AIBRIEF
Tim Gowers, who holds the Fields Medal — math's top honor — reads OpenAI's 10 problem sweep and spots a pattern: the marquee wins are counterexamples to long standing conjectures, not proofs of new theorems.
In a post written days after OpenAI said it had solved ten major problems in mathematics and theoretical computer science, Tim Gowers, a Fields medalist (math's highest honor), sat down to look at the list. The pattern he spotted is sharper than the announcement itself.
Most of the marquee results are counterexamples: a single case that breaks a long-standing conjecture, rather than a proof of a new positive claim. The list includes the first construction of a non-sofic group and a proof that the 3-colour Ramsey number grows superexponentially. Both are "here is a thing everyone thought was impossible" results, not "here is a new structure everyone now believes." Gowers also flags earlier LLM counterexamples on the Jacobian conjecture and the unit distance conjecture, which asks how many points on a plane can sit exactly one unit apart.
His read: LLMs are unusually good at exploring combinatorial search spaces and finding the rare object that breaks a pattern, and less good at the long, structured arguments that produce a new theorem. The falsifier is simple. If LLMs were truly better than all human mathematicians, the preprint servers would already be flooded. They are not.
Gowers does not claim a clean theory yet. His proposed human-level test: the proof that, with hindsight, comes to seem beautiful and natural, the kind a search-heavy system would stumble onto only by accident. Whether the current results clear that bar is the open question he leaves the reader with.