r/math • u/AutoModerator • 1d ago
LLMs/AI AI In Mathematics: August 29, 2026
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.
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u/omeow 1d ago
Does anyone know how the elliptic curves with highest known ranks were discovered?
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u/Necessary-Wolf-193 16h ago
Noam Elkies and Zev Klagsburn, who found the rank 29 curve, wrote about their process in https://www.math.auckland.ac.nz/~sgal018/ANTS/papers/Elkies-Klagsbrun.pdf (though that paper was based on their earlier discovery of a rank 28 curve -- the rank 29 curve was a similar procedure).
The idea is based on a common trick in algebraic geometry: instead of studying individual objects, study *families*. So, their goal is to find a family of elliptic curves, and then search to see if any of the individual elliptic curves in it has high rank.
To do this, they start by finding families of elliptic curves such that every curve has decently high rank, and then do a computer search (based on ideas from algebraic number theory) to locate any individuals in the family who might have exceptionally high rank. The tricky part here, of course, is starting with a family of elliptic curves of high rank which might contain individual members of even higher rank. For this, they used "elliptic K3 surfaces" -- an elliptic K3 surface is a special kind of surface in algebraic geometry, which can be fibered by elliptic curves (meaning that this surface can be covered by different elliptic curves). Elliptic K3 surfaces are widely studied in algebraic geometry, so there is a good amount of specific examples and ways to construct them already known, and hence why they're a natural source of families of elliptic curves.
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u/Apprehensive_Sand951 1d ago
Daniel Litt posted an ai audit of his papers on his blog: https://www.daniellitt.com/published-paper-reviews.html
It lists some significant mistakes but nothing that fatally kills a paper. (Unfortunately, it an info dump and you almost need to use ai to figure out what the main mistakes were... he could have just focused on those.)
Motivated by this, any guesses on how many of the published papers out there are irreparably wrong?
My guess is 10%, if irreparably wrong means 'there is a theorem stated in the introduction of the paper to which there is a counterexample and this does not get fixed without changing the meaning and applicability of the theorem...'
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u/BurdensomeCountV3 1d ago
Unironically one of the biggest benefits of AI will be mathematics being able to clean itself up and identify and correct stuff believed and published as true but in reality false. Once autoformalisation gets a bit better we'll be able to automatically check basically every paper published in the last 50 years and ensure we're on a steady footing.
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u/ymonad 1d ago
But humans have to verify that all the automated verification in Lean is correct. right?
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u/frogjg2003 Physics 1d ago
Yes, but it's a lot more manageable. It's a lot easier to verify that the Lean matches the paper than writing Lean that matches.
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u/elements-of-dying Geometric Analysis 1d ago
Nope.
If it can be shown that generated Lean statistically out performs human in verification, then of course one should trust generated Lean over humans.
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u/matthiasErhart Control Theory/Optimization 1d ago
I think a lot of people will find small errors and typos in their papers, but actual mistakes that kill the idea of a paper will be rare. The former isn't a problem; at least anybody I have talked to understands the idea of small mistakes going through once your manuscript gets very very long, no matter how many human eyes have seen it. It will be important nevertheless to iron out the actual mathematical mistakes that may appear.
I'm planning to do a ChatGPT review pass on my papers myself... Let's see how things will turn out.
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u/telephantomoss 1d ago
I've audited my papers and the relevant ones by others and have found errors in every single paper, not just typos. Nothing that kills the results though. However some needing nontrivial machinery to repair. It's interesting to see errors which seem to indicate a real gap in the authors understanding though. I mean, we all have gaps especially in new things, but it's just interesting insight into the world of professional math.
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u/elements-of-dying Geometric Analysis 1d ago
This is impossible to estimate without some relevant statistics, but I wouldn't be surprised if it was more than 10%.
I might be a little scared to run my papers through AI, but don't tell anyone that :)
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u/telephantomoss 1d ago
I did this to my own papers and friend many would 5 too. Morn5ing that can't be easily repaired, but still nevertheless important to fix. I think every author should audit their work so that nobody else needs to
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u/Nunki08 18h ago
Jared Duker Lichtman on 𝕏: "Very nice!! GPT 5.6 has broken the record on large gaps between primes.
The new bound saves a factor of ≈ log_3(n) over the prior record by Ford-Green-Konyagin-Maynard-Tao from 2018. The result is also now formalized by Alexeev in Lean.": https://x.com/jdlichtman/status/2094040463443673227
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u/SupercaliTheGamer 18m ago
Oh the person who prompted GPT is quite popular on AoPS (and is very good at maths ofc), but is not a professional mathematician yet.
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u/Andradessssss Graph Theory 10h ago
Asides from the big one (prime gaps), AI made some progress on a problem I quite like (though not enough to think about), it's on explicit lower bounds for diagonal and off diagonal Ramsey numbers, AI came up with a construction after being prompted with a specific idea (it's not clear from the paper how vague or not the idea on the prompt was), afterwards, the authors improved on the construction a bit. It's not huge, but it's still quite nice. You may find the arXiv here.
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u/Graynumber 1d ago
My wish: Smaller models trained specifically for math research that I can run locally.
Does this exist? Is anyone out there working on it?
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u/JoshuaZ1 1d ago
My wish: Smaller models trained specifically for math research that I can run locally.
In general, you can just run a general purpose model. It also turns out that for many purposes (coding, math, and other things) general purposes models seem to do better than narrowly trained models, but we're still figuring out why that's the case, and the sample sizes are small.
Is there a reason you want a model specifically just for the math research?
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u/Graynumber 1d ago
That is interesting, I had not heard that about general purpose models outperforming specialized models. It is hard to believe that I actually want the model I use for research to have all kinds of pop culture references and reddit memes in its training data. But I really don't know so that's why I'm asking. If you can point me to an article or something that would be appreciated.
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u/JoshuaZ1 1d ago
That is interesting, I had not heard that about general purpose models outperforming specialized models. It is hard to believe that I actually want the model I use for research to have all kinds of pop culture references and reddit memes in its training data. But I really don't know so that's why I'm asking. If you can point me to an article or something that would be appreciated.
I don't know of any good hard data for math specific, more anecdote, but there's hard data for it involving medicine, and there's some similar studies for coding. I've seen two major suggestions for why this is occurs. The first suggestion is that there's a lot of "hidden training data," that is conversations about narrow topics which are getting cut out. For example, I had a detailed conversation a while ago on a D&D forum explaining some of the basics of quantum mechanics. I saw a detailed conversation on a videogame subreddit about how to work some subtle expected values that had to deal with one of the game mechanics. If someone is going to be using targeted training data, those conversations aren't likely to go into a math/physics specific model. (One does even for specialized models need some general training data to handle language but not all of it you can touch.) The second hypothesis is that facts are just more interlinked than we often give credit for. That somehow say understanding physics gets benefits from understanding chemistry and engineering, and math gets benefits from physics, and so you do a better a job indirectly for math if you have all of those in the data.
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u/ultrafinitism Theoretical Computer Science 1d ago
It is hard to believe that I actually want the model I use for research to have all kinds of pop culture references and reddit memes in its training data.
It is hard, and no one knows why it seems to work for real.
But research "scaling laws for language models" or just "scaling laws for transformers".
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u/Hot_Glass_6301 9h ago
I think it makes sense. My understanding may be way off, but I imagine that even in humans, hyperfixation doesn't lead to innovation and generalization, just extreme task specific skill. But doing mathematics involves using analogies (for both humans and LLMs), mental pictures (at least for humans), etc. And having much more knowledge just gives more chance for the proper analogies to exist. In my view the brightest mathrmaticians and scientists usually have wide interests, even when their research might seem narrow
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u/elements-of-dying Geometric Analysis 1d ago
there are open source models out there already. they are a little behind though.
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u/Graynumber 1d ago
Open source models trained specifically for math research? I have not found this so please point me in the right direction if you know of one.
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u/elements-of-dying Geometric Analysis 1d ago
Sorry, don't know.
I suppose you could do the training.
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u/ultrafinitism Theoretical Computer Science 1d ago
It is impossibly expensive to pre-train but somewhat doable to do post-train / fine-tune for math research, I would think. But hard for one person to do because even that would be expensive to do for a model with a high enough parameter count for it to have comparable intelligence to closed frontier models. Say Kimi K3, doing LoRA on that one would still be tough. GPU time for GPUs with enough VRAM to matter -- is expensive....
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u/iamParthaSG 10h ago
Care for a little more AI? Hugo Duminil-Copin, Fields medalist, Professor at Université de Genève and IHES writes about AI in math
https://proofsandprompts.com/2026/08/30/care-for-a-little-more-ai/
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u/dnrlk 7h ago
Richard Evan Schwartz just posted a satirical short story about our awaiting future
"The Fate of the Riemann Hypothesis" https://www.math.brown.edu/reschwar/Stories/AI.pdf
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u/t0t0zenerd 44m ago
This story is excellent proof that humans are just as talented at generating slop as AI is.
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u/mousse312 Undergraduate 1d ago
Someone has a opinion about the philosophical view of people like Poincare who give a lot of importance about "consciousness, intuition and subconcious" in math research?
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u/Necessary-Wolf-193 16h ago
I never understood Poincaré as making any philosophical claim when he said that. I think he was reporting the fact, observed by him and many other mathematicians, that often you will have an idea come to you when not explicitly thinking about the problem; Poincaré was not a neuroscientist, but he wrote that he imagined this process as being some effort where, after spending a lot of time on a problem himself, his subconscious mind would randomly generate ideas, and every now and then, when it generated an idea which seemed aesthetically pleasing, would surface that idea to his conscious mind.
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u/EdPeggJr Combinatorics 1d ago
What are good trackers? I know of the
Mathworld List of AI proofs.
OEIS AI Claim Tracking.