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OpenAI releases 166‑page Navier‑Stokes proof draft

1 reports1 sources10/17/2026 updated

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OpenAI announced a 166‑page draft of a Navier‑Stokes proof written in the Lean formal language, claiming to follow the approach of Spanish mathematicians Diego Córdoba and Luis Martínez‑Zoroa. The draft is presented as a potential solution to one of mathematics’ most famous unsolved problems, but it has not yet undergone peer review. Mathematicians have expressed doubts that OpenAI fully grasps the proof, suggesting that the draft may contain logical gaps or omit essential steps. This critique indicates that, while the draft has been released, its conclusions are not yet accepted by the academic community. OpenAI has not announced any plans to further validate or revise the proof, and scholars continue to assess its feasibility and completeness.

Written with AI from the reporting · updated 10/17/2026

Latest developmentOct 17, 17:00
OpenAI claims proof for Navier-Stokes equation, mathematicians disagree on approach
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  1. 1Unclassified fact stationOct 17, 17:26single sourcereport-time onlyrevised

    OpenAI presented potential Navier-Stokes proof

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    Subject：
    openai
    Action：
    presented
    Object：
    166-page potential solution to the Navier-Stokes problem
    Occurred (fact side)：
    not recorded
    The Decoder ↗Report pageRevision 2 · currently revised
    Published (valid side)：
    Oct 17, 17:00
    First seen (known side)：
    Oct 17, 17:26
    Fact stationSingle source · one-sided claimRevisedReport-time only

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Oct 17
  1. The DecoderRelated fact: single sourceFact occurrence time unverifiedSource report revised
    OpenAI claims proof for Navier-Stokes equation, mathematicians disagree on approach

    Report first recorded Oct 17, 17:26

    OpenAI presented a 166-page potential solution to the Navier-Stokes equation in early September, claiming it follows the approach of Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa. However, several expert groups, including mathematician Gonzalo Cao-Labora of EPFL, state the similarities are only surface-level and the approach is fundamentally different. The proof, written in the formal language Lean, has been under review by the Clay Mathematics Institute. Disputes arose when NYU mathematician Tristan Buckmaster accused OpenAI of building on his and Levent Alpöge's prior work, which OpenAI denied. Furthermore, OpenAI researcher Noam Brown revealed that the project deployed roughly 10,000 model instances for 88 hours using 130 billion tokens, but admits less than 10 percent of the success is attributable to the multi-agent setup, stating the base model itself is what matters.

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