OpenAI announced on September 8, 2026 that an internal model, described as stronger than its Astra model, orchestrated approximately 10,000 agents to produce a proposed finite-time singularity proof for the Navier-Stokes equations in 88 hours, accompanied by Lean verification code. The run consumed 2.7 million agent messages and approximately 130 billion output tokens; at retail API prices the compute cost roughly $22 million, with internal marginal costs estimated at several million dollars. OpenAI stated it would not claim the $1 million Clay Mathematics Institute prize. The Clay Mathematics Institute still lists the problem as unsolved and requires a two-year review window before accepting any solution.
The announcement generated a credit dispute. Tristan Buckmaster (NYU) and Levent Alpöge (Anthropic) had achieved a Lean-verified proof for the 3D Euler equations by August 22, forcing early publication without time to produce readable proofs. Buckmaster alleged that during September 6 calls, OpenAI's Sébastien Bubeck twice pressed to have Alpöge removed from authorship, citing his employment at Anthropic. Buckmaster also said he was warned "Why would you ruin your career?" Bubeck called the account "false and inflammatory" and Noam Brown denied wrongdoing. OpenAI acknowledged it "cannot rule out that de-identified data derived from their usage of our products helped improve our models." Quanta Magazine reported that OpenAI concedes priority for the 3D Euler result to Buckmaster and Alpöge but claims priority for the Navier-Stokes result, while noting the details of their interactions remain murky.
The foundational program underlying this work was originated by Diego Córdoba and Luis Martínez-Zoroa; Buckmaster stated he believes Martínez-Zoroa deserves a Fields Medal for originating it.
On September 21, OpenAI announced an independent advisory group of mathematicians to guide how it shares AI advances in mathematics. The group can offer unsolicited advice, make recommendations public, and change its own membership; members will not be paid by OpenAI. The group will not advise on the pace of OpenAI's internal mathematical progress. The formation followed backlash from mathematicians after the Navier-Stokes announcement, including a joint declaration signed by twenty-five Fields Medal winners arguing that "the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics" and that announcements are made "in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others."
Separately, OpenAI's Astra model resolved ten open mathematical problems in August 2026, releasing a 249-page manuscript and Lean 4 proof certificates with a 'sorry' count of zero. Those results included an explicit construction of a non-sofic group, disproving Connes's rigidity conjecture on von Neumann algebras, proving Ehrhart's volume conjecture, and resolving problems from Paul Erdős's catalog. OpenAI's subsequent Astra-2 model has reportedly resolved more than 100 long-standing open problems across most areas of mathematics, with rumors of major progress on additional Millennium Prize problems; OpenAI is coordinating disclosure through the advisory committee.