They are useful repeatedly because they derive from fundamental properties of the observable universe. We can imagine other sorts of universes - one with hyperbolic geometry as opposed to flat, for instance ( https://en.wikipedia.org/wiki/Shape_of_the_universe ). Parts of geometry would work differently there, and laws of motion as well. But interestingly, many fundamental rules of math would still apply. Just with different outcomes which are less useful for predicting results here.

Kind of like trying to prove Euclid's Fifth Postulate, which we know now is truly a postulate and not an axiom.