Two mathematicians spent close to a year working toward a breakthrough, using AI coding tools to help with the work. Days after word of that breakthrough got out, OpenAI’s own coding agents produced a resolution to a closely related problem in 88 hours. One of the two mathematicians wants to know exactly what OpenAI knew, and when.

What happened

Tristan Buckmaster, a mathematics professor at NYU’s Courant Institute, and Levent Alpöge, a mathematician who works at Anthropic, spent close to a year on the Navier-Stokes existence and smoothness problem. That’s a long-standing open question about whether the equations describing how fluids like water and air flow always produce well-behaved solutions, or can spiral into a mathematical breakdown. It’s one of seven Millennium Prize Problems that have each carried a $1 million reward since May 24, 2000. Working with Claude (Anthropic’s AI assistant) and Codex (OpenAI’s AI coding agent), Buckmaster and Alpöge reached a breakthrough on August 15, 2026.

Word of that breakthrough reached OpenAI. Buckmaster and Alpöge then learned OpenAI already had a team pursuing a closely related problem using a similar approach, and reached out to ask what OpenAI knew and when its own effort had actually started. In a statement he later published, Buckmaster described pressing OpenAI for a straight answer:

“I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting a […]”

OpenAI’s own account of its result, published alongside its proof, says its agents produced a resolution in 88 hours, work that launched September 1 and finished September 5. That effort alone used 2.7 million agent messages (individual steps in the agent’s automated back-and-forth work) and roughly 130 billion output tokens (the chunks of text the model generates as it works). OpenAI has said it “did not see any of their work through any means,” while also acknowledging it “cannot rule out that de-identified data derived from their usage,” meaning usage data with directly identifying details stripped out, may have helped train the models involved.

OpenAI offered to publish jointly with Buckmaster, according to his account, but wanted the paper to exclude Alpöge as a co-author, citing his position at Anthropic, a competitor.

Who’s involved

Buckmaster is a professor at NYU’s Courant Institute, one of the country’s leading applied mathematics departments, and a winner of the Clay Research Award, a prize the same institute behind the Millennium Prize Problems gives to recognize major mathematical breakthroughs. Alpöge is a mathematician who works at Anthropic. Neither is speaking as a company spokesperson here; both are describing what they say happened to their own work directly.

What Tao added

Terence Tao, a UCLA mathematics professor and a Fields Medal winner, one of the highest honors in mathematics, posted a warning the same week about a broader version of the same dynamic:

“We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. The incentives may now be pointing in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science and do serious long-term damage to the future of the field.”

Tao’s post doesn’t name Buckmaster’s case directly. But it describes the same shape of event: a private breakthrough, a rumor that reaches a well-resourced AI lab, and an agent-driven effort large enough to reproduce the result within days.

What the evidence establishes, and what it doesn’t

OpenAI’s own numbers establish that its effort was compressed into less than four days, using a volume of automated work no human team could match on its own. OpenAI’s own statement is also notably not a flat denial. “Cannot rule out” is a hedge, not a “no.” And by OpenAI’s own account, its effort’s start traces back to after news of Buckmaster and Alpöge’s work had already reached the company, even if what exactly reached them, a vague rumor or something more specific, isn’t spelled out publicly.

None of this proves OpenAI’s model saw or trained on Buckmaster and Alpöge’s private Codex sessions. Buckmaster’s own statement doesn’t claim that it did either. What it documents is that OpenAI wouldn’t give him a clear answer on the question for some time, and that the two companies ended up in a co-authorship dispute that reads more like a competitive conflict than a research collaboration.

Why it’s notable

AI coding agents have gotten fast and cheap enough to run at scale that a well-resourced lab can now credibly compress what used to be a year of specialized human work into a few days, once it decides a problem is worth chasing. That changes the calculus for anyone doing serious, unpublished work with these tools. Under Tao’s account, the trigger for that kind of effort doesn’t even require a leak or a published paper. A rumor is enough.

What it means for builders

If you’re doing work you consider genuinely valuable and aren’t ready to share, a research result, a product design, a data pipeline, check what your AI coding tool’s data-usage policy actually says before you put that work into it. “De-identified” and “used to improve the model” aren’t the same thing as “walled off from everyone else.” Most providers, including OpenAI, publish a data usage policy describing what you can opt out of on your specific plan. It’s worth reading that policy directly rather than assuming a default setting protects you.

The second lesson is about pace, not just privacy. If a rumor about your work can be enough to trigger a competitor’s AI-driven effort, the old advantage of a quiet head start is worth less than it used to be. That doesn’t mean stop collaborating or sharing direction with trusted partners. It means treat the moment your work becomes known, even informally, as the moment a much faster competitor’s clock starts too.

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