OpenAI posts 722 math papers from unreleased AI model

On Tuesday, Oct. 6, OpenAI posted 722 mathematical manuscripts to a public GitHub repository, sorted into 372 "result families." The company says an unreleased internal frontier model produced them. Scientific American reported that the repository went live at 6 p.m. EDT. Mathematicians are expected to need months to work through the results and judge whether the proofs contain new ideas or mostly recombine existing techniques.openai+2

The release comes a month after OpenAI said on Sept. 8 that the same internal system had proved that three-dimensional Navier-Stokes flows can develop singularities in finite time. That problem is one of the Clay Mathematics Institute's Millennium Prize Problems. The Navier-Stokes announcement has drawn sustained criticism over credit, transparency and how quickly the company is releasing results.scientificamerican+2

What is in the repository

The families are spread across 17 disciplines, with theoretical computer science, combinatorics, algebraic geometry and number theory accounting for the most entries. The catalogue includes claimed results on the irrationality exponent of pi, the Mahler conjectures, NP-hardness, the isomorphism of free group factors and the relativistic Vlasov-Maxwell equations.interestingengineering+2

OpenAI also published Lean formalizations of many of the proofs. Lean is a programming language that lets a computer check each logical step of a proof. Not every manuscript has been formalized, though. The repository's README warns that some of the unformalized results "could have issues," and the formalization manifest lists its review status as "unchecked".kingy+2

The company said the model attempted about 4,000 problems over the course of the evaluation. It said the average result used compute equivalent to "roughly three hours of ChatGPT Pro thinking". Ten abridged summaries of the model's reasoning are included. OpenAI did not disclose a total dollar cost, token counts or a public model name.unite+2

Advisory group's guidance only partly followed

OpenAI said it shaped the release using advice from the independent Advisory Group on Mathematics and Artificial Intelligence, which is hosted at the Institute for Advanced Study in Princeton, New Jersey. The group issued recommendations on Sept. 29. They call for labs to publish the model name, the prompts used and the compute cost for each result, and to deposit results in repositories that no AI lab controls. OpenAI did not release prompts or per-result compute figures. A company spokesperson told Scientific American that OpenAI takes the guidelines seriously but is not bound by them.scientificamerican+2

The same spokesperson said almost every result came from a single prompt given to a single agent, though some may have taken multiple attempts.scientificamerican

Divided reactions

"We should ask for receipts," Andrew Sutherland, a mathematician at MIT, told Scientific American. He said claims about solving problems in one shot should be treated as unverified until the model is released. Daniel Litt of the University of Toronto took the opposite view: "To me, it's going to be a good thing for mathematics".scientificamerican

OpenAI said it plans to fund workshops and conferences aimed at helping mathematicians understand AI-produced results, and that it is working to "responsibly release the model" behind them.openai