Abstract: A classical theorem of Mazur asserts that if X is a separable real Banach space and f is a continuous convex function on X, then the points where f is Gateaux differentiable form a dense G-delta subset of X. I will report on joint work with Shawn Wang about stronger senses in which the set of Gateaux-differentiability points is large, and outline a possible generalization to nonconvex functions.