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I know that this isn't what you mean, but paradoxically mathematics has been used to prove that it can't prove everything: https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
Gödel's incompleteness theorem is one of the main things that I like pointing to when talking about stuff like this, thanks for bringing it up. Its a good supporting piece that helps show there are limits to logic and knowability. I think physics models will eventually have their own version that puts theories of everything in jepoardy.
I do think our current physics theories are inaccurate at the extremes. To quote Zach Weinersmith: