OpenAI and Anthropic AI systems solve Navier-Stokes and Yang-Mills problems

In September 2026, two major scientific problems fell to AI systems within weeks of each other. On September 8, OpenAI announced a proof of the Navier-Stokes existence and smoothness problem, one of the seven Clay Millennium Prize Problems, using roughly 10,000 agents running for 88 hours and exchanging approximately 2.7 million messages. The proof claims a finite-time blowup in the 3D incompressible equations, formally verified using the Lean theorem prover. OpenAI is not seeking the Millennium Prize, meaning the Clay Institute's formal two-year review process has not started, and the Institute has not issued a statement accepting or rejecting the result. Independent mathematicians and Lean specialists will spend weeks to months verifying the proof. A priority dispute emerged with researchers who had related results on the Euler equations.

On September 25, Anthropic published a guest post reporting that its physicists Liam Fitzpatrick and Siddharth Mishra-Sharma used Claude to compute the six-particle scattering amplitude in planar N=4 super Yang-Mills theory at nine loops, surpassing the previous eight-loop record set by Lance Dixon at SLAC in 2023. The computation answered a public challenge posted August 7 by physicist and science writer Matt von Hippel. Dixon independently validated the result, noting the extreme fragility of the calculation, where minor errors typically cause computational collapse. A separate team led by Song He independently reached the same result using a different model around the same time. The computation followed a recipe developed by the physics community rather than producing novel physical insights.

An advisory group published recommendations stating that when AI companies produce proofs no human initially understands, those companies are responsible for funding and supporting work to make the proofs human-comprehensible, and that publishing only an incomprehensible proof means the company did only part of the work. Separately, a Lawfare analysis argued that existing technologies such as confidential computing can build AI verification infrastructure credible to regulators without requiring disclosure of proprietary information. A regulatory commentary proposed recurring 'proof drill' exercises in which cross-functional teams reconstruct a single recent AI-assisted decision into a bounded evidence packet to test whether governance claims are grounded in retrievable records.