What Is Navier-Stokes, the ‘Millennium’ Math Problem OpenAI Claims to Have Solved?

OpenAI announced today that it had solved the problem, one of seven “Millennium Problems” seen as among the most important in higher mathematics.

The top 3

  1. The Six Remaining Millennium Problems: Currently, six of the original seven Millennium Prize Problems remain unsolved: the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, and Yang–Mills existence and mass gap.
  2. The Million-Dollar Prize for Each: Each of the seven Millennium Prize Problems carries a $1 million reward from the Clay Mathematics Institute for the first correct and verified solution.
  3. The Sole Solved Millennium Problem: As of 2026, the Poincaré conjecture is the only Millennium Prize Problem to have been officially solved, with Russian mathematician Grigori Perelman providing the proof in 2002-2003, though he declined the $1 million prize in 2010. Grigori Perelman

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