Tim Gowers: What sort of maths are LLMs good at?
OpenAI announced that its large‑language models solved ten major problems in mathematics and theoretical computer science, including constructing a non‑sofic group and proving superexponential growth of a multicolour Ramsey number. The author observes that while LLMs can produce both proofs and counterexamples, the most celebrated achievements have been counterexample‑type results. He discusses the challenges of defining what counts as a counterexample and suggests that LLM strengths may lie in particular problem structures, though no definitive classification is offered.
- ▪OpenAI reported solving ten significant mathematical and theoretical computer science problems, notably a non‑sofic group construction and a superexponential Ramsey number bound.
- ▪The author notes that LLMs are capable of generating proofs and counterexamples, but the high‑profile successes have largely involved finding counterexamples.
- ▪The article examines the nuanced definition of a counterexample, using Vinogradov’s three‑prime theorem as an example of why not all universal statements lead to counterexamples.
- ▪The discussion is framed as a snapshot of early August 2026, acknowledging that LLM capabilities are rapidly evolving.
- ▪No clear taxonomy is provided for the types of mathematical problems where LLMs excel, highlighting ongoing uncertainty.
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| Original publisher | Gowers's Weblog |
| Canonical URL | https://gowers.wordpress.com/2026/08/12/what-sort-of-maths-are-llms-good-at/ |
| Publication time | Wed, 12 Aug 2026 10:04:25 +0000 |
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Opening excerpt (first ~120 words) tap to expand
For the sake of anyone who might read this blog post in the distant future (a month from now, say), let me mention that I am writing it a few days after OpenAI announced that it had solved ten major problems in mathematics and theoretical computer science, including the first construction of a non-sofic group, and a proof that the multicolour Ramsey number (where there are 3’s) grows superexponentially in . The first was, to judge from various talks I have been to, one of the most important unsolved problems in group theory, and the second was a major open problem in Ramsey theory that I didn’t necessarily expect to see solved in my lifetime, though of course such expectations now have to be revised.
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