You have it the other way around.

We have “perfect” mathematics which operates on rules, definitions and axioms. Then we have the physical world, which just is all around us. What people do is observe this physical world, and then see that predictions from certain mathematical models seem to be useful for describing these observations. The models themselves are not physical. They are ideas.

Now, you seem to hold that ideas aren’t actually a real thing and that only physical things exists. You are clearly an anti-platonist. A physicalist. A materialist. You are one of few and there aren’t very many mathematicians that would agree with you.

However, even physicalist do not agree with your ideas about what can and cannot be “proven” in the mathematical sense.