Especially the four colour theorem - the first mathematical theorem to be proved with software. That said, I believe this discussion pertains to the hypothesis -> theory "upgrade", not to theorems.
To my mind, in this context, the difference between maths and physics is that maths is exhaustive while in physics we don't usually have exhaustive evidence so we have to work with what we've got.
I'm less certain than I was before I read your post, though - so I stand to be corrected :-)