01 · A life in mathematics
The person behind the work
Yu Deng is an analyst born in Shenzhen whose research connects deterministic differential equations with statistical descriptions of large systems. After undergraduate study at Peking University and MIT, he earned his doctorate at Princeton in 2015. At the time of the 2026 medal he was a professor at the University of Chicago. With Zaher Hani and Xiao Ma, he derived the Boltzmann equation from hard-sphere dynamics in a dilute-gas limit. His collaborations also developed wave kinetic limits and probabilistic methods for nonlinear Schrödinger equations. These results clarify when collective laws follow rigorously from microscopic motion.
The contribution, explained
Following every molecule of a gas is hopeless in practice. The Boltzmann equation instead tracks a density: how many particles have a given position and velocity. But a useful equation should also follow from an underlying model. Deng, Hani and Ma studied many small hard spheres moving by Newtonian rules and colliding elastically. In an appropriate low-density limit, they controlled the accumulation of correlations created by repeated collisions and derived the Boltzmann description on long time intervals. This connects two mathematical levels of explanation: exact particle trajectories and the evolving statistical distribution of a gas.
Why it matters
The work supplies a rigorous bridge between Newtonian mechanics and kinetic theory. It advances a central part of Hilbert’s sixth problem and strengthens the mathematical foundations of nonequilibrium statistical physics and related continuum limits.