Tim Gowers: What sort of maths are LLMs good at?

OpenAI recently announced that LLMs solved ten major mathematical problems, including constructing a non-sofic group and proving a superexponential growth result in Ramsey theory, raising questions about where these systems excel. While these achievements are impressive, LLMs do not yet outperform humans across all mathematical domains, and most of their celebrated solutions have involved finding counterexamples rather than constructing proofs. Mathematician Tim Gowers explores whether LLMs have a particular aptitude for counterexample discovery and discusses what criteria should define such success.