OpenAI claims Navier-Stokes solution with 10,000 AI agents as mathematicians raise plagiarism concerns

The Navier-Stokes proof

OpenAI published a 166-page preprint claiming a solution to a specific formulation of the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems established by the Clay Mathematics Institute. The three-dimensional equations govern fluid mechanics, describing phenomena ranging from oceanic currents and airflow around aircraft to turbulent motion. The paper proposes a construction where an initially regular fluid starting from rest develops a singularity in finite time, causing velocity to become unbounded. The mechanism relies on a rotating vortex that stretches and compresses simultaneously, narrowing its core and concentrating kinetic movement into an increasingly small spatial region. To sustain this singularity without exceeding total energy bounds, the researchers introduced an external force that remains smooth and localized in both space and time. The mathematical community must formally inspect and verify the entire proof before determining whether it resolves the century-old question.

Rivalry and attribution dispute

The publication has intensified an existing rivalry between OpenAI and Anthropic, an artificial intelligence company founded in 2021 by former OpenAI executives. During August 2026, New York University mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge achieved substantial progress on the equations, building upon prior mathematical foundations established by Diego Córdoba and Luis Martínez-Zoroa. After rumors circulated that Anthropic was nearing a breakthrough on a Millennium Prize Problem, OpenAI directed its own resources toward the 1 million dollar prize problem. Buckmaster reported receiving hostile inquiries and warnings about his career from OpenAI, including a suggestion from OpenAI researcher Sébastien Bubeck to exclude Alpöge from the research credit because of his Anthropic affiliation.

“When it's two of the biggest companies in the world, they need to get over it. I'm just a bystander in these petty games.”

Compute deployment and data disputes

OpenAI initiated its computational push on 1 September 2026 using an unreleased artificial intelligence model. The company orchestrated 10,000 automated agents operating concurrently for 88 hours, processing 300 billion output tokens at an estimated computational cost of 22.5 million dollars. OpenAI announced the resulting 166-page proof on Tuesday, finishing the derivation in under a week. The rapid release triggered disputes across social media regarding whether OpenAI had improperly ingested Buckmaster's recent mathematical work. OpenAI stated to The New York Times that its AI system was categorically uninfluenced by Buckmaster's activities over the prior two months, although company representatives acknowledged to Xataka that they could not entirely dismiss possible data intake resulting from Buckmaster's use of the OpenAI Codex tool.

“I love math, and I just wanted to be part of history.”

Backlash from Fields medalists

The release provoked coordinated criticism from prominent figures in global mathematics. A group of Fields Medal laureates (15 according to eldiario.es, 25 according to Xataka) issued an open manifesto titled "A severe misalignment of AI in mathematics". The document asserts that commercial technology companies treat fundamental mathematics as competitive benchmarks rather than scientific inquiry, creating broad risks for intellectual disciplines. The signatories emphasized that rushed publications fail to provide adequate write-ups, obscure the development of new mathematical techniques, and neglect proper attribution of preceding academic work, generating acute concerns about plagiarism and academic credit.