> I think if the purpose is merely to transmit proofs and axioms unambiguously, I think we can have a language that performs just that and nothing else
Mathematical notation is not easily computer parseable / checkable. And I'm not sure it's really standardized (no standards body that I could find) or even unambiguous for that matter. You could maybe call it a de facto standard.
Please read my other comment: https://news.ycombinator.com/item?id=7348666