I do not believe in the existence of fire-breathing dragons outside of fiction, but I can't prove they don't exist. See also: UFOs, angels, god(s), and so on. In logic, the onus is on the person making the positive claim (that such things do exist) to furnish the evidence to back it up. The skeptic's lack of knowledge is not proof of non-existence, of course.

I'm talking about mathematical truths for which establishing non-existence follows directly from proving a positive assertion, not that white ravens don't exist.

I understand that, but 'proving a negative' is philosophical shorthand for the latter rather than the former. You are just going to have to put up with the slight vagueness of the term.