On 23 July 2026, at the International Congress of Mathematicians in Philadelphia, four mathematicians received the Fields Medal: Yu Deng, John Pardon, Jacob Tsimerman and Hong Wang. Their work sounds forbidding — the official citations mention Fukaya categories and o-minimal techniques — but each one starts from a question you can explain at a kitchen table. This guide does exactly that, and shows how each result links back to maths you meet at school.
The distinction students often miss
What a Fields Medal is — and isn't
It is awarded every four years to two to four mathematicians under 40, for outstanding work and future promise. It is not a prize for solving one particular famous problem (unlike the $1 million Millennium Prizes in our Millennium Prize Problems guide), and there is no Nobel Prize in mathematics — which is partly why the Fields Medal is so widely described as maths' highest honour.
The four medallists at a glance
Yu Deng
University of Chicago
Partial differential equations and mathematical physics
John Pardon
Stony Brook University
Symplectic geometry and topology
Jacob Tsimerman
University of Toronto
Number theory and arithmetic geometry
Hong Wang
New York University and IHES (France)
Harmonic analysis and geometric measure theory
Yu Deng
University of Chicago · Partial differential equations and mathematical physics
Undergraduate extension Physics describes a gas in two very different ways: as trillions of tiny balls bouncing off each other, or as a smooth flowing substance described by equations. Proving, with full mathematical rigour, that the first picture really leads to the second has been a goal since David Hilbert listed it among his famous problems in 1900. Deng (with collaborators) derived the Boltzmann equation — the key bridge between the two pictures — directly from colliding hard spheres.
Illustration — from colliding balls to a smooth gas
Official citation: “for his work in partial differential equations, including 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.”
Connects to: A-Level mechanics (collisions, momentum) and the gas laws.
John Pardon
Stony Brook University · Symplectic geometry and topology
Undergraduate extension Some of the most important questions in modern geometry are about counting: how many curves of a certain kind fit inside a complicated shape? Making those counts precise is notoriously hard. Pardon built new foundations for this kind of counting and used them on special shapes called Calabi–Yau 3-folds — which also appear in string theory — proving a conjecture that had been open for about 20 years.
Illustration — counting curves on a shape
Official citation: “for his achievements in symplectic geometry, including new approaches to virtual fundamental cycles, Fukaya categories of Liouville manifolds and counting holomorphic curves, and for his contributions to other areas of geometry and topology, including group actions on 3-manifolds and knot theory.”
Connects to: curves and shapes in GCSE geometry, taken many dimensions further.
Jacob Tsimerman
University of Toronto · Number theory and arithmetic geometry
Undergraduate extension O-minimality comes from mathematical logic: it describes 'tame' shapes that cannot wiggle infinitely in nasty ways. Tsimerman showed how powerful this idea is for questions about whole-number solutions and geometry, and with collaborators proved Griffiths' conjecture, which says certain complicated-looking maps actually produce shapes defined by polynomial equations. His work connects to the Hodge Conjecture, one of the Millennium Prize Problems.
Illustration — a 'tame' curve and a 'wild' one
Official citation: “for his role in the vast extension of the scope of o-minimal techniques within arithmetic and complex algebraic geometry, including the proof of Griffiths' conjecture on the algebraicity of images of the period maps.”
Connects to: polynomial equations and their graphs, A-Level algebra.
Hong Wang
New York University and IHES (France) · Harmonic analysis and geometric measure theory
Undergraduate extension In 1917 Sōichi Kakeya asked how little room you need to turn a needle all the way round. The modern three-dimensional version asks whether a set containing a needle pointing in every direction must be fully three-dimensional. In February 2025 Wang and Joshua Zahl posted a 127-page proof that it must — a result experts called one of the biggest of the century so far, because Kakeya sits underneath many problems about waves and Fourier analysis.
Illustration — turning a needle all the way round
Official citation: “for her work in harmonic analysis and geometric measure theory, including applications of multiscale and decoupling techniques to the local smoothing conjecture for the planar wave equation, and major advances in Fourier restriction, Falconer distance sets, Furstenberg sets in the plane, and the Kakeya problem in three dimensions.”
Connects to: vectors and directions, and the sine waves of A-Level trigonometry.
Quick check
Which statement about the 2026 Fields Medals is correct?
The other 2026 prizes
- IMU Abacus Medal (mathematical aspects of computer science): Shayan Oveis Gharan, University of Washington.
- Chern Medal (lifetime achievement): Graeme Segal, University of Oxford.
- Carl Friedrich Gauss Prize (applications of mathematics): Yurii Nesterov, UCLouvain, Belgium — whose optimisation methods sit underneath much of modern machine learning.
- Leelavati Prize (public outreach): Hannah Fry, University of Cambridge — familiar to many UK students from television and the Royal Institution Christmas Lectures.
Why this matters if you are studying maths
None of these results is on a syllabus, but the questions behind them are. Collisions and momentum, polynomial graphs, directions and vectors, waves and sine curves: every 2026 medal grew out of ideas you meet at GCSE and A-Level, followed much further. If one of these stories caught your interest, our Unresolved Mathematical Mysteries hub shows which big questions are still open — and which, like Kakeya, have recently fallen.
Sources and further reading
- 2026 Fields Medals Awarded to Four of World's Top Mathematicians — Simons Foundation (23 Jul 2026) — names, institutions, citations and the other IMU prizes
- International Mathematical Union — Fields Medal
- 'Once in a Century' Proof Settles Math's Kakeya Conjecture — Quanta Magazine (14 Mar 2025)
- Terence Tao — The three-dimensional Kakeya conjecture, after Wang and Zahl
Last reviewed: 3 October 2026. Figures are typical published values and rules can change. Exam wording varies by specification, so check yours.
Frequently asked questions
What is the Fields Medal?
It is awarded every four years by the International Mathematical Union at the International Congress of Mathematicians, to between two and four mathematicians who have not turned 40 before 1 January of that year. It recognises outstanding achievement and the promise of future work, and is often described as the highest honour in mathematics.
Who won the Fields Medal in 2026?
Yu Deng (University of Chicago), John Pardon (Stony Brook University), Jacob Tsimerman (University of Toronto) and Hong Wang (New York University and IHES). The medals were presented on 23 July 2026 at the International Congress of Mathematicians in Philadelphia.
How many women have won the Fields Medal?
Three. Maryam Mirzakhani was the first, in 2014, followed by Maryna Viazovska in 2022 and Hong Wang in 2026.
Were any other prizes awarded in 2026?
Yes. The IMU Abacus Medal (mathematics of computer science) went to Shayan Oveis Gharan, the Chern Medal (lifetime achievement) to Graeme Segal, the Carl Friedrich Gauss Prize (applied mathematics) to Yurii Nesterov, and the Leelavati Prize (public outreach) to Hannah Fry.
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