> the thing answering the math portion of the questions is definitely a computer
The conversation has to be computer-mediated since there's no guarantee all parties are human, so this seems to reduce to the "human using a computer" case, which would qualify as "not an AI".
> Even looking up random facts, the computer will be faster
On reflection, I don't suppose there is any reason we should require there only be one human at either end of the conversation. Maybe we have one person carrying the conversation (to provide a consistent "voice") while others operate equation solvers, Wikipedia, etc.
That said, "can an AI prove it is not an arbitrary number of humans with access to arbitrary computation and knowledge bases" probably isn't as interesting a question.