In a dramatic escalation of tensions between the world’s leading AI lab and the academic community, mathematician Tristan Buckmaster has accused an OpenAI researcher of pressuring him to remove a co-author who works at Anthropic, threatening his career, and attempting to claim priority on a groundbreaking solution to the Navier-Stokes equations. The allegations, detailed in a public statement from Buckmaster, come just hours after OpenAI published its own proof of the same problem — a proof produced by roughly 10,000 coordinated AI agents over 88 hours, at a computing cost in the millions of dollars. The dispute has ignited a fierce debate over research ethics, data privacy, and the role of artificial intelligence in mathematical discovery.
OpenAI Publishes Navier-Stokes Proof, Denies Buckmaster’s Allegations
OpenAI has officially released its results on the Navier-Stokes equations, one of the seven Clay Millennium Problems that have stumped mathematicians for decades. In an official blog post, the company presented a proof formalized in the Lean theorem prover, achieved by a swarm of AI agents running an internal model described as “significantly more capable than GPT-6 Astra.” Research lead Mark Chen noted that the compute alone cost “in the millions of dollars.”
OpenAI developer Noam Brown pointed to a familiar pattern of rapid cost decline: When OpenAI launched o3, hitting 87.5 percent on the ARC-AGI benchmark cost about $500,000; today, Astra can do more for roughly $20. The 2025 Math Olympiad required massive compute from both OpenAI and Google Deepmind; by 2026, anyone with a $20 ChatGPT subscription could match that performance. “I believe that a year from now everyone will have an AI at their fingertips capable of solving problems of this caliber,” Brown wrote.
During a press briefing reported by WIRED, OpenAI pushed back against Buckmaster’s allegations. “We, whether it’s the researchers or the agents, did not see any of their work until it was released publicly last night,” said Sébastien Bubeck. He wanted to “be extremely clear” that OpenAI recognizes the priority of Alpöge and Buckmaster’s work and congratulates them on their “monumental achievement.” OpenAI mathematician Ven Chandrasekaran stated that the company’s solution differs fundamentally from the approach Buckmaster and Alpöge took.
Bubeck said OpenAI began training a new model with advanced math capabilities on August 28. After hearing rumors about progress at Anthropic, the company shifted more resources toward the Navier-Stokes problem. “On Sunday morning we had the final solution, Lean-formalized, and everything.”
In its blog post, OpenAI says its work began on September 1 after hearing a rumor that later turned out to be related to Alpöge and Buckmaster. After completing the project and Lean verification on September 6, the company reached out to propose a concurrent release and a joint announcement recognizing their priority. Only then did OpenAI learn that the two had solved the forced Euler problem, not Navier-Stokes. OpenAI says it offered them visibility into all prompts used and later access to the proof.
“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,” OpenAI writes. “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).”
Buckmaster responded on Mastodon: “Note that they are openly admitting they used training data from a period after we found our result. Is it ethical to use customer’s data to try to scoop their customer?” Whether Buckmaster had opted out of OpenAI’s default setting that allows the company to use customer data for model training is not known.
What Are the Navier-Stokes Equations and Why Do They Matter?
The Navier-Stokes equations describe the motion of viscous fluid substances — everything from airflow over an airplane wing to ocean currents and blood flow. Despite their everyday relevance, proving that solutions always exist and are smooth (or finding a counterexample) is one of the seven Clay Millennium Problems, each carrying a $1 million prize. The problem has remained unsolved since the Clay Mathematics Institute announced the prize list in 2000. A breakthrough would have profound implications for physics, engineering, climate modeling, and our fundamental understanding of turbulence.
Buckmaster’s Detailed Allegations: Pressure, Threats, and a Request to Remove a Co-Author
Tristan Buckmaster, a mathematician at the Courant Institute of Mathematical Sciences, and his co-author Levent Alpöge, a mathematician known for work in number theory, spent months using various AI models — including Anthropic’s Claude and OpenAI’s Codex running GPT-5.6 Sol — to make progress on the Navier-Stokes problem. By mid-August, they say they’d achieved several breakthroughs. They also believe they found a result for a specific Navier-Stokes variant, though it hasn’t been published or formally verified yet. A recognized proof would be a massive deal for mathematics and a landmark for AI-assisted research.
In early September, rumors about a major math breakthrough started circulating. According to Buckmaster, Alpöge got word that information about their work had been passed along to OpenAI. On September 3, Buckmaster proactively reached out to a mathematician at OpenAI to set the record straight, stressing that the work was a purely personal collaboration with no institutional agreements.
OpenAI responded the same day, asked for details, and offered compute resources. Buckmaster suggested a call the following week, but OpenAI pushed harder. On Friday, they asked if he could talk that same day. On Sunday at 12:45 p.m., they wanted to know if he was available “at any point today.”
That Sunday, Sébastien Bubeck joined the conversation. During two phone calls, OpenAI told Buckmaster that an internal model had produced a roughly 100-page proof for the Navier-Stokes equations with forcing, according to his account. At first, OpenAI said “very little human input” was needed. As the conversation went on, a different picture emerged: a whole team had worked on the problem, easier problems had been used as stepping stones, and massive compute was thrown at it.
Buckmaster says the mention of forced Navier-Stokes suggested that OpenAI was pursuing the same unusual route he and Alpöge had chosen, one that he says almost nobody else was working on. He and Alpöge had put all their drafts throughout the project into OpenAI Codex sessions. When he asked whether OpenAI’s model had been trained on or had access to those sessions, he says he was told the model did not look up user data. When he asked specifically about training, he says he received no answer.
OpenAI developer Noam Brown, during the Astra launch in early August, had said that OpenAI had been attempting the Millennium Problems but hadn’t found a solution, and that they hadn’t put much compute toward the effort.
The Demand to Drop the Anthropic Co-Author
OpenAI made two proposals, according to Buckmaster. In the first, Buckmaster and Alpöge post their Euler result, and OpenAI posts its own the next day, with OpenAI declaring them the “closest humans to the problem.” In the second, Buckmaster alone presents the Navier-Stokes result and acknowledges an internal OpenAI model. In both scenarios, Bubeck twice “asserted” that he wanted Alpöge removed from authorship. The reason, according to Buckmaster, is that it was “so annoying” that Alpöge works at Anthropic.
Buckmaster rejected both proposals and said he’d go public if OpenAI published its result in the proposed form. The response, according to Buckmaster: “Why would you ruin your career?” When he replied that he’s an academic, Bubeck allegedly said: “If you don’t want me to be nice, then I don’t have to be nice.” Buckmaster reports that Bubeck later texted Alpöge separately, telling him: “I don’t know if Tristan is being fully rational right now.” Alpöge declined to engage.
Buckmaster explicitly states he isn’t accusing anyone of data theft. He hasn’t seen OpenAI’s proof and doesn’t know whether their data was used. He’s sharing the facts because, as he puts it, “the alternative is to let a sequence of announcements say something I know to be false.”
The Deep Blue–Kasparov Moment for AI-Assisted Mathematics
What Buckmaster had actually wanted to talk about was something very different: that a mathematician working with a language model can now accomplish in a month what used to take much longer. “This is a Deep Blue–Kasparov moment,” he writes, referencing the 1997 chess match that marked a turning point in human-machine collaboration. The Navier-Stokes breakthrough, whether achieved by humans with AI tools or by an autonomous AI system, signals a new era in mathematical research. The ability to generate, verify, and formalize proofs at scale could accelerate progress on the hardest open problems — but it also raises uncomfortable questions about credit, ownership, and the power dynamics between academic researchers and corporate AI labs.
Ethical Questions Around Data Usage and Research Priorities
The core of the dispute hinges on whether OpenAI used data from Buckmaster and Alpöge’s Codex sessions — either through direct access or via model training — to guide its own solution. OpenAI denies any direct access but admits that de-identified usage data could have been used to improve models. Buckmaster’s point is sharp: if OpenAI trains on customer data by default (users can opt out), and if that data includes sensitive research drafts, then the line between legitimate product improvement and competitive intelligence becomes dangerously blurred.
OpenAI’s standard privacy policy allows the company to use customer data to improve model performance, with an opt-out option. Whether Buckmaster and Alpöge had opted out is unknown. But the incident highlights a structural problem: when a company both provides the tools for research and competes with researchers on the same problems, conflicts of interest are inevitable. Anthropic’s Claude was also used by the mathematicians, raising the question of whether Anthropic might face similar accusations in the future.
What This Means for the Future of Mathematical Discovery
The Navier-Stokes affair is not merely a spat between an academic and a tech giant. It is a preview of the tensions that will define AI-driven research in the coming years. As AI models become capable of solving problems that once required years of human genius, the norms of scientific attribution, peer review, and priority are being stress-tested. Buckmaster’s decision to go public — with a detailed timeline and a refusal to be silenced — may set a precedent for how researchers protect their work in the age of AI. Meanwhile, OpenAI’s claim that its proof was produced autonomously, without seeing the academics’ work, suggests that the company believes it can achieve results independently. But the timing, the specificity of the approach, and the pressure to remove an Anthropic employee all raise doubts that will not be easily resolved.
One thing is certain: the era of AI-assisted mathematical discovery has arrived, and with it comes a host of questions that cannot be answered by algorithms alone. How should credit be assigned when an AI model trained on vast amounts of human knowledge produces a proof? Should researchers who use AI tools be required to disclose which models and what data they used? And when a company that both builds the tools and pursues the same problems as its users, how can the integrity of the scientific process be preserved? These are not hypothetical questions — they are playing out in real time, with a million-dollar prize and the reputation of a leading AI lab on the line.
