OpenAI announced on September 8, 2026 that an internal model, described as significantly more capable than GPT-6 Astra, orchestrated approximately 10,000 AI agents to produce a 166-page claimed proof of finite-time singularity in the 3D incompressible Navier-Stokes equations, verified using the Lean theorem prover. The system consumed 2.7 million agent messages and approximately 130 billion output tokens for the Navier-Stokes work; across all Millennium Prize Problem work the full run reached 4.9 million messages and 300 billion output tokens. At retail API prices the compute would have cost approximately $22 million; internal marginal costs were estimated at several million dollars. OpenAI has said it does not intend to claim the $1 million Clay Mathematics Institute prize. The Clay Mathematics Institute has not accepted the proof and no independent peer review has taken place.
The announcement sits inside an unresolved credit dispute. NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had independently produced a Lean-verified proof of the 3D incompressible Euler equations by August 22, building on a program originated by Diego Córdoba and Luis Martínez-Zoroa. OpenAI concedes priority for the forced 3D Euler result to Buckmaster and Alpöge but claims priority for its unforced Euler and Navier-Stokes proofs. Buckmaster alleges that OpenAI mathematician Sébastien Bubeck twice insisted Alpöge be removed from authorship, citing Alpöge's Anthropic employment, offered him two proposals for how to proceed, and said 'If you don't want me to be nice, then I don't have to be nice' and 'Why would you ruin your career?' Bubeck and OpenAI deny wrongdoing. OpenAI acknowledged it cannot fully rule out that de-identified data from the researchers' product usage influenced its models.
Twenty-five Fields Medal winners, including Terence Tao, published a joint declaration arguing that AI companies' race to solve famous math problems as benchmarks is detrimental to mathematical science, undermines conceptual understanding, and raises attribution and plagiarism concerns. Sam Altman described AI's math progression over three summers as moving from below grade-school proficiency to an IMO gold medal to a Millennium Prize proof.