Hilbert’s Sixth Problem concerns systems in statistical physics and kinetic theory that have huge (N~10^23) degrees of freedom. The goal is to rigorously derive the macroscopic laws of motion, from these microscopic systems, in the kinetic limit N->∞.

Such systems arise in both classical particle and quantum/wave settings, leading to the classical kinetic theory and the modern theory of wave turbulence. In this talk I will review the state of art of Hilbert’s Sixth Problem in both settings, including recent joint works with Zaher Hani (Michigan) that lead to major advancements in the wave turbulence setting.