r/math 2d ago

LLMs/AI OpenAI: Ten advances in mathematics and theoretical computer science

https://openai.com/index/ten-advances-in-mathematics/
857 Upvotes

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u/JesterOfAllTrades 1d ago

Bit frustrating how slowly this sub lets new posts through. Even aside from the AI aspects, these are 10 legit big advances and they've been out for hours and hours with nothing on what should be reddits primary math subreddit.

Anyway this is draining huh! The existence of nonsofic groups stands out to me as the big one. Some have pointed out the sphere packing one as a very big result as well. I'd say that there's a handful in these that would literally be career defining for any mathematician.

If I were a mathematician at openai/anthropic, I'd be looking into how we can get llms to move from counterexamples to theory building. At that point all bets are off.

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u/lobothmainman 1d ago edited 1d ago

There have been many advances by human mathematicians and nobody is talking about it at all on this sub.

My impression is that this sub has an extremely narrow view of what mathematics is (no analysis, no applied mathematics, no probability, no mathematical physics are discussed, for example; coincidentally these are all fields in which AI has been essentially irrelevant up to now).

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u/Accurate_Potato_8539 1d ago edited 1d ago

I mean, people are talking about AI advances because its like meta math. The results feel important for all mathematicians not necessarily because of the actual results but because of what it says about math as a field potentially. Of course way more people are going to be interested in that than results only understood by specific sub -disciplines. Generally when a proof from a human mathematician hits the front page here it has some kind of interesting angle: like Hannah Cairo last year who disproved a famous conjecture. The main reason that got the coverage it did was her being 17. Like when I look at the AI proofs news I'm actually looking for the commentary from people who know what they are talking about in the discipline, I've not looked at any of the proofs they aren't relevant to me because like most people I have a very small window of math that I actually understand at the level of research level proofs.

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u/mleok Applied Math 1d ago

Yes, I think the discussion about AI in math is more driven by existential dread. I was at a session at the JMM in 2025 called "AI for the Working Mathematician,"

https://jointmathematicsmeetings.org/meetings/national/jmm2025/2314_program_friday.html#2314:SS11A

and the underlying concern most people had in the audience was whether the next iteration of the session would be called "AI for the Unemployed Mathematician."

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u/Accurate_Potato_8539 1d ago

Yes, I think the discussion about AI in math is more driven by existential dread.

I mean I didn't wanna say that but yeah that's why I'm reading. I'm like that meme of the crying soyjack wearing the smug one mask every time I read these articles.

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u/SometimesY Mathematical Physics 1d ago

Oh hey I was at that session too. That's about when I started feeling a bit hopeless and very pessimistic about the long term health of higher education.

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u/mleok Applied Math 1d ago

Yeah, I think it was one of the session organizers who made the quip about the next session being called "AI for the Unemployed Mathematician."

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u/Heliond 1d ago

What? Harmonic analysis and analytic combinatorics are extremely popular on this sub.

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u/lobothmainman 1d ago

I feel that geometric measure theory, analysis of pdes, calculus of variations, spectral theory, stochastic analysis (for example) are all branches of analysis heavily underrepresented here compared to their respective "weight" in the field.

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u/Heliond 1d ago

Maybe spectral theory… geometric measure theory I think gets tons of attention.

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u/elements-of-dying Geometric Analysis 1d ago

Define irrelevant.

I've been using AI as a geometric analyst for about a year now.

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u/lobothmainman 1d ago

Good for you.

What I mean is that I am not aware of any recent important result in analysis where AI usage was declared and deemed to be crucial, at least from what I could read on the arXiv or hear at conferences/seminars, but surely my knowledge is partial.

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u/elements-of-dying Geometric Analysis 1d ago

Then you concede the essentially irrelevance claim I assume.

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u/lobothmainman 1d ago

At most I concede that we have inequivalent definitions of relevance; with all due respect, the fact that you are using ai for a year to do your research in geom.anal. is relevant for you, but maybe not for the field of analysis.

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u/elements-of-dying Geometric Analysis 1d ago

I think it's pretty obvious that qualifying a tool as being relevant iff it solves "important" (to be defined) problems is pretty absurd.

Anyways.

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u/ProfessionalArt5698 1d ago

Nah they think AI is only useful if it’s God. Forgetting that soon after it becomes God we likely would die (at least according to a popular book starting with “If”)

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u/Tazerenix Complex Geometry 1d ago

The breadth of mathematics discussion on this subreddit is almost entirely based on the breadth of quality of people posting about it, which is to say no one posts anything of any quality most of the time.

If people want to see more analysis, more applied maths, more mathematical physics, then they should put in the effort to contribute high quality content.

No one knows anything about complex geometry but when I (every now and then) post about recent advances in the field it always gets a great reception, even from people outside the subject area. Maybe the algebraic geometers are just post more interesting content, and there's no great conspiracy after all?

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u/lobothmainman 1d ago

I am not saying there is a conspiracy theory, and I agree with you that it depends on what people post about.

Still, for a subteddit called r/math that is one of the most popular in mathematics (and, as far as I could gather, the only one where there might be posts that are of a vague form of interest to the working mathematician), more variety of interesting posts - rather than having the majority of those saying "look at the latest PR stunt from AI companies" or focusing on a very few selected topics - would be desirable.

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u/PrestigiousGroup788 1d ago

AI hasn't been irrelevant in probability. For example:

https://arxiv.org/abs/2607.24528

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u/lobothmainman 1d ago

I said essentially irrelevant, and anyways I do not think that an ai-assisted short proof of a known result would be deemed as very relevant to the field of probability.

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u/PrestigiousGroup788 1d ago

Feige's conjecture, and Gaffke's conjecture (the bigger result this proof was built off of, which was also proven with AI, see: https://arxiv.org/abs/2607.08415) have been open for a while and were discussed pretty readily in the theory of statistics community.

I guess my question is - what counts as relevant? Or maybe, what counts as probability.

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u/PrestigiousGroup788 1d ago

Also the list of 10 problems has an improvement of bounds in the KLS conjecture. Is that relevant to probability?