Physicists concluded last month, beyond a statistical shadow of a doubt, that Higgs Bosons really exist, at least inside the big circle shown in Figure 1. The theory, widely accepted by physicists, that requires the existence of Higgs Bosons has not yet itself been shown to exist in the eyes of mathematicians.

The Yang-Mills fields that are part of the theory provide the forces that hold everything small together. The Yang-Mills heat equation is a nonlinear, degenerate, parabolic equation that offers a means for regularizing the terribly singular connection forms that nature favors. In this talk, I will show how one might use the Yang-Mills heat equation in a proof of internal consistency of that theory.