In September 2026, a mathematical dispute emerged over advanced work on the Navier-Stokes equations, with a New York University professor accusing OpenAI of attempting to misappropriate research discoveries and exclude a collaborator from Anthropic.
The Million-Dollar Mathematical Puzzle and the Navier-Stokes Stakes
The mathematical community is reckoning with a high-stakes controversy surrounding the Navier-Stokes equations, one of the famous Millennium Prize problems defined by the Clay Mathematics Institute in 2000. Each of the seven problems carries a reward of one million dollars (approximately 860,000 €), with only one—the Poincaré conjecture, demonstrated by the Russian Grigori Perelman, who had refused both the prize and the Fields Medal—resolved to date. The Navier-Stokes equations, which describe the macroscopic movement of a fluid at the level of a liquid or gas and its turbulence (such as air flowing around a car or an airplane wing, water displaced when a ship passes, a submarine sliding through the abyss, or ocean dynamics), continue to resist a general solution for the smooth case.
Public dispute erupted on September 8, 2026, when Tristan Buckmaster, a professor at the Courant Institute of Mathematical Sciences at New York University, announced via Mastodon that he and Levent Alpöge—a mathematician working for Anthropic, OpenAI’s grand rival—had obtained three important mathematical results. According to the announcement, these findings address finite-time blowup with smooth forcing for incompressible porous media, for Boussinesq, and for 3D incompressible Euler.
Terence Tao and the Path Toward Unlocking Fluid Dynamics
The published demonstrations immediately drew attention from prominent figures in the discipline, including Fields Medalist Terence Tao (2006). Writing on Mastodon, Tao characterized the work as an accomplissement remarquable,
because Alpöge and Buckmaster managed to advance one of the leading promising approaches for constructing blowup solutions to the equations of fluid mechanics.
Building on prior advancements, Tao noted that the methods developed by Buckmaster and Alpöge could potentially extend to the full Navier-Stokes problem. While the researchers did not formally solve the million-dollar challenge, their contributions on these related equations represent a major step forward.
OpenAI Accusations and Corporate Rivalry
The mathematical breakthrough quickly became entangled in corporate friction. Buckmaster accused OpenAI of attempting to rafler la découverte and sideline a mathematician working at Anthropic, turning the resolution of a millennium prize problem into a math drama.
The Deep Roots of Theoretical Computing Challenges
The intersection of calculation and fundamental theory stretches back decades. Another foundational enigma in theoretical computer science, the P = NP problem (the fundamental problem of mathematical calculation concerning whether what we can find quickly when we have a chance can be found just as fast by intelligent calculation, or if intelligence can replace luck), shares the Clay Mathematics Institute list from the year 2000. Historical correspondence underscores the deep roots of these computational limits.
Kurt Gödel, an Austrian mathematician, in a recently rediscovered letter sent to John von Neumann in 1956 a few months before von Neumann died, was the first to clearly formulate the question while insisting on its practical importance in mathematics. He explained there that if P = NP (without using that notation, which was introduced in 1972):
If P equals NP, well many mathematical questions will become easy by the procedure detailed in what follows. To solve an open question Q, one will search among all demonstrations of length n in a given system of writing demonstrations if there is one bringing the answer.— Kurt Gödel, in a letter to John von Neumann in 1956
As researchers continue to push the boundaries of what automated reasoning and human collaboration can achieve on millennium problems, the exact resolution of Navier-Stokes and the final attribution of these breakthrough methodologies remain central focuses for both the mathematical community and the technology sector.
