Tim Gowers: LLMs Solve Maths Problems by Getting Lucky at Scale, and Almost Every Recent Win Was a Counterexample, Not a Proof

Tim Gowers·medium signalXBlueskyLinkedInCopy link

The Fields medalist published an assessment on August 12 arguing that LLMs excel precisely at problems amenable to "try lots of things till you get lucky" — breadth of knowledge plus speed — and not at the search-tree pruning humans use to navigate proof discovery. His observation about the recent run of ten solved major problems (first non-sofic group, superexponential growth for multicolor Ramsey numbers, Jacobian conjecture, unit distance conjecture) is that they predominantly involved finding counterexamples rather than constructing proofs. Testing ChatGPT 5.6 Pro, he found it frequently offers "promising approaches" that don't survive scrutiny. Read alongside Anthropic's Riemann zeta result the same week, it's the sharpest available framing of what these systems are actually doing in mathematics.