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The purpose of this question is to collect examples where large language models (LLMs) like ChatGPT have led to notable mathematical developments.

The emphasis in this question is on LLMs, but answers about other machine-learning tools are also welcome.

This question complements two questions that I asked before: Experimental mathematics leading to major advances (January 2010) and The use of computers leading to major mathematical advances II (June 2021). I think it will be useful to keep track of mathematical achievements based on LLMs or assisted by LLMs since it is considered a serious possibility that LLM's have the potential to change (and automatize) or at least assist research in mathematics.

I relaxed the threshold from "major" (in the previous two questions) to "notable" to allow more answers.

A related question specifically about Deep Mind is this: What mathematical problems can be attacked using DeepMind's recent mathematical breakthroughs? ; Another related question referring to deep learning is What are possible applications of deep learning to research mathematics?

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    $\begingroup$ There have been many similar questions on MO to this about the use of AI/machine learning in research math; see, e.g., mathoverflow.net/questions/463937 and other questions linked there. $\endgroup$ Commented 23 hours ago
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    $\begingroup$ I haven't voted on the question (in either way), but I consider it likely that answers - if you get some - will lead to a lot of discussion regarding how significant the LLM contribution actually was. $\endgroup$ Commented 23 hours ago
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    $\begingroup$ @JochenGlueck I am interested in examples of significant mathematical developments assisted by LLMs as reported by the authors. $\endgroup$ Commented 23 hours ago
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    $\begingroup$ My instinct is to downvote the question, though I don't have any better justification than that I hate the intrusion of AI into every sphere, and would rather not see t here; but that's unreasonable personal bias, so I just won't vote. But it does seem nonsensioal to me that the question would be at 9 – 7 while both answers, reasonable as far as I can tell, are at 0 – 2. I hope downvoters will consider leaving a comment about what they think is an appropriate answer. $\endgroup$ Commented 20 hours ago
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    $\begingroup$ @LSpice: I haven't voted on any of the answers (yet), but I'm inclined to point out that the answer by Zach Teitler has precisely the kind of issue about the significance of the LLM's contribution that I was mentioning in my previous comment. $\endgroup$ Commented 20 hours ago

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Here is an example Counterexample to majority optimality in NICD with erasures

From the abstract:

We asked GPT-5 Pro to look for counterexamples among a public list of open problems (the Simons ``Real Analysis in Computer Science'' collection). After several numerical experiments, it suggested a counterexample for the Non-Interactive Correlation Distillation (NICD) with erasures question: namely, a Boolean function on 5 bits that achieves a strictly larger value of E|f(z)| than the 5-bit majority function when the erasure parameter is p=0.40. In this very short note we record the finding, state the problem precisely, give the explicit function, and verify the computation step by step by hand so that it can be checked without a computer. In addition, we show that for each fixed odd n the majority is optimal (among unbiased Boolean functions) in a neighborhood of p=0. We view this as a little spark of an AI contribution in Theoretical Computer Science: while modern Large Language Models (LLMs) often assist with literature and numerics, here a concrete finite counterexample emerged.

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Not exactly a notable result, but in my recent preprint Evaluation of GPT-5 on an Advanced Extension of Kashihara's Problem I describe how GPT-5 has been able to improve the general version of an extended combinatorial problem I originally solved in 2010.

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This paper

Sergey Avvakumov, Roman Karasev, Tensor rank of the determinant and periodic triangulations of $\mathbb{R}^n$

https://arxiv.org/abs/2509.22333

includes in the Acknowledgments "We also thank ChatGPT 5 for pointing out that the lower bound in the proof of Theorem 1.5 can be stated in tensor language and is thus equal to the determinant’s tensor rank."

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    $\begingroup$ Thanks, Zach! I knew the paper and I met Sergey today, but did not know about the role of ChatGPT :) $\endgroup$ Commented 20 hours ago
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Scott Aaronson Phillip Harris, Freek Witteveen have a recent paper on the bounds of amplification of QMA (quantum Merlin-Author). A critical part of the paper involved a linear algebra trick suggested by GPT5. See Aaronson's blog entry here.

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