There is a big difference between contemplating something and computing something.That really gets to the point of the question, and why I stipulated "in principle", because if by mathematics you mean the contemplations of a mathematician's physical brain, then what prevents one from imagining a computer sufficiently sophisticated (in principle) simulating a mathematician's brain contemplating these things?
We can contemplate (say) zero sharp. We can define it and study its properties. And we can study results based on it's existence.
But we can't compute it. Ever.