OpenAI’s Navier–Stokes Claim: The Proof and the Data Update

OpenAI announced an AI-generated Navier–Stokes proof on 8 September 2026. Two days later, it updated its account to say that Tristan Buckmaster’s recent Codex prompts could not have influenced the system, including through training.

The mathematical claim and its limits

The problem is called Navier–Stokes.

Forget the maths.

It is basically a 90-year-old question about whether the equations we use to describe moving water and air can suddenly break down.

OpenAI says its new internal AI cracked it.

Around 10,000 AI agents worked on the problem.

88 hours later, they had a proof.

That alone could become one of the biggest moments in the history of AI-assisted science.

But then the story gets uncomfortable.

Two mathematicians, Tristan Buckmaster and Levent Alpöge, had spent months working on a closely related approach.

They were using AI to help them.

Including OpenAI’s Codex.

Buckmaster says they had been putting all of their unpublished drafts into Codex throughout the project.

Then word of their progress reached OpenAI.

OpenAI confirms that those rumours prompted it to send its new internal model after the Millennium Prize problems.

Days later, its AI had gone further and produced the Navier–Stokes proof.

Now, there is no evidence that OpenAI simply stole their work.

At the time of the original September reporting, Buckmaster said he did not know whether their data had been used. OpenAI’s subsequent investigation gave the more specific account set out below.

And OpenAI says neither its researchers nor its AI agents accessed their specific private work.

The 10 September data update

OpenAI subsequently updated its account after investigating whether the researchers’ use of its products could have influenced the result.

In a 10 September 2026 update, OpenAI said its investigation confirmed that Buckmaster’s Codex prompts over the preceding two months could not have influenced the system, including through training.

That update changes the specific allegation of possible data influence in this case.

Because this is no longer really a story about mathematics.

We are increasingly giving AI the work we haven’t shown the world yet.

Our code.

Our research.

Our business plans.

Our inventions.

Our best unfinished ideas.

And we naturally think of the AI as a tool working for us.

But what happens when the company behind that tool can also build a much more powerful version that works without us?

There are protections. OpenAI says Business, Enterprise and API data isn’t used for training by default, and consumer users can turn training off.

OpenAI’s updated account does not establish that private work influenced this result. The wider question is how researchers can verify confidentiality before sharing unpublished work with an AI service.

Would you put your best unpublished idea into an AI assistant if there were even a small chance the company behind it could learn from it?

Sources and context

• OpenAI: dated announcement and research context (Company or research source)