If mathematics is so vast the human mind is feeble to it, then it’s also too vast for exhaustive search. Axioms aren’t even beliefs. They are first principles a

If mathematics is so vast the human mind is feeble to it, then it’s also too vast for exhaustive search. Axioms aren’t even beliefs. They are first principles at the service of solving mathematical problems. If we want to solve other problems, we can change the axioms. That goes all the way back to Plato. We treat them as if they were true to solve the problems at hand. (It’s called as-ifism if you want to google it). Since logical and mathematical space is infinite; exhaustive search is the wrong approach.