OpenAI Announces AI-Generated Solution to Navier-Stokes Millennium Problem

OpenAI announced that its latest AI model solved the Navier-Stokes problem, one of the seven Clay Mathematics Institute Millennium Prize Problems that carry a $1 million reward. The company deployed roughly 10,000 autonomous AI agents on the task, with an estimated development cost of $15 million. The solution builds on prior work by mathematicians Diego Córdoba and Luis Martinez-Zoroa of Madrid. OpenAI later denied allegations that its model had learned from the unpublished research of Prof Tristan Buckmaster (New York University) and Levent Alpöge (Anthropic), who had been using OpenAI tools for related investigations.

The Guardian

Mathematicians expressed a mix of shock and concern. Prof James Robinson of the University of Warwick called the development “irreversible” and suggested it could diminish the creative fuel that drives mathematics.

The Guardian

The rapid proof generation raises questions about verification. Traditional peer review, which once uncovered gaps such as the 1993 flaw in Andrew Wiles’s proof of Fermat’s Last Theorem, may now need to contend with AI-produced proofs that require extensive auditing. Professors noted that undergraduate coursework could become “dead” if assignments cannot be authenticated, and lecturers are grappling with policies that restrict AI use for some problems while encouraging it for others.

The Guardian

OpenAI’s spokesperson reiterated that the Navier-Stokes solution was derived independently of any external unpublished work and denied claims of data leakage from Buckmaster’s or Alpöge’s projects. The university representatives for Buckmaster and Alpöge have not issued public comments beyond acknowledging their prior use of OpenAI tools.

The Guardian

• “We’re all just waiting to see what happens. It’s coming so fast.” — Prof David Silvester, a mathematician at the University of Manchester

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• “This is irreversible. This is not going to change.” — Prof James Robinson, a mathematician at the University of Warwick

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• “Without that, the subject seems completely different to me,” — Prof David Silvester, a mathematician at the University of Manchester

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• “There’s a real sense of ‘I could spend the next month thinking about something and somebody else does it by pushing a button’,” — Prof Colva Roney-Dougal, the head of pure mathematics at the University of St Andrews

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• “There’s no point in doing it because we can’t vouch for its authenticity,” — Silvester. Lecturers

The Guardian