Tuesday 15 September 2026
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OpenAI's Navier-Stokes breakthrough marred by plagiarism accusations

Researcher says OpenAI scraped private Codex session and threatened his career

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By LineZotpaper
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OpenAI has announced that its researchers and AI models have solved a portion of the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. However, the claim has been overshadowed by allegations from mathematician Tristan Buckmaster that OpenAI plagiarised work he had been conducting with Anthropic staff member Levent Alpöge and then issued career threats.

OpenAI has published a solution to the conditions set forth in the Navier-Stokes Millennium Prize problem, a longstanding open question in fluid dynamics worth $1 million. But the announcement has drawn immediate criticism from Tristan Buckmaster, a scientist at New York University, who claims the company may have plagiarised his year-long collaboration with Levent Alpöge.

Buckmaster and Alpöge had been working on proving Euler's equations, a related stepping-stone problem, using AI assistants including Anthropic Claude and OpenAI Codex. According to Buckmaster, the pair obtained blowup results for both Boussinesq and Euler equations on August 15, 2026, and verified the proof using the Lean programming language on August 22. Buckmaster described the AI-generated proof as "AI slop" but confirmed it was mathematically correct.

On September 3, Alpöge heard rumours that Anthropic had solved an important mathematical problem, which Buckmaster suspected referred to their work. Buckmaster then emailed an unnamed prominent mathematician at OpenAI to clarify the collaboration was personal and unrelated to Anthropic. After several days of discussions with OpenAI's Sébastien Bubeck, Buckmaster was told that OpenAI had proven a finite-time blowup for the forced Navier-Stokes equations. Buckmaster alleges that OpenAI scraped his Codex session and issued career threats, though the full details of the alleged threat were not provided in the available sources.

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Analysis

Why This Matters

  • The Navier-Stokes problem is one of seven Millennium Prize Problems; a verified solution would be a landmark achievement in mathematics and fluid dynamics.
  • The plagiarism controversy raises serious questions about research ethics and intellectual property in AI-assisted mathematics, especially when companies like OpenAI have access to user data from their own tools.
  • The outcome could affect how researchers collaborate with AI companies and whether they trust using AI assistants for sensitive work.

Background

The Navier-Stokes equations describe the motion of fluid substances. The Millennium Prize Problem asks whether smooth, globally defined solutions always exist. Buckmaster and Alpöge were working on a related problem, Euler's equations, which is considered a stepping stone. They used AI tools for busywork and logic checks, paying for compute time themselves. OpenAI's claimed solution addresses a subset of the Navier-Stokes problem, but the exact scope remains unclear.

Key Perspectives

Tristan Buckmaster and Levent Alpöge: The researchers claim their personal collaboration was misappropriated by OpenAI. Buckmaster says the company scraped his Codex session and threatened his career. They believe their work, based on prior results by Córdoba and Martínez-Zoroa, should be credited independently. OpenAI: The company has published a solution and apparently believes it is original. Through Sébastien Bubeck, OpenAI offered Buckmaster compute time and discussed the work, but the company's version of events has not been detailed. Critics/Skeptics: The controversy highlights the risk of AI tools being used to monitor or copy user work. Without independent verification, both the mathematical merit and the originality of OpenAI's solution remain in doubt.

What to Watch

  • Whether OpenAI releases a full, verified proof with Lean or another formal verification system.
  • Any formal response from OpenAI addressing the plagiarism allegations, including whether they used Codex session data.
  • The reaction of the mathematics community and the Clay Mathematics Institute regarding validation of the solution.

Sources

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Articles published under the Zotpaper byline are synthesized from multiple source publications by our AI editor and reviewed by our editorial process. Each story combines reporting from credible outlets to give readers a balanced, comprehensive view.

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