The 2026 Fields Medals were presented on 23 July at the opening ceremony of the International Congress of Mathematicians in Philadelphia. Four researchers received the award, each recognised for decisive progress on questions that had resisted resolution for decades.
Yu Deng of the University of Chicago was honoured for work on partial differential equations. His contributions include the rigorous derivation of the Boltzmann equation from hard-sphere dynamics for rarefied gases, the derivation of wave kinetic equations from nonlinear dispersive systems, and probabilistic approaches to nonlinear Schrödinger dynamics. These results tighten the connection between microscopic particle models and the macroscopic equations used across physics.
John Pardon of Stony Brook University earned the medal for advances in symplectic geometry. He developed new approaches to virtual fundamental cycles, Fukaya categories of Liouville manifolds and the counting of holomorphic curves. His techniques have also illuminated group actions on 3-manifolds and questions in knot theory.
Jacob Tsimerman of the University of Toronto recast o-minimality as a core tool in arithmetic and complex algebraic geometry. This shift helped prove several central conjectures, among them Griffiths' conjecture on the algebraicity of images of period maps and the André-Oort conjecture for Siegel modular varieties.
Hong Wang of New York University and the Institut des Hautes Études Scientifiques received the medal for progress in harmonic analysis and geometric measure theory. Her applications of multiscale and decoupling techniques resolved the local smoothing conjecture for the planar wave equation. She has also made major advances on Fourier restriction, Falconer distance sets, Furstenberg sets in the plane and the Kakeya problem in three dimensions.
Merit and method
The Fields Medal is awarded every four years by the International Mathematical Union to mathematicians under 40. It remains one of the clearest expressions of a tradition that values objective truth pursued through rigorous proof. In an era when many fields face pressure to subordinate discovery to external criteria, these awards quietly reaffirm that enduring scientific progress rests on merit alone.