So "the rock solid foundation" of math is not the real world, but rather sets of self-consistent axioms. You're mostly right, but there's a fun twist. The self

So "the rock solid foundation" of math is not the real world, but rather sets of self-consistent axioms. You're mostly right, but there's a fun twist. The self-consistency of e.g. Peano arithmetic (natural numbers) ultimately rests on our intuitions about the real world - it can't be proven starting from nothingness.