The Boltzmann equation is a fundamental model in kinetic theory, providing a statistical description of a typical particle in a dilute gas. It acts as a middle ground between a microscopic model tracking every particle, and the macroscopic models of fluid mechanics. A key hypothesis in its derivation is the puzzling assumption of molecular chaos: any two gas particles are considered independent before they collide, disregarding their previous interactions that should correlate them. In 1956, Mark Kac proposed to prove molecular chaos by starting from a microscopic Markov jump process of N colliding particles, and showing that the particles indeed become approximately independent for large N. This limiting process is now known as propagation of chaos.

In this talk, I will first present the Boltzmann equation, and then delve into Kac's program. I will give a proof of propagation of chaos in a simple setting, that can be extended to cover the full range of physically-relevent parameters in the Boltzmann equation.