Comment by otabdeveloper4
11 hours ago
> AI math is happening and there's no going back
"Math" is about uncovering the epistemological foundations of the universe.
Adding AI here does nothing and is probably a regression in that it diverts resources from actual "math" into some sort of LLM wankery that nobody wants.
That depends on whether the AI-generated mathematics helps with the project of "uncovering the epistemological foundations of the universe".
Which depends on (1) whether there are actual good ideas in it, (2) whether as well as finding the proofs the AIs can explain their ideas in ways humans (and other AIs) can use, and (3) whether the results they prove are ones that really contribute to that rather than being isolated curiosities that don't go anywhere.
I am not expert enough in all these fields, and haven't looked enough at the papers, to assess #1, but in general the way mathematicians have bet is that if you can solve things regarded as important problems you'll usually do so in a way that contains more broadly useful ideas. Differences between how today's AI systems do mathematics and how humans do mathematics might make that less true when it's an AI that solves the problem, but I would still bet that way. I'd be surprised if OpenAI's big math dump didn't turn out to contain some ideas, and connections between ideas, that humans find useful.
At the moment the AIs are worse than good humans at #2. (But some humans are also really bad at #2, including some humans who are very good at proving theorems.) It looks to me as if they're getting better, and I would expect them to continue to do so. I also suspect (but this is only guesswork) that today's publicly-available frontier AIs may be able to answer questions along the lines of "please take a look at this AI-written paper, and tell me what key new ideas it contains and how they relate to other things in the field" well enough to be useful to human mathematicians. (Even when the paper itself was written by a proprietary AI that no one outside OpenAI or Anthropic or Hypothetical New AI Mathematics Lab has access to.)
As for #3, that's always been something of a crapshoot. A lot of mathematicians' effort goes into proving things that approximately no one ever reads or builds on, just as a lot of industrial R&D goes into trying things that don't turn out to make good products. The recent OpenAI dump contains things that sure seem like important building blocks for future mathematics (e.g., the "quasi-Riemann-Hypothesis" thing) but it's hard to know for sure and also hard to know whether, if they do prove things that turn out to be useful, it's only because they've read the human-written literature and aimed at things human beings have said seem likely to be useful.
None of this seems to me like "adding AI here does nothing". Whether what AIs are doing to mathematics at the moment is good on balance is highly debatable, of course, but it's a matter of trading off costs and benefits, rather than there being costs and no benefits.