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Abstract: The interior regularity for viscosity solutions of the sigma-2 equation is the remaining case of the Monge-Ampere sigma-k family to be understood. The dimension two case was done in the 1950’s by Heinz, and the dimension three case was done in 2008 by Warren and Yuan. In joint works with Yu Yuan, we show regularity in dimension four for sigma-2. Our argument uses a doubling inequality for the Hessian. A similar argument gives a proof of interior regularity for strictly convex solutions of the Monge-Ampere (sigma-n) equation in all dimensions, using a geometric approach distinct from Pogorelov’s maximum principle of the 70’s.