I have taken plenty of high level math classes for fun and easy A's, I even had a department head yell at me for not getting a PHD. So, I can speak the lingo.

But, the absurd results are not generalizable outside of their assumptions sorry Axioms. Set theory being one of the most obvious cases.

It's sadly like a religion in many ways, follow enough false statements and you can prove anything. Yet, if you find a contradiction then don't actually accept at least one of your assumptions are false.