Mathematician Alleges OpenAI Pressured Researchers Over Navier-Stokes Breakthrough

Mathematicians Tristan Buckmaster and Levent Alpöge have announced a breakthrough regarding finite-time blowup for 3D incompressible Euler and other equations, sparking a public dispute over AI ethics. Buckmaster has released a statement alleging that OpenAI attempted to pressure the researchers into a coordinated release of similar results.

The researchers achieved their results for incompressible porous media, Boussinesq, and 3D incompressible Euler equations by combining human mathematical direction with Large Language Models (LLMs)—including Claude, Astra, and Codex/GPT-5.6 Sol—and Lean verification. They credit the fundamental idea of their program to Diego Córdoba and Luis Martínez-Zoroa. Following these results, Buckmaster alleges that OpenAI presented two proposals: one suggesting both parties post their results on consecutive days, and another in which Buckmaster would alone author the Navier-Stokes paper while acknowledging that an OpenAI model had solved it.

The Conflict Over Authorship

Beyond the coordination of the release, Buckmaster claims that OpenAI's Sebastien Bubeck suggested that Levent Alpöge be removed from the authorship of the work. According to Buckmaster, this suggestion was made because Alpöge is employed by Anthropic, a direct competitor to OpenAI. This allegation highlights a growing tension between the collaborative nature of academic mathematics and the proprietary interests of the AI labs providing the tools used to reach these conclusions.

A Shift in Mathematical Proof

The Navier-Stokes existence and smoothness problem remains one of the seven Millennium Prize Problems, representing one of the most difficult challenges in physics and mathematics. By using LLMs to push existing "rough forcing" results toward "smooth forcing" and eventually to the incompressible Euler equations, Buckmaster and Alpöge have demonstrated a significant shift in how complex proofs are constructed. This methodology allows researchers to accelerate processes that previously took years into a matter of months, potentially marking a "Deep Blue-Kasparov moment" for the field of mathematics.

Industry Implications

This dispute raises critical questions about the privacy of researcher data and the conduct of AI labs when competing with independent academics. Buckmaster has expressed concern that private Codex sessions may have been used for training, suggesting a potential conflict of interest when AI companies develop models that can solve the very problems researchers are pursuing using those same tools. As Buckmaster noted, the significance of this shift regarding how credit is assigned and how students are trained "cannot be under-stated."

What Remains Unconfirmed

While the researchers' results have been announced, several claims regarding OpenAI's internal capabilities remain unverified. Buckmaster has alleged that an internal OpenAI model produced a 100-page proof of finite-time blowup for forced Navier-Stokes equations, but this proof has not been independently seen or verified. It remains to be seen if OpenAI will formally respond to the allegations regarding the pressure placed on the researchers or the suggestions regarding authorship removal.