Nash’s 1958 paper about the continuity of solutions to divergence form parabolic and elliptic equations contains two key ideas. The first of these is a Sobolev type inequality, and the second is an ingenious application of the Poincar ́e inequality for Gauss In this lecture, I will explain how these two ideas can be used to prove sharp versions Aronson’s estimates on the fundamental solution to the heat flows determined by non-degenerate, divergence form operators. Using techniques introduced by Moser and refined by Krylov and Safonov, one can easily derive both Nash’s continuity result and Moser’s Harnack principle.