Summary
OpenAI says an AI model solved the Navier–Stokes problem. The claim is awaiting peer review and has prompted a wider debate about credit for ideas shared with chatbots.
OpenAI says it used an artificial-intelligence model to solve the Navier–Stokes problem, one of seven Millennium Prize Problems selected by the Clay Mathematics Institute. The company made the announcement on 8 September 2026, but the result still has to pass the institute’s publication and community-review process before it can be considered a valid solution for the prize.
The announcement has also raised a broader question: how should mathematicians receive credit when researchers use chatbots to develop ideas, and when those conversations may later become part of the material used to train AI systems?
The claim and the formal-checking step
The Navier–Stokes equations provide a mathematical framework for describing fluid motion. Questions about these equations have remained among the most prominent unresolved problems in mathematics and fluid dynamics.
OpenAI says it checked its proof using Lean, a programming language and proof-assistant system that allows mathematical arguments to be written in a form that software can examine step by step. That process gives the company a way to test the formal proof it encoded. It is separate from the Clay Mathematics Institute’s process for deciding whether the result qualifies as a solution to the Millennium Prize Problem.
The institute says it will consider a solution only after the results have been published in a peer-reviewed publication and examined further by the mathematical community. The prize attached to each selected problem is US$1 million.
Why AI changes the credit trail
The announcement followed work by Tristan Buckmaster of New York University and Levent Alpöge of Harvard University on an aspect of the Navier–Stokes problem. They had used tools from OpenAI and Anthropic during their research. Buckmaster said he had worked with OpenAI tools for about a year across three ChatGPT accounts; on two of those accounts, he had opted out of the setting that permits conversations to be used to train models.
A day before OpenAI confirmed that it was preparing its announcement, Buckmaster raised concerns that the company’s model might have learned from interactions connected with his work. OpenAI said its system could not have been influenced by user inputs after 3 July, that it began working on the problem on 1 September, and that it had not seen Buckmaster and Alpöge’s work through any means before the researchers released it publicly.
Researchers familiar with the Navier–Stokes problem have argued that substantial credit should also go to Buckmaster and Alpöge, as well as Diego Córdoba of the Institute of Mathematical Sciences and Luis Martínez Zoroa of CUNEF University. How credit is eventually divided will depend partly on whether the proposed solution survives mathematical review.
A similar issue has emerged in work on non-sofic groups, a category of mathematical groups. Andreas Thom of Dresden University of Technology said he had used ChatGPT for brainstorming about a strategy in that area. In August, OpenAI posted a preprint describing what it presented as the first example of such a group, using a strategy similar to Thom’s. The paper cited earlier published work by Thom and his collaborators, but it is not established whether the model also drew on Thom’s private chatbot conversations. Thom had not opted out of model training until late June.
Human researchers commonly acknowledge useful private discussions in papers. AI systems, however, do not currently provide an equivalent, reliable record of which conversations contributed to an idea. That difference becomes more significant when researchers use chatbots for informal problem-solving rather than only for drafting or routine assistance.
The Navier–Stokes announcement therefore has two tests ahead: whether the proof is accepted by mathematicians, and how the research community develops workable standards for recognising contributions made through AI-assisted discussions.