Mathematics rewards patience more than most disciplines, and the 2026 Fields Medals are a portrait of that. Announced on 23 July at the opening of the International Congress of Mathematicians in Philadelphia, the four awards went to researchers who each finished off a question that had resisted the field for decades — in two cases, for more than a century.
The recipients are Hong Wang of New York University and the Institut des Hautes Études Scientifiques near Paris, Yu Deng of the University of Chicago, John Pardon of Stony Brook University and Jacob Tsimerman of the University of Toronto. The medal is given only once every four years, and only to mathematicians under 40; in its 90-year history Wang is the third woman to receive one, after Maryam Mirzakhani in 2014 and Maryna Viazovska in 2022. She and Deng, both born and raised in China, join Shing-Tung Yau, who won in 1982, as the only Chinese-born laureates.
Wang's citation rests on harmonic analysis and geometric measure theory, and above all on the three-dimensional Kakeya conjecture, which she settled in 2025 with Joshua Zahl. The question sounds like a parlour game: swivel a pencil so that it points in every direction, using as little space as possible. How small can that space be? Mathematicians had chased the answer for some fifty years. Nets Katz of Rice University calls it the field's "holy grail" problem and Wang a central figure in the area. She earned her PhD at MIT in 2019 under Larry Guth.
Deng's work reaches back to a challenge David Hilbert posed at the congress of 1900: reconcile the smooth, continuous behaviour of a fluid with the fact that it is really a crowd of jostling molecules. With collaborators, in a series of very long papers released in 2024 and 2025, he proved that the equations describing fluids at those two scales are the same equations — including a rigorous derivation of the Boltzmann equation from the dynamics of hard spheres. The proof also clarifies why microscopic physics can look identical played backwards while a mixture of hot and cold gas never unmixes itself.
Two alumni, one department
Pardon was honoured for symplectic and contact geometry, including problems thrown up by string theory, work that began with a paper written while he was still at secondary school. Tsimerman was recognised in number theory, for Diophantine equations and the higher-dimensional objects called Shimura varieties.
Both Deng and Wang passed through MIT — Deng as an undergraduate, finishing his mathematics degree in 2011, Wang as a doctoral student. Their department head, Michel Goemans, described the two achievements as monumental. Prizes reward individuals; the pipeline behind them is slower and quieter, and pays out over decades.