[bitL]

> nothing in our world outside of math is ever truly proven

Just biting a bit: depends on the logic you use. The logic might not be true in our Universe, just in mathematicians' heads/idealistic Universe. And even on those idealistic Universes there is no real consensus if they/which are true, or just useful.

Imagine you add Maybe as third value between True and False. Later you might find one Maybe is not enough, you might need four different Maybes. Then suddenly it dawns on you that countable amount of Maybes is the minimum. Then you throw away such logic because it's practically useless, even if it models reality better with the side effect of breaking established math as well. Then you wonder why simple binary logic is quite good in describing many things in real Universe, but you have no means to prove any relation between this logic, math derived from it, and reality you live and observe.

[AstralStorm]

None of the logics mentions even touch the idea of quantifiers. Which is the way most math proofs are written nowadays. It is strictly more powerful than any multivalued logic.