{"id":80337,"date":"2026-09-08T16:34:49","date_gmt":"2026-09-08T20:34:49","guid":{"rendered":"https:\/\/overcentral.com\/en\/?p=80337"},"modified":"2026-09-08T16:34:49","modified_gmt":"2026-09-08T20:34:49","slug":"openai-navier-stokes-dispute-80337","status":"publish","type":"post","link":"https:\/\/overcentral.com\/en\/openai-navier-stokes-dispute-80337\/","title":{"rendered":"OpenAI Researcher Pressures Mathematician to Remove Anthropic Co-Author"},"content":{"rendered":"

In a dramatic escalation of tensions between the world\u2019s 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<\/a>, 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 \u2014 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.<\/p>\n

OpenAI Publishes Navier-Stokes Proof, Denies Buckmaster\u2019s Allegations<\/h2>\n

OpenAI has officially released its results on the Navier-Stokes equations, one of the seven Clay Millennium Problems<\/a> that have stumped mathematicians for decades. In an official blog post<\/a>, the company presented a proof<\/a> formalized in the Lean theorem prover, achieved by a swarm of AI agents running an internal model described as \u201csignificantly more capable than GPT-6 Astra<\/a>.\u201d Research lead Mark Chen noted that the compute alone cost \u201cin the millions of dollars.\u201d<\/p>\n

OpenAI developer Noam Brown pointed to a familiar pattern of rapid cost decline<\/a>: 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. \u201cI believe that a year from now everyone will have an AI at their fingertips capable of solving problems of this caliber,\u201d Brown wrote.<\/p>\n

During a press briefing reported by WIRED<\/a>, OpenAI pushed back against Buckmaster\u2019s allegations. \u201cWe, whether it\u2019s the researchers or the agents, did not see any of their work until it was released publicly last night,\u201d said S\u00e9bastien Bubeck. He wanted to \u201cbe extremely clear\u201d that OpenAI recognizes the priority of Alp\u00f6ge and Buckmaster\u2019s work and congratulates them on their \u201cmonumental achievement.\u201d OpenAI mathematician Ven Chandrasekaran stated that the company\u2019s solution differs fundamentally from the approach Buckmaster and Alp\u00f6ge took.<\/p>\n

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. \u201cOn Sunday morning we had the final solution, Lean-formalized, and everything.\u201d<\/p>\n

In its blog post, OpenAI says its work began on September 1 after hearing a rumor that later turned out to be related to Alp\u00f6ge 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.<\/p>\n

\u201cWe (the researchers and the agents) did not see any of their work through any means until they released it publicly \u2014 in particular, no specific user data was accessed in order to solve this problem,\u201d OpenAI writes. \u201cWhile 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).\u201d<\/p>\n

Buckmaster responded on Mastodon<\/a>: \u201cNote that they are openly admitting they used training data from a period after we found our result. Is it ethical to use customer\u2019s data to try to scoop their customer?\u201d Whether Buckmaster had opted out of OpenAI\u2019s default setting that allows the company to use customer data for model training is not known.<\/p>\n

What Are the Navier-Stokes Equations and Why Do They Matter?<\/h2>\n

The Navier-Stokes equations describe the motion of viscous fluid substances \u2014 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.<\/p>\n

Buckmaster\u2019s Detailed Allegations: Pressure, Threats, and a Request to Remove a Co-Author<\/h2>\n

Tristan Buckmaster, a mathematician at the Courant Institute of Mathematical Sciences, and his co-author Levent Alp\u00f6ge, a mathematician known for work in number theory, spent months using various AI models \u2014 including Anthropic\u2019s Claude and OpenAI\u2019s Codex running GPT-5.6 Sol \u2014 to make progress on the Navier-Stokes problem. By mid-August, they say they\u2019d achieved several breakthroughs. They also believe they found a result for a specific Navier-Stokes variant, though it hasn\u2019t been published or formally verified yet. A recognized proof would be a massive deal for mathematics and a landmark for AI-assisted research.<\/p>\n

In early September, rumors about a major math breakthrough started circulating. According to Buckmaster, Alp\u00f6ge 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.<\/p>\n

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 \u201cat any point today.\u201d<\/p>\n

That Sunday, S\u00e9bastien 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 \u201cvery little human input\u201d 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.<\/p>\n

Buckmaster says the mention of forced Navier-Stokes suggested that OpenAI was pursuing the same unusual route he and Alp\u00f6ge had chosen, one that he says almost nobody else was working on. He and Alp\u00f6ge had put all their drafts throughout the project into OpenAI Codex sessions. When he asked whether OpenAI\u2019s 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.<\/p>\n

OpenAI developer Noam Brown, during the Astra launch in early August, had said that OpenAI had been attempting the Millennium Problems but hadn\u2019t found a solution, and that they hadn\u2019t put much compute toward the effort.<\/p>\n

The Demand to Drop the Anthropic Co-Author<\/h3>\n

OpenAI made two proposals, according to Buckmaster. In the first, Buckmaster and Alp\u00f6ge post their Euler result, and OpenAI posts its own the next day, with OpenAI declaring them the \u201cclosest humans to the problem.\u201d In the second, Buckmaster alone presents the Navier-Stokes result and acknowledges an internal OpenAI model. In both scenarios, Bubeck twice \u201casserted\u201d that he wanted Alp\u00f6ge removed from authorship. The reason, according to Buckmaster, is that it was \u201cso annoying\u201d that Alp\u00f6ge works at Anthropic.<\/p>\n

Buckmaster rejected both proposals and said he\u2019d go public if OpenAI published its result in the proposed form. The response, according to Buckmaster: \u201cWhy would you ruin your career?\u201d When he replied that he\u2019s an academic, Bubeck allegedly said: \u201cIf you don\u2019t want me to be nice, then I don\u2019t have to be nice.\u201d Buckmaster reports that Bubeck later texted Alp\u00f6ge separately, telling him: \u201cI don\u2019t know if Tristan is being fully rational right now.\u201d Alp\u00f6ge declined to engage.<\/p>\n

Buckmaster explicitly states he isn\u2019t accusing anyone of data theft. He hasn\u2019t seen OpenAI\u2019s proof and doesn\u2019t know whether their data was used. He\u2019s sharing the facts because, as he puts it, \u201cthe alternative is to let a sequence of announcements say something I know to be false.\u201d<\/p>\n

The Deep Blue\u2013Kasparov Moment for AI-Assisted Mathematics<\/h2>\n

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. \u201cThis is a Deep Blue\u2013Kasparov moment,\u201d 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 \u2014 but it also raises uncomfortable questions about credit, ownership, and the power dynamics between academic researchers and corporate AI labs.<\/p>\n

Ethical Questions Around Data Usage and Research Priorities<\/h2>\n

The core of the dispute hinges on whether OpenAI used data from Buckmaster and Alp\u00f6ge\u2019s Codex sessions \u2014 either through direct access or via model training \u2014 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\u2019s 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.<\/p>\n

OpenAI\u2019s standard privacy policy allows the company to use customer data to improve model performance, with an opt-out option. Whether Buckmaster and Alp\u00f6ge 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\u2019s Claude was also used by the mathematicians, raising the question of whether Anthropic might face similar accusations in the future.<\/p>\n

What This Means for the Future of Mathematical Discovery<\/h2>\n

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\u2019s decision to go public \u2014 with a detailed timeline and a refusal to be silenced \u2014 may set a precedent for how researchers protect their work in the age of AI. Meanwhile, OpenAI\u2019s claim that its proof was produced autonomously, without seeing the academics\u2019 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.<\/p>\n

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 \u2014 they are playing out in real time, with a million-dollar prize and the reputation of a leading AI lab on the line.<\/p>\n","protected":false},"excerpt":{"rendered":"

In a dramatic escalation of tensions between the world\u2019s 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 […]<\/p>\n","protected":false},"author":7,"featured_media":83134,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/cards.overcentral.com\/cards\/en\/80337.png","fifu_image_alt":"OpenAI Researcher Pressures Mathematician to Remove Anthropic Co-Author","footnotes":""},"categories":[31],"tags":[],"class_list":["post-80337","post","type-post","status-publish","format-standard","has-post-thumbnail","category-technology"],"fifu_image_url":"https:\/\/cards.overcentral.com\/cards\/en\/80337.png","fifu_image_alt":"OpenAI Researcher Pressures Mathematician to Remove Anthropic Co-Author","_links":{"self":[{"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/posts\/80337","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/comments?post=80337"}],"version-history":[{"count":0,"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/posts\/80337\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/media\/83134"}],"wp:attachment":[{"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/media?parent=80337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/categories?post=80337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/overcentral.com\/en\/wp-json\/wp\/v2\/tags?post=80337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}