OpenAI publishes 722 maths papers written by a model it has not released

OpenAI has published 722 maths manuscripts from an internal model it has not released. The papers fall into 372 families of results. The company announced the release on Tuesday and put them all in a public GitHub repository .

It is the same model behind OpenAI’s Navier-Stokes proof last month. OpenAI gave it about 4,000 problems during the evaluation, the repository says. On average, each result used about three hours of ChatGPT Pro thinking compute.

Many of the proofs come with formal versions in Lean, a programming language that lets a computer check a proof. Not all do. OpenAI says some of the results without a formal version could have issues, and it will fix them quickly. Every earlier version will stay public, and each paper has its own citation block.

OpenAI also published ten summaries of the model’s reasoning. Two results did not follow the standard procedure. One is a zero-free region for the Riemann zeta function, whose write-up a human edited for readability. The other is a proof of the Hodge conjecture for CM abelian varieties.

Nearly every paper came from a single prompt to a single AI agent, OpenAI told Scientific American . The company will fund workshops, conferences and special programmes on results produced by AI. It says it is also working to release the model responsibly.

OpenAI said it drew on advice from an independent panel of mathematicians . The Advisory Group on Mathematics and Artificial Intelligence (AGMAI) is hosted by the Institute for Advanced Study. In its 29 September guidelines , it asked AI labs to stop testing hard maths problems on private models. It also asked them to publish the prompts, time and compute cost behind each result.

“The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field,” the group wrote.

On Tuesday night, AGMAI said its advice was not an endorsement of the results, or of how OpenAI got them.

“This release is the beginning, not the completion, of the process of human understanding,” the group wrote.

Dan Roberts, OpenAI’s research lead, told The New York Times that testing internal models helps build better tools. The proofs were a byproduct, he said.

Tristan Buckmaster, a New York University mathematician, was working on the Navier-Stokes problem before OpenAI solved it. He told the Times he doubted OpenAI had checked so many results released at once.

“I don’t think they’ve done their sort of due diligence at all,” Buckmaster said.

MIT mathematician Andrew Sutherland told Scientific American to treat the single-agent claims as unverified. That should hold until others can run the model and repeat the results, he said.