Tim Gowers, writing shortly after OpenAI announced solving ten major math problems including the first construction of a non-sofic group and a proof that the multicolour Ramsey number grows superexponentially, reflects on LLMs' current capabilities. He notes that while these results are impressive, LLMs are not yet superior in all aspects of mathematics; if they were, the flood of results would be much greater. He suggests LLMs may be particularly good at finding counterexamples, as most famous solved problems involve counterexamples rather than proofs.\n\nGowers cautions that defining 'finding a counterexample' is not trivial.

Using Vinogradov's theorem as an example, he explains that not all universal statements negated yield counterexamples; the nature of quantification matters. He also discusses the Banach-Mazur compactum, where Gluskin solved the diameter problem, and Fritz John's theorem provides an upper bound. These examples illustrate the complexity of classifying what LLMs excel at.\n\nGowers concludes that while LLMs are powerful, their strengths seem to lie in specific problem types, and a crisp classification remains elusive.

He expects rapid changes in their capabilities, making his observations a snapshot from early August 2026.