[skissane]

> Most mathematicians aren't interested in refactoring their mathematical "codebase", nor experimenting with axioms. They simply want to understand and discover more math.

Experimenting with axioms is one way you discover more math. For example, set theory: there’s a lot of math assuming ZF(C), but even more if you start looking at alternatives to it (like NBG, NF(U), constructive set theories, non-well-founded set theories, paraconsistent set theories, etc)

[giraj]

You're not wrong, but most mathematicians aren't working on (or even interested in) foundations. Not saying what you mentioned isn't math (I think it is), but my point still stands.

[mejutoco]

Very insightful. I can add famously, the parallel lines axiom of classical geometry that when changed created hyperbolic geometry.