The Fields Medals for 2026 were awarded to four mathematicians for advances in unifying physical laws and solving longstanding geometry problems. The prizes were presented on 23 July at the International Congress of Mathematicians in Philadelphia. Hong Wang became only the third woman to receive the award in its nearly 90-year history.
Yu Deng of the University of Chicago derived the Boltzmann equation from a microscopic model of hard spheres. This work resolved a question posed by David Hilbert in 1900 on connecting microscopic particle motion to macroscopic gas behaviour.
John Pardon of Stony Brook University solved problems in topology involving knots on doughnut-shaped toruses. He also proved the MNOP conjecture on curves in geometric shapes, which relates to quantum theories of the universe.
Hong Wang of New York University resolved the three-dimensional Kakeya conjecture on the minimum space needed for a needle to point in every direction. Jacob Tsimerman of the University of Toronto applied o-minimality from mathematical logic to algebraic geometry and advanced progress on the Hodge conjecture.
The awards recognise mathematicians under the age of 40 and are given every four years.
