Isn't it the other way around? You start out with assumptions and a model (which usually involves some math), and then you show that you've made the correct assumptions by empirically testing it. You can't prove something in the mathematical sense about physical reality.
You have to prove that math actually maps to reality. I don't think you can do that. With the possibility that it's all a simulation, our universe doesn't even have to be consistent.
In Physics, this might be true, at least for generalizations (I can prove to myself that I currently write this text, for suitable definitions of "I, write, text". I might not be able to prove it to you.). In Math, it's not.
In math, this is fine, as long as you can show that your assumptions are consistent.
If you disprove something in physics, you at the same time prove the negative of the something. Of course the negative of a theory is not really a theory by itself.
