❯ OpenAI releases 722 mathematical manuscripts from an internal model, covering 372 groups of new results, most still awaiting review by mathematicians

722 at onceOpenAI announced on October 6 that it is releasing a batch of new mathematical results produced by an internal frontier model: 722 manuscripts, grouped into 372 families of related results, in a public GitHub repository. According to Runtime Wire, they came from about 4,000 research problems posed to the model, with the average result using compute equivalent to about three hours of ChatGPT Pro thinking. The model that produced them is unreleased and unnamed.

One prompt, one agentAccording to Scientific American, nearly all 372 results came from the same procedure: a single prompt handed to a single AI agent, with some possibly taking multiple attempts. They span number theory, combinatorics, theoretical computer science and mathematical physics. A few results did not follow the standard procedure, including work on the Riemann zeta function and on a case of the Hodge conjecture.

Not all verifiedThe repository includes Lean formalizations for many results, meaning proofs a computer can check step by step, but many manuscripts still lack them. OpenAI itself warns that unformalized results could contain issues and that citations and exposition need more work. It says the release drew on advice from the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, which has no decision-making power.

Unease among mathematiciansWIRED reports that in August OpenAI convened around 40 mathematicians to discuss what to do if AI outpaces humans in the field, and hinted that its models had solved hundreds of longstanding problems. Attendees say the company assured them it would not release everything at once, an assurance an OpenAI spokesperson says the company is “not aware of.” One mathematician told WIRED there is “a perception of mobster behavior” from leading AI companies. With hundreds of proofs arriving together, the work of checking each one’s correctness and value falls to mathematicians.

▮ SIGNALOnce proofs can be produced in bulk, the scarce step in mathematics shifts from finding a proof to confirming one, and that still depends on people.