This posting is mainly intended to provide some links to material about AI in math and physics that I’ve found interesting. I confess that to a large degree I’m trying to avoid seriously learning about exactly what is going on, so my own opinions and thoughts about this topic aren’t grounded in any expertise. If you have interesting things about this topic to point to in the comments, please do so, but for general discussion, try some other venue managed by someone better informed.
- A Future of Mathematics event just started a few minutes ago at Stanford. You’ll find a link to the livestream there and talks should be on Youtube.
- You can easily find people announcing that AI is about to make mathematicians obsolete. We’ll see. In the meantime what I’ve found interesting is that AI is motivating deeper thinking about what what it is that mathematicians really do, and how to protect the valuable parts of this. For good examples of this, see the substacks of Michael Harris and David Bessis. I especially like this recent posting. Also, it was from Michael Harris I learned that Peter Scholze has publicly expressed the opinion that
I already consider the influence of AI to be strongly negative, for humanity, for democracy, and for the planet.
- One of the main problems with AI agents in general is that they are better at saying things that are convincing than they are at saying things that are true. Their potential application in mathematics has the big advantage over other fields that one can use these agents together with formalization and proof-verification to deal with this problem. Scholze has been involved in a major effort using proof verification and I don’t think his remarks about AI apply to this. For a very interesting recent interview with him, see here, which includes some comments about why he hasn’t found formalization that useful.
Something useful that may come out of this is a conclusive demonstration that there’s a gap in the Mochizuki abc proof. There’s a project working on formalizing this proof announced here. From what I can tell, the situation so far is that the very few who think Mochizuki has a proof have been unable to explain to anyone else how the proof is supposed to work at the point where Scholze/Stix pointed to a gap, and this includes the people charged with trying to formalize this part of the proof.
- In fundamental theoretical physics, formalization is generally not relevant (except perhaps in some areas that could be described as mathematical physics). Given the fact that the subject has been stuck for a long time, with a lot of research devoted to ever-more irrelevant calculations, it seems clear that AI agents likely will soon be able to do this better than humans. For an example of what I mean, see here.
There is a huge amount of money being thrown in this direction. As an example, the DOE is promoting a Genesis Mission. I’ve no idea how fruitful this will be for most of its goals, but the one relevant to fundamental theoretical physics is “Unifying Physics from Quarks to the Cosmos”. The idea is that
An AI that internalizes the Standard Model could accelerate analysis by orders of magnitude, identify anomalies pointing to new physics, and propose theoretical extensions consistent with all data—a leap from pattern matching to physics reasoning.
which doesn’t look at all promising.
David Kaplan tells us here that in 2-3 years AI agents will be replacing the best of IAS theorists. Seems unlikely to me, but we’ll see soon…
