The strange thing about mathematics, as opposed to other noncorporeal ideas, is that it is nearly uniquely suited to being transmitted between brains. My idea of the number "three" and your idea the number "three" are probably very similar. This sort sensation that they have an independent existence leads people to the Platonic notion of a mathematical "realm" or "universe".

(personally I think mathematics exists in our brains, but also and crucially in the interactions between our brains, since a proof is never accepted until it is reviewed and so on. A proof that's just in my brain is no proof at all, even if it happens to be correct)