I share Kasra Rafi and Bruce Schneier’s impression that recent mathematical breakthroughs by AI consist in clever recombination of existing ideas, not development of truly novel theory (No, AI doesn’t mean the end of mathematics – at least not yet, 25 August). The question is: what happens to mathematics if this changes?
Like many mathematicians, I have done much soul-searching in recent weeks, especially since a key problem in my own field of group theory (the existence of non-sofic groups) was solved this month by OpenAI’s Astra model. Astra’s proof consists largely in a slight twist on theorems by my colleagues Gabor Kun and Andreas Thom. That said, even a few months ago I would have found the idea that AI was capable of such a breakthrough incredible, so it seems foolhardy now to bet against AIs achieving superhuman capabilities in all areas of mathematical thought in the coming years.
