“I think there's a revolution in mathematics around the corner. I think that … people will look back on the fin-de-siècle of the twentieth century and say ‘Then is when it happened’ (just like we look back at the Greeks for inventing the concept of proof and at the nineteenth century for making analysis rigorous). I really believe that. And it amazes me that no one seems to notice.

“Never before have the Platonic mathematical world and the physical world been this similar, this close. Is it strange that I expect leakage between these two worlds? That I think the proof strings will find their way to the computer memories?…

“What I expect is that some kind of computer system will be created, a proof checker, that all mathematicians will start using to check their work, their proofs, their mathematics. I have no idea what shape such a system will take. But I expect some system to come into being that is past some threshold so that it is practical enough for real work, and then quite suddenly some kind of ‘phase transition’ will occur and everyone will be using that system.”