AI copyright

OpenAI’s claim that an AI system solved the Navier-Stokes equations, one of mathematics’ seven Millennium Prize Problems, has drawn immediate pushback from an NYU professor who says his unpublished work may have been used without credit. The dispute underscores emerging tensions over attribution and intellectual property as AI systems train on researcher data and approach solutions to fundamental problems.

• OpenAI deployed 10,000 AI agents working together for 88 hours to produce the proof of the Navier-Stokes problem.
• NYU mathematician Tristan Buckmaster says his unpublished work with Anthropic researcher Levent Alpöge was stored in OpenAI’s Codex model.
• OpenAI declined to claim the $1 million Clay Mathematics Institute prize but cannot rule out that researcher product use shaped the model’s training.

• 88 hours Time OpenAI’s agents spent collectively reaching the Navier-Stokes proof
• 17 hours Time GPT-6 Astra spent verifying the proof’s logical validity
• $1 million Prize amount offered by Clay Mathematics Institute for solving the problem
• 10,000 AI agents deployed by OpenAI to work together on the solution

OpenAI announced on September 8, 2026, that an unreleased AI model significantly more capable than its released GPT-6 Astra system had solved the Navier-Stokes problem, one of seven Millennium Prize Problems considered among mathematics’ most difficult unsolved questions. The Navier-Stokes equations describe the behavior of fluid flow in systems such as air and water. OpenAI’s proof suggests that the equations can reach finite-time blowup, a state in which fluid velocities become infinite rather than remaining smooth and continuous.

The Navier-Stokes problem has captivated mathematicians since the 19th century, with applications spanning aerodynamics, weather prediction, and climate modeling. The Clay Mathematics Institute established the Millennium Prize Problems in 2000 to highlight seven of the most important open questions in mathematics and theoretical computer science. A rigorous proof of the Navier-Stokes existence and smoothness conjecture has remained beyond the reach of the mathematical community for over a century, making OpenAI’s announcement potentially historic.

OpenAI’s Proof And The Model Behind It

The company said that 10,000 AI agents worked in concert for 88 hours to produce the proof using the unreleased model. Following the agents’ work, GPT-6 Astra spent an additional 17 hours verifying the logical structure and validity of the proof. OpenAI stated it would not claim the $1 million prize offered by the Clay Mathematics Institute for solving any of the seven Millennium Prize Problems.

The proof emerged from an AI system OpenAI described as substantially more advanced than GPT-6 Astra, its most capable publicly available model to date. The use of multiple AI agents working in parallel represents an emerging strategy in AI research, where distributed reasoning across many instances can explore solution spaces more comprehensively than single models. The 88-hour computation window reflects the intensive computational resources required for cutting-edge mathematical research.

OpenAI’s decision to forgo the prize money raises questions about the company’s motivations and internal policy regarding major scientific breakthroughs. The refusal suggests either uncertainty about the proof’s final acceptance by the mathematics community or internal principles prioritizing caution in claiming credit for such significant results.

Buckmaster’s Challenge To OpenAI’s Attribution

Tristan Buckmaster, a mathematician at New York University, disputes OpenAI’s sole claim to the breakthrough. Buckmaster says that he and Levent Alpöge, a mathematician at Anthropic, had developed work closely related to the Navier-Stokes solution. The two researchers’ unpublished findings were stored within OpenAI’s Codex, a coding-focused AI model, potentially exposing their intellectual work to OpenAI’s research team.

Buckmaster’s concerns highlight a growing friction point in the AI research ecosystem. Researchers frequently use commercial AI tools for preliminary work, collaboration, and problem-solving, often before publication. This practice creates potential pathways for unpublished research to influence the training data of those same AI systems, particularly if researchers share code, mathematical derivations, or conceptual frameworks through platform interactions.

I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything.

Tristan Buckmaster, NYU mathematician

Sebastien Bubeck, an OpenAI researcher, responded at a press briefing and denied that the company had accessed or used Buckmaster and Alpöge’s unpublished work. However, OpenAI also made a notable concession: the company acknowledged that it cannot rule out the possibility that the researchers’ product use of its systems shaped the model’s training data.

This admission reflects the opacity inherent in modern large language model training. Most AI companies incorporate data from multiple sources, including user interactions, public repositories, and licensed datasets. Once training occurs, isolating the influence of any single contribution becomes nearly impossible without extensive analysis and documentation.

Intellectual Property Questions Amid Company Valuations

The attribution dispute arrives as OpenAI prepares for a reported $1 trillion public listing, while Anthropic is pursuing an even larger valuation through its own initial public offering push. Both companies are moving toward major capital events while managing competing claims over the origins of their breakthrough research results.

The timing raises questions about how such disputes might affect investor confidence or regulatory scrutiny of AI companies. Unresolved intellectual property claims could complicate the financial disclosure process required for public companies. Additionally, as AI systems tackle increasingly sophisticated scientific and mathematical problems, establishing clear attribution standards becomes more pressing.

OpenAI has not provided detailed documentation of how the researchers’ prior work might have entered its training pipeline, and the company has not specified what additional measures it will take to clarify the attribution of the Navier-Stokes proof going forward. Industry observers suggest that clearer data provenance tracking and researcher notification protocols may become necessary as AI systems continue advancing toward domain-specific breakthroughs.