing the geometric Langlands program through novel harmonic bundles and wild harmonic sheaves.^[23] Daniel A. Spielman of Yale University was honored in 2023 for his pioneering contributions to theoretical computer science and algorithms, including the solution to the Kadison-Singer problem, advances in spectral graph theory, and compressed sensing that have broad impacts on data processing and optimization.^[24] The 2024 prize was awarded to Simon Brendle of Columbia University for his transformative work in differential geometry, encompassing sharp geometric inequalities, the theory of minimal surfaces, and breakthroughs in the analysis of Ricci flow that resolved key aspects of the Yamabe problem and mean curvature flow.^[25] Finally, in 2025, Dennis Gaitsgory of the Max Planck Institute for Mathematics was recognized for his central role in the proof of the geometric Langlands conjecture, a landmark achievement connecting number theory, representation theory, and algebraic geometry through categorical methods.^[18]

New Horizons Recipients

The New Horizons in Mathematics Prize, awarded annually since 2015, recognizes up to three early-career mathematicians under the age of 40 for their promising and impactful contributions, each receiving $100,000.^[1] In 2016, the recipients were Larry Guth of the Massachusetts Institute of Technology, for his profound and original insights into analytic number theory, combinatorics, and geometry with connections to topology and computer science; and André Arroja Neves of Imperial College London, for outstanding work on geometric measure theory, partial differential equations, and symplectic geometry, including the resolution of the Willmore conjecture.^[13] The 2017 prize went to Geordie Williamson of the Max Planck Institute for Mathematics in Bonn, for his groundbreaking work on geometric representation theory and the development of positivity in the theory of algebraic groups.^[26] In 2018, Zhiwei Yun of the Massachusetts Institute of Technology received the award for his profound contributions to the geometric Langlands program, multiple Dirac operators, and endoscopy in automorphic forms.^[20] The 2019 prize was awarded to Chenyang Xu of Princeton University for transformative contributions to the minimal model program for algebraic varieties and birational geometry.^[27] In 2020, Tim Austin of the University of California, Los Angeles was honored for his fundamental advances in ergodic theory, graph theory, and additive combinatorics.^[21] In 2021, the recipients were Bhargav Bhatt of the University of Michigan, for his outstanding work in commutative algebra and arithmetic algebraic geometry, particularly on the development of p-adic cohomology theories; Aleksandr Logunov of Princeton University, for novel techniques to study solutions to elliptic equations and their application to long-standing problems in nodal geometry; and Song Sun of the University of California, Berkeley, for many groundbreaking contributions to complex differential geometry, including existence results for Kähler-Einstein metrics and connections with moduli questions and singularities.^[22] The 2022 laureates included Aaron Brown of Northwestern University and Sebastián Hurtado Salazar of the University of Chicago (joint award), for contributions to the proof of Zimmer’s conjecture in the dynamics of group actions on manifolds; Jack Thorne of the University of Cambridge, 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; and Jacob Tsimerman of the University of Toronto, for outstanding work in analytic number theory and arithmetic geometry, including breakthroughs on the André-Oort and Griffiths conjectures.^[23] For 2023, the prize went to Ana Caraiani of Imperial College London and the University of Bonn, for diverse transformative contributions to the Langlands program, particularly work with Peter Scholze on the Hodge-Tate period map for Shimura varieties and its applications; Ronen Eldan of the Weizmann Institute of Science and Microsoft Research, for creating the stochastic localization method, leading to progress in high-dimensional geometry and probability, including Jean Bourgain's slicing problem and the KLS conjecture; and James Maynard of the University of Oxford and the Institute for Advanced Study, for multiple contributions to analytic number theory, especially the distribution of prime numbers.^[24] In 2024, recipients were Roland Bauerschmidt of New York University, for outstanding contributions to probability theory and the development of renormalization group techniques; Michael Groechenig of the 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; and Angkana Rüland of the 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.^[25] The 2025 awardees were Ewain Gwynne of the University of Chicago, for contributions to conformal probability, in particular to the understanding of the Liouville quantum gravity metric; John Pardon of Stony Brook University, for contributions to symplectic topology and other areas of geometry and topology; and Sam Raskin of Yale University, for contributions to the geometric Langlands program, including the theory of the Whittaker model and the proof of the geometric Langlands conjecture in characteristic 0.^[18]

Maryam Mirzakhani New Frontiers Recipients

The Maryam Mirzakhani New Frontiers Prize annually awards $50,000 to up to three outstanding women mathematicians who completed their PhDs within the preceding two years, recognizing their promising early-career contributions.^[1] In 2021, the inaugural recipients were Nina Holden of ETH Zürich (PhD, ETH Zürich, 2018), for her pioneering work in random geometry and probability theory, particularly on the scaling limits of random maps and Liouville quantum gravity; Urmila Mahadev of the California Institute of Technology (PhD, University of California, Berkeley, 2019), for her innovative contributions to quantum complexity theory, including results on the power of quantum interactive proofs; and Lisa Piccirillo of the Massachusetts Institute of Technology (PhD, University of Texas at Austin, 2019), for her breakthrough work in knot theory and four-dimensional topology, resolving the longstanding Property R conjecture.^[22] In 2022, the recipients were Sarah Peluse of the Institute for Advanced Study and Princeton University (PhD, Stanford University, 2019), for her work in arithmetic combinatorics and analytic number theory, including breakthroughs on the density of polynomial patterns in sets of integers. Peluse's early research established new bounds on multidimensional Szemerédi-type problems, resolving long-standing questions about arithmetic progressions in sparse sets.^[23] Hong Wang of the University of California, Los Angeles (PhD, MIT, 2019), honored for advances in harmonic analysis, particularly on the restriction and local smoothing conjectures for Fourier transforms. Her field-defining work provided novel decoupling inequalities that improved estimates for oscillatory integrals, impacting problems in partial differential equations.^[23] Yilin Wang of MIT (PhD, ETH Zürich, 2019), recognized for innovative contributions to Liouville quantum gravity and the Schramm-Loewner evolution (SLE), including studies on the Loewner energy of planar curves. Her early papers connected Gaussian free fields to SLE processes, yielding exact formulas for welding probabilities in quantum surfaces.^[23] The 2023 laureates included Maggie Miller of Stanford University and the Clay Mathematics Institute (PhD, Princeton University, 2020), for contributions to low-dimensional topology, focusing on fibered ribbon knots and embedded surfaces in 4-dimensional manifolds. Miller's seminal early work classified ribbon concordance classes and advanced understanding of contact structures on manifolds.^[24] Jinyoung Park of Stanford University (PhD, Rutgers University, 2020), awarded for resolving key conjectures on threshold phenomena in combinatorics, including the Kahn-Kalai conjecture on influences in Boolean functions. Her research introduced breakthrough methods for analyzing sharp thresholds in random graphs and hypergraphs.^[24] Vera Traub of the University of Bonn (PhD, University of Bonn, 2020), praised for advances in approximation algorithms for combinatorial optimization, such as improved ratios for the traveling salesman problem and Steiner tree problems. Traub's early contributions developed polyhedral techniques that tightened integrality gaps in linear programming relaxations.^[24] For 2024, Hannah Larson of the University of California, Berkeley (PhD, Stanford University, 2022), received the prize for work in algebraic geometry, particularly Brill-Noether theory and the geometry of moduli spaces of curves. Her field-defining results included explicit constructions of special linear series on curves, resolving cases of the Brill-Noether-Petri theorem.^[25] Laura Monk of the University of Bristol (PhD, University of Strasbourg, 2021), honored for discoveries in random geometry, including the structure of random hyperbolic surfaces of large genus. Monk's early investigations revealed phase transitions in the geometry of random surfaces, linking to Weil-Petersson geometry.^[25] Mayuko Yamashita of Kyoto University (PhD, University of Tokyo, 2022), recognized for contributions to topological phases of matter through index theory in mathematical physics. Her work formalized equivariant K-theory for gapped systems, providing tools for classifying topological insulators.^[25] The 2025 recipients were Si Ying Lee of Stanford University (PhD, Harvard University, 2022), for advances in the geometric Langlands program via the theory of Shimura varieties. Lee's early research constructed integral models and studied Rapoport-Zink spaces, bridging algebraic geometry and representation theory.^[18] Rajula Srivastava of the University of Bonn and Max Planck Institute for Mathematics (PhD, University of Wisconsin, 2022), awarded for progress in additive combinatorics and harmonic analysis, including estimates on rational points near smooth manifolds. Her seminal work improved sum-product bounds and applications to Diophantine approximation.^[18] Ewin Tang of the University of California, Berkeley (PhD, University of Washington, 2023), honored for innovations in quantum algorithms and derandomization, particularly classical sampling algorithms mimicking quantum methods for recommendation systems. Tang's thesis demonstrated dequantization of the Harrow-Hassidim-Lloyd algorithm, impacting theoretical computer science.^[18]

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