OpenAI Can't Rule Out User Data Behind Its Millennium Proof

A second mathematician has accused OpenAI of obscuring where its training data comes from, days after the company published a 166-page proof of a Millennium Prize problem.

The complaint lands on a specific sentence. OpenAI says no specific user data was accessed to solve the problem — but it will not rule out that de-identified data derived from how people use its products helped improve the models that did. For anyone doing unpublished work inside ChatGPT or Codex, those two statements are not the same guarantee.

What OpenAI announced, and how fast

OpenAI said on September 8 that an unreleased internal model, which it describes as significantly more capable than GPT-6 Astra, worked with roughly 10,000 concurrent agents to produce a solution to the Navier-Stokes existence and smoothness problem — one of the seven Millennium Prize Problems the Clay Mathematics Institute listed in 2000. The company published a 166-page proof alongside Lean code that a machine can check step by step.

The run was short. Training on the new model began August 28. The agent swarm launched September 1, found the result on September 5 about 88 hours in, and GPT-6 Astra then spent roughly 17 more hours formalizing it in Lean. Across the whole run the agents sent about 4.9 million messages and produced around 300 billion output tokens, with about 2.7 million messages and 130 billion tokens going to Navier-Stokes alone.

OpenAI researcher Sebastien Bubeck said the final stage cost emphatically millions of dollars, roughly 1,000 times what the company spent on earlier mathematical results. OpenAI says it will not claim the $1 million prize, and Clay Mathematics Institute president Martin Bridson noted that evaluation is deliberately unhurried: a solution needs peer-reviewed publication and two years of acceptance in the mathematical community before a committee is even convened.

Two mathematicians, one carefully scoped denial

The dispute started before the announcement had settled. On September 7, NYU mathematician Tristan Buckmaster and Levent Alpöge, who works at Anthropic, published AI-assisted results on three related equations, including Euler with a smooth forcing term. Buckmaster said OpenAI only took up the problem after word of his research spread, and asked whether the Codex sessions where he and Alpöge kept drafts had fed into the model.

Now a second researcher has gone public. In posts on Mastodon, mathematician Andreas Thom raised concerns that interactions he and his colleagues had with ChatGPT before OpenAI's announcement may have contributed to its success, according to The Verge. One of the 10 results OpenAI announced last month involved Thom's area of expertise — non-sofic groups — and OpenAI acknowledged that its result built heavily on previous work by Thom and fellow mathematician Gábor Kun. The Verge reports the company was widely criticized in mathematical circles for failing to credit Thom and Kun, and quietly amended its writeup.

Thom said he was struck by "OpenAI's detailed command of our techniques," which he said were neither the most obvious nor the most promising routes to a solution at the time. He emailed OpenAI researchers Sébastien Bubeck and Mark Sellke to ask whether his ChatGPT interactions were "part of the training data or accessible to the reasoning process." The reply, he said, addressed only whether his conversations could be accessed directly — not whether they had entered the training pools. "No such qualification, explanation, or evidence was given," he wrote. "I take this as dishonesty to say the least."

OpenAI's public wording follows the same shape. In the blog post announcing the Navier-Stokes solution, the company said: "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." It then added: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."

Thom's answer to that distinction is the sharpest line in the episode: "De-identification may remove a name; it does not remove the intellectual content of a mathematical idea." OpenAI did not immediately respond to The Verge's request for comment.

Why the wording matters if your team ships unpublished work

Read the two statements as an engineer reads a spec, because that is what they are. The denial covers direct access and specific user data for one project. The caveat covers something else entirely: aggregate, de-identified data that improved the model in general. A company can hold both positions honestly and still have benefited from your drafts.

The practical takeaways, and this is our analysis rather than anyone's claim: treat product tier as a data boundary, not a billing choice, and confirm in writing which surfaces exclude your inputs from training. Keep unpublished results out of any surface where that exclusion is a setting rather than a contract term. And note that neither Buckmaster nor Thom is asking for a payout — both are asking for disclosure, which is a thing a vendor can supply and a setting cannot.

The cost the field is now pricing in

Numerous researchers told The Verge they worry behavior like this pushes mathematics into a more secretive state, if researchers know that even rumors of a near-breakthrough can ignite a race with a well-resourced tech company. That is the durable risk here, and it is not hypothetical: OpenAI has said the unusual reason it picked up Navier-Stokes was hearing that others had made progress. Terence Tao made a related argument separately — that good open problems are a resource being mined non-renewably.

What to watch

• Verification, not announcement. Bridson's timeline means the proof needs peer review plus two years of community acceptance before a prize committee convenes. Any claim that the problem is "solved" before that is a claim about a preprint.
• Whether OpenAI discloses datasets. Thom's stated ask is disclosure of the relevant datasets and the terms governing data use. A denial without that is unfalsifiable from the outside; researchers cannot reverse-engineer a training pipeline.
• Whether a third researcher comes forward. Two in four days, both in areas OpenAI announced results in, is a pattern worth counting.