What sort of maths are LLMs good at?
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Gowers reflects on LLM mathematical strengths after OpenAI solves major problems.
Timothy Gowers examines the types of mathematics at which LLMs excel, following OpenAI's announcement of solving ten major problems including a non-sofic group construction and superexponential Ramsey number growth. He focuses on whether LLMs are especially good at finding counterexamples versus proofs. Gowers argues that classifying problems as "counterexample" versus "theorem" is nuanced and depends on quantifier structure and the role of variables. He compares Vinogradov's three-primes theorem with Gluskin's diameter-of-Banach-Mazur-compactum result to illustrate the distinction.
Gowers suggests future signs of human-level mathematical reasoning will include proofs that are surprising yet beautiful and natural, not easily stumbled upon by accident.
What commenters are saying
Top commenters praise the post as measured and thoughtful. A lengthy off-topic thread criticizes LLMs as "parlour tricks" for failing practical agentic tasks like job searches in specific European countries, with users debating prompt quality and verifying with logs. Another commenter ties the post to test-time scaling and sampling, noting verification is easier for counterexamples than proofs. A user questions whether Gowers has examined his own notions of "beauty" and "natural" in mathematics.