Mathematician Says OpenAI Pressured Him Over Navier-Stokes Credit

Tristan Buckmaster, the NYU mathematician who won a 2019 Clay Research Award for proving Navier-Stokes solutions aren't unique, published a statement on his university page on the morning of September 8, 2026, announcing three new finite-time blowup proofs built with heavy help from large language models, and accusing OpenAI of pressuring him over credit for a related, unpublished result. The statement landed on Hacker News within the hour and pulled in a second story nobody had confirmed yet: whether an AI model had quietly closed in on a Millennium Prize problem.

• Buckmaster and Levent Alpöge, a mathematician who works at Anthropic, posted three finite-time blowup proofs, for the incompressible porous media equation, the Boussinesq equations, and 3D incompressible Euler, all with smooth forcing, building on a program started by Diego Córdoba and Luis Martínez-Zoroa.
• They say they likely also have a blowup proof for hypo-dissipative Navier-Stokes, a close cousin of the still-unsolved Millennium Prize problem, but are withholding it until a Lean formal verification finishes.
• Buckmaster says that after word of his progress reached OpenAI, researcher Sebastien Bubeck told him on a Sunday call that an internal OpenAI model had already produced a roughly 100-page proof of forced Navier-Stokes blowup, then proposed publication plans that would drop Alpöge from authorship or hand OpenAI top billing.
• Nobody, Buckmaster included, has proven the actual unforced Navier-Stokes problem that carries the $1 million Clay Prize; both the OpenAI claim and Buckmaster's own results concern easier "forced" variants of the equation.

What did Buckmaster and Alpöge actually prove?

The three results are finite-time blowup theorems: proofs that a fluid equation, given smooth starting conditions and a smooth external forcing term, can develop a genuine singularity in finite time rather than staying well-behaved forever. They got there for the incompressible porous media equation, for Boussinesq, and for 3D incompressible Euler, the inviscid cousin of Navier-Stokes. Buckmaster is explicit that the underlying idea isn't his: Diego Córdoba and Luis Martínez-Zoroa spent years building a program for constructing forced blowups with rough forcing, and Buckmaster says plainly that "Luis Martínez-Zoroa deserves a Fields Medal" for it. What he and Alpöge added was pushing that program from rough to smooth forcing using LLMs, mainly Anthropic's Claude and OpenAI's Codex running GPT-5.6 Sol, with a newer model called Astra used only for writeups and auditing arguments. Buckmaster is unusually candid that the results aren't dressed up: he calls the Euler writeup "AI slop" and says he wanted weeks to turn the LLM-generated proofs into something readable before publishing, time he says outside pressure didn't leave him.

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Why does "forced" versus "unforced" matter here?

The official Clay Institute problem, written up by Charles Fefferman, doesn't ask just one question, it lists several variants: whole space or a periodic torus, with or without an external forcing term. Adding a forcing term, especially a smooth one, makes the blowup question meaningfully easier to attack, because the forcing can be engineered to actively push the fluid toward a singularity instead of the mathematician having to find one hiding inside a completely free-flowing system. Córdoba and Martínez-Zoroa's route runs through exactly that door, using smooth forcing as it's defined in Fefferman's options (c) and (d). Buckmaster says almost nobody else was working that specific angle, which is why, when Bubeck described OpenAI's alleged internal result as forced blowup, it read to him as an oddly precise coincidence rather than a model independently rediscovering the same narrow path in days.

What does Buckmaster say happened with OpenAI?

By his account, a rumor started circulating around September 3 that Anthropic had resolved a major open problem, and Levent Alpöge had separately heard that details of their joint work had reached OpenAI. Buckmaster emailed a mathematician at OpenAI to get ahead of the confusion, stressing the project was a personal collaboration with no institutional backing from either of their employers. He was offered compute and a call. On Sunday, September 6, Sebastien Bubeck joined that call and told him an internal OpenAI model had produced a roughly 100-page proof of forced Navier-Stokes blowup after being given only the problem statement, with "very little human input." Over the course of the conversation, Buckmaster says, that claim unraveled: internal Slack-style messages relayed to Bubeck mid-call revealed an entire team had been working the problem, that the model had first been set on easier warm-up cases including Euler, and that the prompt itself had been machine-generated. OpenAI was then unable or unwilling to say clearly when the first prompt was sent, other than "the past few days," after Buckmaster and Alpöge's own progress had reportedly reached them.

Two proposals followed, per Buckmaster's account: either the two groups publish on consecutive days with OpenAI's Navier-Stokes result following his Euler paper, or Buckmaster alone write up the Navier-Stokes result crediting an unnamed internal OpenAI model, with Alpöge dropped from authorship because, as Bubeck reportedly put it, it was "annoying" that Alpöge works at Anthropic. Buckmaster says he declined both and warned he'd go public if OpenAI released its version this way, drawing the reply "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." Bubeck separately texted Alpöge asking to speak one-on-one because he wasn't sure "Tristan is being fully rational right now"; Alpöge declined. Buckmaster is careful to note what he isn't claiming: he hasn't seen OpenAI's proof, doesn't know what their model actually did, and isn't accusing anyone of a specific violation. He says he's publishing his account only because he didn't want a future announcement to rewrite what actually happened.

1. Aug 15, 2026Blowup results land for Boussinesq and Euler Smooth forcing, after months of slower progress on porous media.
2. Aug 22, 2026Lean formally verifies the proofs Buckmaster calls the first LLM-generated draft "the most horrendous I have ever read."
3. Sep 3, 2026Buckmaster emails an OpenAI mathematician Trying to get ahead of a rumor that Anthropic had solved a major open problem.
4. Sep 6, 2026Sebastien Bubeck joins two calls Describes an alleged internal forced-Navier-Stokes proof and proposes credit arrangements.
5. Sep 7, 2026Bubeck requests a Monday call Buckmaster does not respond.
6. Sep 8, 2026Buckmaster publishes his statement Alongside the three finite-time blowup papers, on his NYU page.

Why is Alpöge's employer the flashpoint?

Alpöge works at Anthropic, and that detail is doing more work in this story than it should. Days before Buckmaster's post, an unrelated Anthropic research effort had already been generating buzz: an unreleased Claude model reportedly raised the confirmed share of Riemann zeta zeros satisfying the Riemann Hypothesis from about 41.6 percent to 67.2 percent, real incremental progress on a completely different Millennium Prize problem, that got garbled in retelling into rumors that Claude had cracked Navier-Stokes outright. Buckmaster says a colleague at Courant heard the rumor secondhand and it named him. By the time Bubeck was twice asking that Alpöge be removed from the Navier-Stokes authorship specifically because he works at Anthropic, two separate stories, an unrelated Riemann Hypothesis result and a personal side project on fluid blowups, had fused into one narrative about which company's AI was "closer" to a Millennium Prize.

Did AI actually solve the Navier-Stokes Millennium Problem?

No, and this is the detail getting lost. Every result in this story, Buckmaster and Alpöge's three proofs and OpenAI's alleged internal one, concerns a forced version of a fluid equation. The Clay Institute's actual million-dollar problem, unforced existence and smoothness for 3D Navier-Stokes, remains open, and mathematician Terence Tao has separately clarified that earlier remarks of his were being misread as confirming a breakthrough that hasn't happened. What's real here is narrower and, in its own way, more interesting: a mathematician says two frontier labs' competitive instincts around AI-generated math results moved faster than either lab's willingness to show its work.

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What it means for the AI labs' credibility

Both OpenAI and Anthropic have spent 2026 treating frontier math results as capability marketing, evidence a model can do research-grade reasoning, not just answer questions. That's a real signal investors and enterprise buyers watch when sizing up which lab's models are worth building on. Buckmaster's account, if it holds up, is a costly one for OpenAI specifically: it suggests at least one such claim arrived dressed as a lone model's cold-start proof when it was actually a team effort assembled after word of a rival's progress leaked in. A verification gap like that matters more than the underlying math to anyone deciding how much to trust the next capability claim either company makes.

Our take

Set the drama aside for a second and the actual math here is a genuine milestone: a mathematician and two LLMs took an existing human research program and pushed it from rough to smooth forcing in about a month, then caught their own worst proof draft with a formal verifier before showing it to anyone. That's a legitimately new way research mathematics can move. What makes this story land differently is the contrast Buckmaster draws between that discipline and what he says he was offered instead: an unverified, unseen 100-page proof, assembled by a team after a competitor's progress leaked, wrapped in a story about a lone model and a few days of "very little human input." If a frontier lab's public capability claims are only as good as the version of events it's willing to let its own text messages contradict on a call, that's the more important story for anyone deciding which lab's word to take at face value.

Original analysis by GenZTech, based on Tristan Buckmaster's published statement and the Clay Mathematics Institute's official problem description. Source