AI Firm Announces Landmark Proof of Fluid Equations, But Accusations Swirl
OpenAI has announced that its internal model proved the Navier-Stokes equations can 'blow up' in rare cases, a result that would solve one of the Millennium Problems. The claim follows allegations from mathematician Tristan Buckmaster that OpenAI used his and a colleague's method without credit, which OpenAI denies. The proof has been verified using the Lean programming language.
The proof demonstrates that the Navier-Stokes equations, which model fluid flow, can produce infinite velocities under rare conditions. This result was formally verified using the Lean programming language, offering near-certain mathematical certainty. It represents only the second solution to a Millennium Problem in history.
The controversy centers on the "forcing" method, originally created by Diego Córdoba and Luis Martínez-Zoroa. Mathematician Tristan Buckmaster claims OpenAI adopted his and Levent Alpöge's recent Euler-equation breakthrough after learning of it. OpenAI's Sebastien Bubeck insists their model independently solved the Euler problem differently, though the Navier-Stokes proof uses a similar approach.
This development could reshape the relationship between academia and private AI firms. Mathematicians may face increased pressure to publish quickly to avoid being scooped by automated systems. The verified proof could accelerate research in fluid dynamics, potentially impacting engineering and climate modeling. However, the dispute over credit may erode trust in AI-driven discoveries, prompting calls for clearer provenance standards and collaborative frameworks between human researchers and corporate labs.