That is only as pedantic as it is pedantic to say that science can't prove things right. There is no fundamental quality that makes a statement "positive" or "n

That is only as pedantic as it is pedantic to say that science can't prove things right. There is no fundamental quality that makes a statement "positive" or "negative", so "proving X wrong" is always "proving ⌐X right". It's possible to be very precise about what we mean when we talk about evidence and logic, so coming up with these wishy-washy principles like "science can only prove things wrong; oh, you know what I mean" just confuses things. As for applying that to math, yes that's true to some extent. And on rare occasion, mathematical proofs are found to have flaws in them years after they have become commonly accepted. I think there's an important distinction to be made, though, between the certainty of deductive reasoning, and the uncertainty of deductive reasoning as interpreted by humans.