I think physicists are way ahead of mathematics in many areas. The area I know a little about is SLE (Stochastic Loewner Evolution), which is a tool to prove r

I think physicists are way ahead of mathematics in many areas. The area I know a little about is SLE (Stochastic Loewner Evolution), which is a tool to prove results about a family of conformally invariant processes. Most of the results were known to physicists much earlier, because they just assumed conformal invariance of some limits (supported by simulation) and used that to make calculations. I've seen the distinction made between mathematics (proven things) and mathematical sciences (experimentally verified beyond any reasonable double).