A machine proves what a career could not, and nobody can read the proof
OpenAI this week published 722 mathematical manuscripts, grouped into 372 families of results, all produced by an internal model that has not been released. By the account of the computer scientist Scott Aaronson, the model was given about three hours on each problem and worked alone, with no swarm of agents behind it.
Among the results is a proof of the Unique Games Conjecture, a question in the theory of computation that has stood since 2002. It comes with a certificate from Lean, a program that checks each logical step. Aaronson's wife, the complexity theorist Dana Moshkovitz, has worked towards that proof for the whole of her career.
The certificate says the logic holds. It does not make the paper readable. Aaronson reports that Moshkovitz found it close to impossible to follow without asking an AI model to explain it, and that the proof builds a new kind of code no mathematician had tried.
The release is not all on that footing. OpenAI's own repository says about 42 per cent of the headline results are formalised, 300 of 719, and warns that the rest could have issues. Three papers were withdrawn within a day over a sign error.
An advisory group of mathematicians, asked about the release, would neither endorse nor condemn it. Only the mathematical community, it said, can judge what has been proved.