It's interesting to realize: that's why something like quantum mechanics can't be approached by thinking purely in axioms. We have to push forward first; it's

It's interesting to realize: that's why something like quantum mechanics can't be approached by thinking purely in axioms. We have to push forward first; it's only after we've correctly approximated nature (via some informal model) that we can go back and try to prove our assumptions. One obvious exception to this is Einstein coming up with relativity before it was ever observed in nature and approximated by people. But if you think about it, Einstein wasn't proving aximos; he was presenting a theoretical model (a guess) which turned out to precisely correspond with nature. It was still a guess. So my point is... "results" are subjective, and don't require proofs. Proofs are very useful for checking your theories, but probably not for discovering new phenomena.