This is missing a lot of historical intrigues and “mistakes” in mathematics. Firstly, the way modern mathematical theorems and proofs are built up from axioms is relatively new (a couple hundred years or so). If you go back to Euclid, there are in fact contradictions that can be drawn from his work because he was defining his axioms inappropriately.

In more modern times we have discussions around the “axiom of choice”, and whole fields such as set theory and Fourier analysis faced some major hurdles in just being established.

My point is that math is constantly changing, also on a fundamental level, because new systems and axioms are being introduced. These rarely invalidate old systems, but sometimes they reveal a contradiction in terms that puts limitations on when some system is valid.

This is very similar to when Einstein developed a new framework for describing gravity: It didn’t “disprove” Newton in the sense that Newton’s laws still apply for all practical purposes in a huge range of situations, it just put clearer limits to when they apply and gave a more general explanation to why they apply.