Tim Gowers: What Sort of Maths Are LLMs Good At?

In the wake of OpenAI's announcement that it had solved ten major problems in mathematics and theoretical computer science, including the first construction of a non-sofic group and a superexponential lower bound for multicolour Ramsey numbers, Gowers reflects on the current capabilities of LLMs. He argues that while LLMs have achieved remarkable results, they are not yet superior to humans in all aspects of mathematics. He examines the nature of these successes, particularly the prevalence of counterexamples over proofs, and explores what distinguishes a counterexample from a theorem, using Vinogradov's theorem and Gluskin's theorem as illustrative cases.