Clay Institute says Navier-Stokes Millennium Prize problem apparently settled

September 14, 2026 at 06:01 PM2 min

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The Clay Mathematics Institute said the Navier-Stokes Millennium Prize Problem has apparently been settled. The solution is now under review, with the institute promising updates. The announcement comes amid a dispute in which mathematician Tristan Buckmaster accuses OpenAI of misusing his research and excluding his co-author Levent Alpöge from authorship.

Key Facts

The Clay Mathematics Institute said the Navier-Stokes Millennium Prize Problem has apparently been settled.
The Navier-Stokes problem is one of seven Millennium Prize Problems announced in Paris in 2000, each worth $1 million.
The solution is now under review, and the institute said it will provide updates.
Mathematician Tristan Buckmaster accuses OpenAI of redirecting resources toward the problem after rumors about his research leaked.
Buckmaster also accuses OpenAI of using his drafts in training data and rejecting his co-author Levent Alpöge, who works at Anthropic, from authorship.

The Millennium Prize Problem

The Clay Mathematics Institute announced the Navier-Stokes problem as one of seven Millennium Prize Problems in Paris in 2000. Each problem carries a $1 million prize. The Navier-Stokes problem asks whether the equations governing fluid motion in three-dimensional space always have a smooth, complete solution. The institute said the problem has apparently been settled.

Review and Anticipation

The solution is now under review by the Clay Mathematics Institute. The institute described the process as deliberately unhurried and said it will provide updates. It also noted that the increasing ability of new technologies to accelerate mathematical research has heightened this sense of anticipation. The institute hopes to see waves of new human understanding unleashed as the innovations behind this work are analyzed and interrogated.

Authorship Dispute

Mathematician Tristan Buckmaster accuses OpenAI of redirecting resources toward the problem after rumors about his research leaked. Buckmaster also accuses OpenAI of using his drafts in training data. He further accuses OpenAI of rejecting his co-author Levent Alpöge, who works at Anthropic, from authorship.