Well look at Godels Incompleteness Theorem... Not every statement in mathematics actually even has a proof inside mathematics. So math doesn't even have the tools to fully investigate itself.

That's an awesome point. The poor saps have to hand-waive around axioms within their own field. No way they're going to accept divine interventions and invisible dragons in some other line of work :)

Because supernatural is by definition super-natural.

If it was real and explainable by science, we won't call them supernatural