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

Math is an abstract creation.

For example, there is euclidean geometry, elliptical geometry, and hyperbolic geometry. Each has a different set of axioms, and each has different applications in the real world.

So the real question is “how do you decide which mathematical model to use in the real world?”

And the simplest answer is “we use the model that most closely agrees with what we observe in reality”…