

That’s not how physics works. If you are really interested in such issues read a book on foundations of physics or history of physics to see how physicists arrived at the most famous equations (Einstein,Dirac, Schroedinger or Newton), they are basically “bets” guided by physical and mathematical assumptions, but that is far from being “proved” or “derived”, there are no rigorous proofs or derivations involved. The uncertainty remains until an experiment or observation confirms it or rejects it. There’s no such a thing as “proving” a physical theory, for the simple reason that any physical theory works in a limited regime or range of validity. Newtonian gravitation and General Relativity are both valid and succesfull theories within their range of validity, but they contradict each other mathematically, in one theory gravity is a scalar field and in the other is a tensor field, so you could use the mathematics of one theory to refute the other, so it makes no sense the concept of proving a physical theory mathematically. You only try to axiomize a theory once is well established, but it’s irrelevant concerning its validity.
Just came across this beautiful video of Richard Feynman.