OpenAI Claims Navier-Stokes Proof, Substantial Progress on Another Millennium Problem

According to The New York Times, OpenAI said in a Wednesday evening statement that it has completed a proof of the existence and smoothness problem for the Navier-Stokes equations, and that since finishing it has made substantial progress on another Millennium Prize Problem, "deliberating how to share these results appropriately." This marks the second time in a short period that OpenAI has come close to one of the Clay Mathematics Institute's bounty problems, drawing intense attention from both the mathematics and AI communities.

Confirmed

• In interviews with The New York Times and in its statement, OpenAI said it has completed the Navier-Stokes proof and made substantial progress on another Millennium Problem, but has not disclosed which one.
• The Navier-Stokes work is connected to NYU mathematician Tristan Buckmaster and his collaborators.
• Each of the seven Millennium Problems carries a $1 million prize.

Not Yet Confirmed

• OpenAI has not revealed which other Millennium Problem it has progressed on.
• The Navier-Stokes proof itself has not gone through full public peer review, so its mathematical correctness remains to be confirmed.
• According to reports relayed by @basedjensen, after Buckmaster and collaborators made major progress in August, OpenAI announced the answer in less than a week; outsiders (as @socoolandawesome noted) have raised questions about attribution of the Levent/Buckmaster-related work and academic process, and the specific details of the dispute remain to be verified.

Why It Matters

• The Millennium Prize Problems are among the hardest problems in mathematics; an AI lab claiming to crack them could reshape both mathematical research and how AI capabilities are evaluated. @DrSingularity accordingly predicts at least 3 Millennium Problems may be solved in succession.
• If the practice of preempting collaborators' results is confirmed, it will spark debate over academic credit allocation and the conduct norms of AI labs.

2026-09-10 ~ 2026-09-11 · 6 related posts

Full story(3 episodes)→

• Episode 1: OpenAI's 10,000 Agents Crack the Navier-Stokes Millennium Problem in 88 Hours(2026-09-09, 9 posts)
• Episode 2: Existence Proof Effect: Rumor of Solvability Drove OpenAI's Navier-Stokes Attempt(2026-09-09, 3 posts)
• Episode 3: OpenAI Claims Navier-Stokes Proof, Substantial Progress on Another Millennium Problem(2026-09-10, 6 posts)

• OpenAI claims Navier-Stokes breakthrough, says another Millennium Prize problem near — basedjensen · 2026-09-10
• [source] OpenAI says it has made substantial progress on another Millennium Prize problem — ilkamoi · 2026-09-11
• After Navier-Stokes, researchers report substantial progress on another Millennium Prize problem — soumitrashukla9 · 2026-09-11

3 near-duplicate retellings: socoolandawesome · Dr_Singularity · Dr_Singularity