| 2015 | Mountain View, US | Simon Donaldson | Stony Brook University, US & Imperial College London, UK | Stony Brook University, US & Imperial College London, UK | “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.” |
| 2015 | Mountain View, US | Maxim Kontsevich | Institut des Hautes Études Scientifiques, France | Institut des Hautes Études Scientifiques, 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.” |
| 2015 | Mountain View, US | Jacob Lurie | Harvard University, US | Institute for Advanced Study, US | “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.” |
| 2015 | Mountain View, US | Terence Tao | University of California, Los Angeles, US | University of California, Los Angeles, US | “For numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory.” |
| 2015 | Mountain View, US | Richard Taylor | Institute for Advanced Study, US | Stanford University, US | “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.” |
| 2016 | Mountain View, US | Ian Agol | University of California, Berkeley, US & Institute for Advanced Study, US | University of California, Berkeley, US | “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.” |
| 2017 | Mountain View, US | Jean Bourgain | Institute for Advanced Study, US | Institute for Advanced Study, US (Deceased) | “For multiple transformative contributions to analysis, combinatorics, partial differential equations, high-dimensional geometry and number theory.” |
| 2018 | Mountain View, US | Christopher Hacon | University of Utah, US | University of Utah, US | “For transformational contributions to birational algebraic geometry, especially to the minimal model program in all dimensions.” |
| 2018 | Mountain View, US | James McKernan | University of California, San Diego, US | University of California, San Diego, US | “For transformational contributions to birational algebraic geometry, especially to the minimal model program in all dimensions.” |
| 2019 | Mountain View, US | Vincent Lafforgue | CNRS & Université de Grenoble Alpes, France | CNRS & Université de Grenoble Alpes, France | “For ground-breaking contributions to several areas of mathematics, in particular to the Langlands program in the function field case.” |
| 2020 | Mountain View, US | Alex Eskin | University of Chicago, US | University of Chicago, US | “For revolutionary discoveries in the dynamics and geometry of moduli spaces of Abelian differentials, including the proof of the ‘magic wand theorem’ with Maryam Mirzakhani.” |
| 2021 | Los Angeles, US (Virtual) | Martin Hairer | Imperial College London, UK | EPFL, Switzerland | “For transformative contributions to the theory of stochastic analysis, particularly the theory of regularity structures in stochastic partial differential equations.” |
| 2022 | Los Angeles, US (Virtual) | Takuro Mochizuki (望月拓郎) | Kyoto University, Japan | Kyoto University, Japan | “For monumental work leading to a breakthrough in our understanding of the theory of holonomic D-modules, including the proof of the Kashiwara conjecture for semisimple harmonic bundles.” |
| 2023 | Los Angeles, US | Daniel Spielman | Yale University, US | Yale University, US | “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.” |
| 2024 | Los Angeles, US | Simon Brendle | Columbia University, US | Columbia University, US | “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.” |
| 2025 | Los Angeles, US | Dennis Gaitsgory | Max Planck Institute for Mathematics, Germany | Max Planck Institute for Mathematics, Germany | “For breakthroughs in the Langlands program, specifically for the geometric Langlands conjecture.” |
| 2026 | Los Angeles, US | Frank Merle | CY Cergy Paris Université & IHÉS, France | CY Cergy Paris Université & IHÉS, France | “For breakthroughs in nonlinear evolution equations, with regards to their stability, singularity formation, or resolution into solitons.” |
