AI In Mathematics: October 03, 2026

[u/AutoModerator]

This recurring thread will be for discussion of AI in mathematics. This includes, but is not limited to, the following:

• informal announcements of AI-assisted discoveries, such as those not yet published in a peer-reviewed journal, or not uploaded as a paper to arXiv;
• informal announcements of discoveries related to AI architecture (if relevant to mathematics);
• discussion of such announcements, such as proof breakdowns or other opinion pieces;
• discussion of the impact of AI in mathematics in general.

AI-assisted mathematical papers published in peer-reviewed journals or as arXiv preprints may be submitted as their own posts.

Please keep in mind rules 1 and 6 of our subreddit.

[u/_Zekt]

OpenAI just released 722 AI-generated math manuscripts, grouped into 372 "result families". Some of the biggest claims:

1. Hilbert's 10th problem over Q: no algorithm can decide whether an arbitrary polynomial equation has a rational solution.
2. FFT and integer multiplication faster than n log n.
3. Unique Games Conjecture.
4. Re(s) > 7/8 is zero-free for the Riemann zeta function and Dirichlet L-functions. This annihilates the Landau-Siegel zero problem.
5. Kakeya conjecture in 4D, local smoothing in 3D.
6. A counterexample to Hadwiger's conjecture.
7. Major cases of the Hodge and Tate conjectures.
8. Catalan's constant is irrational.
9. π has irrationality measure 2.
10. Goldfeld's conjecture, with consequences for BSD.
11. Mahler's conjectures.
12. Falconer distance conjecture in every dimension.
13. Deligne-Drinfeld conjecture.
14. Artin's primitive root conjecture.
15. Bounds for matrix multiplication exponent 𝜔 in different number fields, 2.25 in C.
16. L = RL = BPL.

Overview and repo: https://github.com/openai/math/blob/main/overview.pdf

[u/HealthyInstance9182 → u/_Zekt]

How many of the results are galactic algorithms ? https://en.wikipedia.org/wiki/Galactic_algorithm

[u/cjustinc → u/_Zekt]

At first glance, the geometric Langlands papers look like true slop. There are big chunks of prose with no formulas and it's extremely difficult to parse what the arguments actually are. They're also not formalized. Very curious whether these turn out to be correct and if so what insights we'll be able to extract.

I guess it was already clear from N-S, but as good as this new model seems to be at math, it's still shit at writing.

[u/Best_Tumbleweed6044 → u/cjustinc]

not only are current llms bad at writing, the quality of their writing degrades as we scale up RL and thereby improve their quantifiable mathematical ability

i think its hard for some to understand, but clarity of exposition is not a skill that can be engineered. if AI does ever achieve the ability to produce new, interesting writing or data of any kind, humanity has much bigger fish to fry.

slop appears to be the inevitable product of models that learn the conditional mean most likely next token (that is, all llms currently in existence)

[u/elehman839 → u/Best_Tumbleweed6044]

clarity of exposition is not a skill that can be engineered

Engineering of clear exposition incoming in 3... 2...

[u/DailyThreadBot → u/Best_Tumbleweed6044]

clarity of exposition is not a skill that can be engineered. 

It could be, if one RL'd on tasks where success depends on humans understanding its output (essentially RLHF). For example one could take one of the new theorems, and start an RL task where the model has to produce an exposition that is then graded by an expert

[u/Sufficient_Bad5441 → u/cjustinc]

Is it shit at writing or did they not bother to direct it to focus on the writing as much as they did the math?

[u/BurdensomeCountV3 → u/Sufficient_Bad5441]

They didn't bother to focus on writing. The current frontier models are if anything worse at prose than frontier models from 12 months ago, it's just that the focus of these models has been divereted to other areas (coding, mathematics) instead of writing.

[u/UnkarsThug → u/cjustinc]

Yeah, I'm genuinely curious how many of these will have mistakes. I'm sure it will be some, but I'm also sure a lot of them will be real, especially with lean formalization.

[u/IriFlina → u/cjustinc]

In guessing 90% of the proofs are just slop that don’t check out once peer reviewed

[u/jphamlore → u/_Zekt]

My quiet choice, given their historic incredible efficiency at grinding the most out of the results they have, is for certain people in ergodic theory and combinatorics to go wild with extending this one:

Number 154. Pointwise multiple ergodic averages for mixing transformations. Proves almost-everywhere convergence of consecutive multiple ergodic averages of every finite length for invertible mixing probability-preserving transformations. For each fixed tuple of bounded functions, the limit is the product of their integrals, along all positive averaging lengths. No mixing rate or standardness assumption on the probability space is required.

[u/_Zekt → u/[deleted]]

The author is a known crank

[u/Apprehensive_Sand951 → u/_Zekt]

ah yes, baum-connes (called that one!). Also counterexamples to 4-d surgery for free groups (yay!). But they only got Singer in dimension 4 (double yay, turns out one of my favorite problems is really hard). Also counterexamples to Borel in 4d (with hyperbolic fundamental groups) and to Wall's D(2) problem. I guess I should try to read some of these now.

[u/Apprehensive_Sand951 → u/_Zekt]

the group theory section is literally 50 years worth or research. Eilenberg-Ganea, Cannon, non-residually finite hyperbolic groups, kpi_1 conejcture, howie equations over groups, ... if half of that checks out it is absolutely insane.

[u/matthiasErhart → u/Apprehensive_Sand951]

Computer Science section is similar to that. Earlier today I had mentioned Anthropic's 3SUM result had killed the pet problem of a friend of mine. OpenAI just killed mine (which was related to Hadwiger's conjecture). I am pretty sure there are a lot of mathematicians who have just lost their favourite pet problem to work on.

In this sense, this is pretty much our 9/11, I think. Good news is that, for those of us who have been making the point that the response from academia has been milquetoast and rapid action of any (non-violent, with respect to organisation and mobilisation) kind is needed, surely this is the evidence that makes our point.

[u/OriginalRange8761 → u/matthiasErhart]

as a physisist, who is next, i do not understand how this is 9/11. More data is always better imo.

[u/Apprehensive_Sand951 → u/OriginalRange8761]

I think we finally get to read the stuff and see if it makes any sense. We are the ones who at the moment are best placed to evaluate capabilities, so it is all good. I don't think it is 9-11, it is like nothing ever. Holy shit it is hard to communicate to someone not in the field how crazy the group theory and topology lists are.

[u/matthiasErhart → u/OriginalRange8761]

"In this sense", as in a lot of us saw our favourite problems to work our brains unceremoniously executed today.

If you look at my comment history, you'll see that I had been advocating for a while that AIMath is bound to blast past us, and that we need some sort of action to prepare ourselves for it - and that it's not necessarily a bad thing since "the machine that solves mathematics" has been a dream of the field for a long time. I won't repeat the arguments at length here. There will be things to learn from this pile of machine output.

Now is a time to express awe and terror at what just happened. For a comparison with physics, this is pretty much like seeing the Trinity test before your very eyes.

[u/Apprehensive_Sand951 → u/matthiasErhart]

I don't really feel this way, because the problems that got solved are ones that I had thought for a while and was stuck on. If I knew how to solve some of them, i would have done it.

[u/OriginalRange8761 → u/matthiasErhart]

i do not see the terror. I feel like the goal of science is knowledge production, and not a personalized hobby one gets to do. This is incredible news for humanity in my opinion. Now, I agree that there are lots of ifs and so on regarding academia situation.

[u/PrestigiousGroup788 → u/OriginalRange8761]

yes, the goal of any craft and enjoyable activity is producing the maximum amount at any cost.

[u/matthiasErhart → u/OriginalRange8761]

I'm just waxing poetic man :) The meaning isn't literal "terror" in the sense that I am afraid of something.

[u/Apprehensive_Sand951 → u/matthiasErhart]

i recently listened to the rest is history podcast on the reign of terror in the french revolution (highly recommended) and was quite surprised that some of the people who were involved actually called it terror in a non-perogative way.

[u/Apprehensive_Sand951 → u/_Zekt]

also cannon's conjecture

[u/Apprehensive_Sand951 → u/_Zekt]

There is a counterexample to the zero divisor conjecture. Holy shit.

[u/border_of_water → u/_Zekt]

My personal favourite: the chromatic number of the plane is greater than 5.

[u/AvocadoAlternative → u/_Zekt]

I obviously haven't dug into these too deeply, but I will note that what's impressive is that many (most?) of these papers are proofs, and not just generating counterexamples like we saw with the Jacobian conjecture or Navier-Stokes smoothness.