OpenAI's 722 machine-generated maths papers: the hard part is now checking them
An unreleased internal model produced 722 manuscripts, including claimed progress on the unique games conjecture. Only part of the main results come with Lean formalizations, and the field is split on what that is worth.
In the Daily Brief of 11 October 2026
On 6 October OpenAI released 722 mathematics manuscripts, grouped into 372 families of results and drawn from about 4,000 posed problems. All of them were produced by an internal model that has not been released. The set includes claimed progress on the unique games conjecture and on a quasi-Riemann hypothesis, and Lean formalizations cover only part of the main results.
Reactions split sharply. Alex Kontorovich said the strongest results would count as Fields-Medal-level work had a human produced them. The Association for Human Mathematics urged colleagues to stop collaborating with OpenAI, and a group of Fields medallists signed an open letter criticising the release.
A new paper by Bastounis, Circelli and Hansen at Cambridge adds a technical objection. It argues that faithful autoformalisation is undecidable in a strong sense, and shows that the Lean proof of the Navier–Stokes blow-up result does not correspond to the argument written in the paper. The authors do not claim the theorem is false: their point is that a proof that compiles is not automatically a proof of what the paper states.