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OpenAI's Navier-Stokes statement on user data has two parts, not a firm "we don't train on your data" promise

A mathematician kept a year of unpublished drafts in Codex, then asked whether they had been used for training and got silence on that half of the question, which is the half every enterprise rollout treats as settled.

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Illustration accompanying OpenAI's Navier-Stokes statement on user data has two parts, not a firm "we don't train on your data" promise
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What happened

  • OpenAI said in a Tuesday blog post that it solved the Navier-Stokes problem using an internal model more powerful than the newly released GPT-6 Astra, running 10,000 concurrent agents.
  • A day earlier, NYU's Tristan Buckmaster posted a proof for a simplified version of the equations, after nearly a year of work with Anthropic researcher Levent Alpoge using public OpenAI and Anthropic models.
  • Buckmaster says the pair had put every draft of the project into Codex, that he was told the model did not look up user data, and that his repeated question about training went unanswered.
  • Buckmaster's document says OpenAI staff offered him co-authorship on a joint paper that dropped Alpoge because he works for Anthropic, an offer the company's denial of the wider accusations does not address.

Why it matters

  • Who's exposed exposure The customer with the most work inside a product has the least covered by a promise about specific user data, because session history accumulates faster than anyone revisits the data settings.
  • What it limits constraint Verification narrows to whoever owns the compute: a result produced by an unreleased model and 10,000 agents cannot be re-run by a referee with a university account.
  • Who has to decide decision Buyers renewing AI seats now have to split one assurance into three and establish which of them sits in a signed agreement rather than a blog post.
  • What doesn't add up contradiction Bubeck's denial and Buckmaster's reading of the same carve-out can both be honest, which means neither party's statement can close the dispute and the argument moves to what the training corpus contained.

Retrieval at inference time is one promise. Training on your content is a second one, and a third, which almost no procurement checklist names, covers de-identified derivatives of your usage. OpenAI's announcement makes the first: no specific user data was accessed in order to solve this problem [7]. It declines the third in writing, saying that while unlikely, it cannot rule out that de-identified data derived from their usage of its products helped improve its models [7]. On the second, Buckmaster says he asked twice and got an answer only about lookup. He was told the model did not look up user data, and when he asked again about training, no answer came [6].

The timing is why that gap carries weight. OpenAI says it started training the internal model on August 28 [10] and announced the proof on September 8 [2], eleven days later [14]. Buckmaster and Alpöge had been working on the problem for close to a year [4], with drafts going into Codex sessions the whole time [6]. Buckmaster's reading of the carve-out, posted on Mastodon, is that OpenAI is "openly admitting they used training data from a period after we found our result" [11]. Sébastien Bubeck of OpenAI says the team saw none of their work until it was public, and that the two proofs differ significantly [16]. Both proofs do use the route pioneered by Diego Córdoba and Luis Martínez-Zoroa, and Javier Gómez-Serrano of Brown University says that approach was one of several thought to hold promise [13], so the shared route settles nothing in either direction.

Teams tell themselves users read the data controls page, work out which toggle governs training, and keep the sensitive material out of the surfaces the toggle does not cover. What users actually do looks different. They put the work where the tool is, for a year, because that is where the tool is useful [6]. Depth of use is the number worth watching. It is also the number that creates the exposure. Someone who pastes one function into an assistant risks little. The customer who has kept an entire unpublished project in one vendor's session history has far more at stake, and is the customer a renewal depends on.

The 2x2 has two axes. First, is the assurance contractual, in a document with a counterparty and a remedy, or is it a statement, in a blog post or a post on X [8]? Second, does it cover only retrieval of your data, or does it also cover derivatives, including de-identified ones? Most assurances an operator can actually produce on request sit in the weakest quadrant, statement plus retrieval only, which is the quadrant OpenAI's language occupies here. The useful exercise is writing out the sentence you would need about your team's unpublished work, then finding which document contains it. If the answer is a blog post, you have a press release where you wanted a term.

Which is where credit lands. A proof produced by an internal model running 10,000 concurrent agents [1] can be checked in detail only by people with access to that setup, and according to Buckmaster's document, the offer of joint authorship came with Alpöge dropped because he works at Anthropic [12]. Attribution here depends on logs that one party can read, and that party's own carve-out says the logs may not settle it.

What to watch

  • Whether rival vendors add or drop a de-identified derivatives clause in their data terms now that OpenAI has put one in writing.
  • Whether Buckmaster and Alpoge release timestamped session records that date their result against OpenAI's August 28 training start.
  • Whether the Clay Mathematics Institute addresses eligibility for an agent-produced proof, given OpenAI says it will not claim the prize.

Clarity's read

What the record supports and how the coverage leans. The claims behind it follow.

Reality

Evidence52
Adoption30
Hype gap+32
Incentives78
Confidence60
Why these scores

Claim ledger

Ranked by verification strength, evidence, and original report placement.

  1. [1]

    OpenAI announced in a Tuesday blog post that it discovered a solution to the Navier-Stokes problem using an internal AI model more powerful than the newly released GPT-6 Astra, alongside 10,000 concurrent agents.

    Reported Supported Source: OpenAI, via The VergeView cited source
  2. [2]

    MIT Technology Review's account, published September 8, 2026, reported that OpenAI announced the solution that day.

    Reported SupportedView cited source
  3. [3]

    On Monday, NYU mathematician Tristan Buckmaster posted a proof on Mastodon showing that a simplified version of the Navier-Stokes equations can break down.

    Reported SupportedView cited source
  4. [4]

    Buckmaster and Levent Alpoge, a researcher at Anthropic, had worked on the problem for almost a year using publicly available models from both OpenAI and Anthropic.

    Reported SupportedView cited source
  5. [5]

    OpenAI says it does not plan to claim the one million dollar prize for solving the problem.

    Reported SupportedView cited source
  6. [6]

    Buckmaster wrote that he and Alpoge had been putting all their drafts for the whole project into OpenAI's Codex, that he asked whether the model had been trained on or had access to those sessions, that he was told the model did not look up user data, and that when he asked again about training he did not get an answer.

    Reported Supported Source: Tristan BuckmasterView cited source
  7. [7]

    OpenAI's Tuesday announcement says "no specific user data was accessed in order to solve this problem" and adds that "while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models".

    Reported Supported Source: OpenAIView cited source
  8. [8]

    When reached for comment, OpenAI pointed The Verge to its statement on X, which echoes its blog post.

    Reported SupportedView cited source
  9. [9]

    The Navier-Stokes existence and smoothness problem is one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000; solutions come with a one million dollar prize, and before this announcement only one other Millennium Prize Problem had been solved.

    Reported SupportedView cited source
  10. [10]

    OpenAI says it started training the internal AI model on August 28th, and that the model has exhibited unprecedented performance in its benchmarks, including mathematics.

    Reported Supported Source: OpenAIView cited source
  11. [11]

    Buckmaster responded in a post on Mastodon claiming that OpenAI is "openly admitting they used training data from a period after we found our result".

    Reported Supported Source: Tristan BuckmasterView cited source
  12. [12]

    According to Buckmaster's document, OpenAI employees presented him with two possibilities: he and Alpoge could post their work and OpenAI would post its Navier-Stokes solution the following day, or he could work with OpenAI on a paper that excluded Alpoge from authorship because of his affiliation with Anthropic.

    Reported Supported Source: Tristan Buckmaster's document, as reported by MIT Technology ReviewView cited source
  13. [13]

    The Buckmaster/Alpoge and OpenAI proofs both use an approach to the Navier-Stokes problem pioneered by Diego Cordoba and Luis Martinez-Zoroa, and Javier Gomez-Serrano, a mathematics professor at Brown University, says this approach was one of several thought to hold promise for solving the problem.

    Reported Supported Source: Javier Gomez-Serrano, Brown UniversityView cited source
  14. [14]

    Eleven days elapsed between OpenAI's stated training start for the internal model and the announcement of the proof.

    Derived Supported
  15. [15]

    Sebastien Bubeck said in a press briefing that the OpenAI team was inspired to pursue the problem after hearing a rumor about Buckmaster and Alpoge's efforts.

    Reported Supported Source: Sebastien Bubeck, OpenAIView cited source
  16. [16]

    Sebastien Bubeck, a member of technical staff at OpenAI, said: "We did not see any of their [Buckmaster and Alpoge's] work until they released it publicly last night. One can in hindsight see that our proofs differ significantly and even the precise results proved are different."

    Reported Contested Source: Sebastien Bubeck, OpenAIView cited source
  17. [17]

    OpenAI has denied accusations that it used Buckmaster and Alpoge's AI-assisted work as a jumping-off point and failed to credit them.

    Reported ContestedView cited source

Sources

2 independent publishers whose own reporting we read for this story.

  1. technologyreview.com

    2 articles · September 8, 2026

    What OpenAI’s latest controversy tells us about the future of math
  2. theverge.com

    1 article · September 8, 2026

    Drama swirls around OpenAI’s legendary mathematical milestone

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