OpenAI says it solved a $1M math problem. A mathematician says they took his answer first.

The short version

OpenAI announced its unreleased frontier model solved the Navier-Stokes existence and smoothness problem — one of math’s seven Millennium Prize Problems, open for roughly 90 years. Worth knowing before you take that at face value: NYU mathematician Tristan Buckmaster says he and Anthropic researcher Levent Alpöge had been quietly working toward the same result, that word of their progress reached OpenAI, and that OpenAI then threw a full team and what he calls “an insane amount of compute” at the same problem starting September 1 — days after learning of his work. OpenAI says it never saw the pair’s actual work before they published it, and its own scientist has called Buckmaster’s account “false and inflammatory.”

What’s actually new

• The claim. OpenAI’s internal system — described as “significantly more capable than GPT-6 Astra,” not the model itself — produced a full proof (plus a machine-checked Lean formalization) that Navier-Stokes fluid dynamics can develop a singularity in finite time. Compute cost is reported inconsistently across coverage — TechCrunch cites roughly 300 billion output tokens and ~$22.5 million; other outlets have cited different figures (one, a $15 million estimate; another, 10,000 concurrent agents run for 88 hours) — the numbers don’t fully reconcile across sources, so treat any single figure as approximate pending OpenAI’s own accounting.
• The timing Buckmaster flags. He says almost no one else was working the same specific mathematical approach he and Alpöge had chosen, and that OpenAI’s effort began September 1 — shortly after he says word of their progress reached the company. He hasn’t offered public proof of exactly how that word traveled.
• The pressure allegation. Buckmaster alleges OpenAI’s Sébastien Bubeck asked him, as part of a proposed compromise, to drop Alpöge’s name from authorship — and that when Buckmaster resisted going public with the dispute, Bubeck told him: “Why would you ruin your career?” and later, “If you don’t want me to be nice, then I don’t have to be nice.”
• OpenAI’s denial. The company says: “We (the researchers and the agents) did not see any of their work through any means until they released it publicly.” It also acknowledges it “cannot rule out” that de-identified data from Buckmaster’s use of its own products (he reportedly used Codex) could theoretically have informed its models — while maintaining the two proofs differ substantially. Separately, Bubeck has publicly called the allegations “false and inflammatory” and said he’d have more to say.

The part worth sitting with

Both things can be true at once: OpenAI’s own account leaves open a door it can’t fully close (data from a researcher’s own tool use “cannot be ruled out” as an influence), and Buckmaster hasn’t shown the public exactly how his private progress reached OpenAI’s ears, if it did. What’s not in dispute is the timeline — a company with enormous compute can go from “hearing a rival has a breakthrough in reach” to “publishing a competing full proof” in about a week. Whether that’s OpenAI’s engineers being extraordinarily fast, or something closer to what Buckmaster alleges, matters far less to the industry than the fact that the gap between “quiet academic progress” and “a frontier lab’s entire compute budget aimed at the same target” is now this small.

Why this matters if you’re building agent systems

Credit and provenance disputes aren’t new in research — what’s new is the speed at which a well-resourced lab can convert a rumor of progress into a finished, published result, using agents rather than researchers as the labor. If tens of thousands of agent-hours can chase down a 90-year-old open problem in roughly a week once a lab decides to try, “who published first” stops being a reliable proxy for “who actually solved it independently” — a governance problem this industry doesn’t have a good answer for yet.

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