[customguy]

I stand corrected, and frankly, since that misunderstanding made me a bit "mad" on behalf that person, I think I would have written my response very very differently if I hadn't made that mistake. I want to apologise for that.

Math is still based on axioms, AFAIK, but since I the author also seems to disagree and I'm the non-mathematician here I don't think I should press on that point, either.

[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.

[Paracompact]

The quote about ineffable/divine/mystical is indeed the one I was implicitly referring to. No worries, I should've been more clear.

Most math people I know don't have a religious conviction in Platonism or anything, but their zeal for math since early childhood often does boil down to awe in something larger, more primordial, more significant than the mundane business of humanity. This tends especially to be the case for pure math people.