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.
\n\n\n\n\n\n\n\n\n\n\n\nThe problem is called Navier–Stokes.
\n\n\n\nForget the maths.
\n\n\n\nIt is basically a 90-year-old question about whether the equations we use to describe moving water and air can suddenly break down.
\n\n\n\nOpenAI says its new internal AI cracked it.
\n\n\n\nAround 10,000 AI agents worked on the problem.
\n\n\n\n88 hours later, they had a proof.
\n\n\n\nThat alone could become one of the biggest moments in the history of AI-assisted science.
\n\n\n\nBut then the story gets uncomfortable.
\n\n\n\nTwo mathematicians, Tristan Buckmaster and Levent Alpöge, had spent months working on a closely related approach.
\n\n\n\nThey were using AI to help them.
\n\n\n\nIncluding OpenAI’s Codex.
\n\n\n\nBuckmaster says they had been putting all of their unpublished drafts into Codex throughout the project.
\n\n\n\nThen word of their progress reached OpenAI.
\n\n\n\nOpenAI confirms that those rumours prompted it to send its new internal model after the Millennium Prize problems.
\n\n\n\nDays later, its AI had gone further and produced the Navier–Stokes proof.
\n\n\n\nNow, there is no evidence that OpenAI simply stole their work.
\n\n\n\nAt 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.
\n\n\n\nAnd OpenAI says neither its researchers nor its AI agents accessed their specific private work.
\n\n\n\nOpenAI subsequently updated its account after investigating whether the researchers’ use of its products could have influenced the result.
\n\n\n\nIn 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.
\n\n\n\nThat update changes the specific allegation of possible data influence in this case.
\n\n\n\nBecause this is no longer really a story about mathematics.
\n\n\n\nWe are increasingly giving AI the work we haven’t shown the world yet.
\n\n\n\nOur code.
\n\n\n\nOur research.
\n\n\n\nOur business plans.
\n\n\n\nOur inventions.
\n\n\n\nOur best unfinished ideas.
\n\n\n\nAnd we naturally think of the AI as a tool working for us.
\n\n\n\nBut what happens when the company behind that tool can also build a much more powerful version that works without us?
\n\n\n\nThere are protections. OpenAI says Business, Enterprise and API data isn’t used for training by default, and consumer users can turn training off.
\n\n\n\nOpenAI’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.
\n\n\n\nWould 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?
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