The International Mathematical Union awarded the 2026 Fields Medals to Yu Deng, John Pardon, Jacob Tsimerman and Hong Wang at the opening of the International Congress of Mathematicians in Philadelphia in July. The medal goes to mathematicians under 40, both for what they have achieved and for the promise of what is to come.
Yu Deng works on partial differential equations. He rigorously derived the Boltzmann equation, which describes thin gases, from the motion of colliding hard spheres, derived the equations that describe how energy spreads through large systems of waves, and developed probabilistic approaches to the nonlinear Schrödinger equation.
John Pardon is honoured for work in symplectic geometry, including new approaches to counting holomorphic curves, and for results in other parts of geometry and topology, among them group actions on three-dimensional manifolds and knot theory.
Jacob Tsimerman turned o-minimality, an idea from mathematical logic, into a basic method of arithmetic and algebraic geometry, and helped prove several central conjectures, including the André–Oort conjecture for Siegel modular varieties and Griffiths' conjecture on the images of period maps.
Hong Wang works in harmonic analysis and geometric measure theory. She made major advances on Fourier restriction, Falconer distance sets and Furstenberg sets, and on the Kakeya problem in three dimensions, which asks how much space a set must take up if it contains a line segment pointing in every direction.
The medals and their cash prizes are paid for by a trust set up by J. C. Fields at the University of Toronto, with extra support this year from the Fields Institute. If you are thinking about a doctorate in mathematics, our guide to contacting PhD supervisors explains how to approach a potential supervisor.
