OpenAI’s proposed solution to a mathematics problem carrying a $1 million prize has sparked a dispute over research credit, unpublished work, and how AI companies compete with academics.
At the centre of this is a mathematician who used OpenAI’s tools while developing related research, then questioned how the company reached its own result.
Published on September 8, this concerns the Navier-Stokes existence and smoothness problem, a decades-old question about whether the equations used to describe fluid motion can break down.
What OpenAI Says It Achieved
As part of the Millennium Prize Problems, the Navier-Stokes equations describe fluid motion and are used in areas including weather forecasting and aircraft design. OpenAI says its proof shows that, under a carefully constructed smooth external force, the equations can produce fluid speeds that grow without limit in a finite time. And this would demonstrate a mathematical breakdown in the model.
According to OpenAI, roughly 10,000 AI agents powered by an internal model reached the result in 88 hours. Formalisation and verification using Lean, software for checking mathematical proofs, took another 17 hours.
Why A Mathematician Challenged OpenAI
New York University professor Tristan Buckmaster had been working with mathematician Levent Alpöge, an Anthropic employee, on related fluid equations. Buckmaster said their collaboration was personal and used both Claude and OpenAI’s Codex, building on ideas developed by Diego Córdoba and Luis Martínez-Zoroa.
In his public statement, Buckmaster questioned whether drafts entered into Codex could have influenced OpenAI’s system, explicitly acknowledging that he did not know whether their data had been used.
He also alleged that OpenAI researcher Sébastien Bubeck proposed having Buckmaster write up OpenAI’s Navier-Stokes result without Alpöge as a co-author because of Alpöge’s Anthropic affiliation. Buckmaster said he declined.
Buckmaster said the pair had wanted additional weeks to turn their AI-assisted proofs into readable papers, but felt pressured to release unfinished explanations.
OpenAI Has Strengthened Its Denial
OpenAI acknowledges that rumours about the researchers’ progress prompted its effort. However, in an update, the company said its investigation established that Buckmaster’s Codex prompts from the preceding two months could not have influenced the system, including through training.
It also recognises the pair’s priority on the related forced Euler problem and says its own proofs differ significantly.
Could Your Chatbot Be Stealing Ideas From You?
Buckmaster’s concern could also matter to people using ChatGPT to develop work they have not published. While OpenAI says personal conversations may be used to train its models unless users opt out, an unfinished article or business idea shared for help could also help improve the company’s technology.
As such, doubts about how their work might be used could make people more reluctant to share it. For companies promoting AI as a research and writing partner, this could make it harder to persuade users to trust these tools with their original work.
The Concern Extends Beyond Credit
On September 11, 25 Fields Medal recipients, including Terence Tao and Maryna Viazovska, issued a broader warning about AI companies’ approach to mathematics.
“The goals of the AI companies and the goals of the mathematical community are severely misaligned,” they wrote.
Their concern is that rushing to announce solutions can leave insufficient time to explain new methods, acknowledge earlier contributions and develop ideas that other researchers can understand and teach. And this explains why an impressive technical result can still face serious academic criticism.
The Clay Mathematics Institute also said on September 11 that the problem had “apparently been settled,” while stressing that evaluating the achievement and assigning credit would follow its deliberately unhurried process.
OpenAI says it does not intend to claim the prize. As such, the next stage will involve examining the proof and establishing how the contributions behind it should be recognised.
