how do mathematicians know that an axiom holds true in every region of the universe?

Question

Since axioms can’t be proved, how do mathematicians know that they’re always true independently of the location? If they don’t, how do they cope with that?

In: 1

Answer 1

If you want a good example of all this in action; the early work of Stephen Hawking, Roger Penrose and others that showed there must be a singularity in a black hole and the Big Bang is all based on the axiom that general relativity is true. Hawking later argued that there probably aren’t actual singularise out there in the universe, on the basis that general relativity probably isn’t valid in those circumstances. That doesn’t make the original maths incorrect though.