News · 2026-09-10

OpenAI says it cannot rule out that user chats improved the model behind its proof

OpenAI wrote in its 8 September 2026 account of the Navier-Stokes result that it "cannot rule out that de-identified data derived from their usage of our products helped improve our models," referring to two mathematicians working on a closely related problem. In the same paragraph the company states that no specific user data was accessed in order to solve the problem. Those two sentences are the reason a mathematics story has turned into a data-consent story.

Key facts

• The sentence appears in OpenAI's own write-up, published 8 September 2026
• The mathematicians named are Levent Alpoge of Anthropic and Tristan Buckmaster of NYU
• OpenAI's agents reached their result on 5 September, about 88 hours after launch
• Primary source: On the Navier-Stokes Millennium Prize Problem

What OpenAI actually said

The full passage matters, because it is being quoted in halves. OpenAI writes: "We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."

Read carefully, these are claims about two different periods. The first covers the effort itself: during the roughly 88 hours in September when OpenAI's coordinating agents worked the problem, nobody pulled up anyone's private chats. The second covers everything before that: whatever went into training the model in the first place.

A company can honestly assert the first and be unable to assert the second, because training data at this scale is not the kind of thing anyone can fully account for after the fact. That is precisely what makes the sentence significant. It is not a confession, and it is not a denial. It is a large lab stating on the record that it cannot answer the question.

How the two efforts collided

OpenAI's own timeline is unusually candid. The company says it began on 1 September "after hearing a rumor" of two Millennium Prize problems being resolved — a rumour it later realised concerned Alpoge and Buckmaster. Inspired by that rumour and by a jump in performance from an internal model it had been training since 28 August, it launched a mass evaluation across every open Millennium problem.

The scale was extraordinary. The group that cracked Navier-Stokes involved "on the order of 10,000 concurrent agents." Across all attempted problems the agents exchanged 4.9 million messages and produced about 300 billion tokens of output. Lean formalisation and verification took a further 17 hours.

On 6 September, believing the two mathematicians also had a Navier-Stokes solution, OpenAI reached out to offer a joint announcement recognising their priority — and discovered they had actually resolved a different problem, the forced Euler case. OpenAI's agents had resolved the unforced version. The company says it offered them visibility into all its prompts and later the proof, and it congratulates them: "We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement."

Why this became the story

The mathematical dispute is, on OpenAI's account, largely dissolved: the two groups proved different things, and the company is not claiming the Millennium Prize. What has not dissolved is the question underneath, which has nothing to do with fluid dynamics.

Researchers use these products as working notebooks. They paste in half-finished arguments, failed approaches and the shape of ideas they have not published. The implicit deal is that a paid tool is a private one. OpenAI's sentence says the deal cannot be fully guaranteed — not that it was broken, but that the company is not in a position to prove it was kept.

That is a governance problem rather than a technical one, and it is why the reaction among mathematicians has been sharper than the specific facts might suggest. Ground Truth previously covered Buckmaster's account of being asked to drop his Anthropic co-author, and the broader question of what a lab owes a researcher whose unpublished work passes through its servers is now being asked in public by people who had not previously thought to ask it.

There is a real counter-argument, and it deserves stating. "Cannot rule out" is the honest answer to almost any question about a training corpus of this size, and a company that said "we can rule it out" would be making a claim it could not support. Penalising OpenAI for candour risks teaching every lab to say less. The fair criticism is not that OpenAI admitted uncertainty; it is that the industry has built systems whose inputs cannot be audited, and then asked researchers to trust them anyway.

The honest caveat

Everything above comes from OpenAI's own account, which is the only detailed public description of what happened and is not independently verifiable. The agent counts, message volumes and timeline are self-reported. Alpoge and Buckmaster's own characterisation of the exchanges may differ from OpenAI's, and mathematical review of both results is only beginning — the Lean formalisation establishes that the proof is internally valid, not that the statement proved is the one the Clay Mathematics Institute posed. Separately, claims circulating on social media that OpenAI has since made progress on a second Millennium Prize problem could not be traced to any OpenAI statement and are not reported here.

Primary source, verified: read the paper →

Ground Truth. (2026, September 10). OpenAI says it cannot rule out that user chats improved the model behind its proof. Ground Truth. https://groundtruth.day/news/openai-says-it-cannot-rule-out-that-user-chats-improved-the-model-that-did-the-proof.html

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  title  = {OpenAI says it cannot rule out that user chats improved the model behind its proof},
  author = {{Ground Truth}},
  year   = {2026},
  month  = {sep},
  url    = {https://groundtruth.day/news/openai-says-it-cannot-rule-out-that-user-chats-improved-the-model-that-did-the-proof.html}
}

Topics: openai · training-data · privacy · mathematics · ai-ethics · consent