Mathematicians say OpenAI’s AI-generated proof is ‘borderline incomprehensible’

OpenAI announced on Monday, September 21, that it is working with an independent Advisory Group on Mathematics and Artificial Intelligence, hosted at Princeton's Institute for Advanced Study, after weeks of fallout from a disputed and largely unreadable AI-generated proof of the Navier-Stokes Millennium Prize problem.openai+1

A Proof No One Can Read

Earlier this month, OpenAI revealed that 10,000 AI agents working for 88 hours had produced a 166-page proof showing that fluids described by the Navier-Stokes equations can develop a singularity in finite time — a result that, if verified, would settle one of six remaining Millennium Prize Problems posed by the Clay Mathematics Institute. Mathematicians broadly accept the proof as technically correct, in part because it was accompanied by a formal verification in the Lean programming language. But human understanding of the result remains elusive.openai+2

"So far it's been very difficult to really extract any human understanding from this new AI proof," James Maynard, a mathematician at the University of Oxford, told NPR. "The paper is not written for humans," echoed Javier Gómez-Serrano, a mathematician at Brown University, who said the proof could help the field after "some serious re-writing" but "as of today, the paper doesn't teach us much".nprillinois

The announcement also sparked an attribution dispute. NYU mathematician Tristan Buckmaster accused OpenAI of building on his unpublished research without credit, claiming the company offered to list him as an author only if he dropped his collaborator, Levent Alpöge, who works at Anthropic. OpenAI denied using Buckmaster's work but acknowledged it "cannot rule out that de-identified data derived from their usage of our products helped improve our models".futurism+2

An Elite Advisory Panel

The new nine-member group includes multiple Fields Medal winners and scholars from Stanford, Harvard, Oxford, Cambridge, and other top institutions. Members will not be paid by OpenAI and can publicly comment on the company's impact on mathematics, offer unsolicited advice, and control their own membership.theverge+2

"Its value depends on its members being able to exercise their own judgement and challenge ours," OpenAI said in a blog post. However, the company made clear the group "will not be responsible for advising us on how to pace our internal progress on mathematics".techcrunch+1

Some mathematicians questioned whether the panel can truly represent the broader community. "It feels like an ivory tower," said Francesco Fournier-Facio, an incoming professor at Heriot-Watt University. Simon Machado, a researcher at ETH Zurich, called the panel's formation "shrouded in mystery" and questioned how members were selected.theverge

What Comes Next

The group's most immediate challenge may be the largest. Alongside the advisory panel announcement, OpenAI disclosed that the same unreleased model has "resolved more than 100 long-standing open problems across most areas of mathematics". The panel said coordinating the release of those results is its first priority.indiatoday+2

Martin Hairer, a panel member and Fields Medalist, wrote in a blog post that the group was formed because AI companies have been "producing some high profile mathematical results" whose "publication and dissemination has been falling far short of acceptable mathematical practice". But he cautioned that members "would be very naïve to believe that the AI labs won't try to spin whatever we say in a way that suits their PR machine".theverge