OpenAI reports 372 AI-produced mathematical results

Science reported that the release comprised 722 preprints covering 372 distinct results.[1] OpenAI says the results came from an internal frontier model, which Science reported was unreleased.[2][1] The work included results concerning famous, difficult problems such as the Riemann hypothesis.[1] OpenAI also says it published the results in a GitHub repository, with protocols for paper revisions and citations.[2] For researchers assessing the work, the size of the release is not itself a measure of how many results are novel or useful: identifying what, if anything, was new and useful was the stated goal.[1]

OpenAI says the model attempted about 4,000 problems to produce its 372 results.[1] The company also says the average result used computing equivalent to roughly three hours of ChatGPT Pro thinking.[2] These figures describe different aspects of the effort: one is the number of attempted problems, while the other is an average compute comparison for each result.[1][2] Science reported a much larger earlier OpenAI effort on Navier-Stokes, using 10,000 agents continuously for 88 hours and likely costing millions of dollars.[1] That comparison is a reminder that AI-assisted mathematical work can involve substantial resources, though the evidence does not establish that the efforts are directly comparable.

OpenAI says the release included formalizations of many proofs in Lean, a programming language that lets computers check mathematical proofs.[2] Science reported that 300 of the 719 papers remaining after withdrawals had been formalized in Lean at the time it went to press.[1] Science also reported that OpenAI had withdrawn three manuscripts and revised 14 as it went to press.[1] The distinction matters for review: Lean verification checks a formal proof, but Science cautioned that it does not establish that the corresponding English-language claim in a paper is true.[1] Readers should therefore treat formal verification as one kind of evidence, not as a complete evaluation of a paper.