The evolution of a gas can be described by different models depending on the scale of observation. A natural question, raised by Hilbert by Hilbert in his sixth problem, is to know if these models provide consistent predictions. In the case of dilute gases of hard spheres, Lanford showed in 1974 that the Boltzmann equation appears as a law of large numbers in the limit where the number of particles particles tends to infinity, at least for very short times. In this talk, we will present Lanford's result and some more recent extensions to understand the fluctuations and large deviations around the Boltzmann equation.