[cweld510]

Math is based on axioms because you need some a priori axioms to do logical deduction, but the axiom selection is also historically fluid. Mathematicians suggest new axioms or move away from old axioms based on their understanding of which results are intuitive or not, and also which are most useful, and most mathematicians that work close to the axioms have some view on how “correct” or not various axioms are. As evidence of this, I’d point to how many mathematicians find the axiom of choice problematic due to results that seem clearly “wrong”, but nevertheless accept it because they need it to prove other things that seem obviously “right”. So the axioms are not the base truth, there is some platonic ideal of mathematics beneath that.