OpenAI claims AI solved Navier-Stokes Millennium Prize problem

September 9, 2026 at 11:15 AM2 min

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OpenAI announced that its internal AI model solved the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems. The company published a proof description and a Lean formalization. NYU mathematician Tristan Buckmaster accused OpenAI of using his work without credit.

Key Facts

OpenAI says its internal AI model solved the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems.
The company published both a proof description and a formalization in the Lean proof assistant.
About 10,000 AI agents worked simultaneously on the Navier-Stokes problem, with access to cached internet data and code execution.
NYU mathematics professor Tristan Buckmaster accused OpenAI of using his and Levent Alpege's work without credit.
OpenAI denied deliberately accessing user logs but acknowledged anonymous user data may have entered its training set.

The Claimed Proof

OpenAI announced that its internal AI model solved the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems. The company stated it is publishing both a description of the proof and its formalization in the Lean proof assistant. The model used for the Navier-Stokes problem significantly outperforms GPT-6 Astra, according to OpenAI. Around 10,000 AI agents were simultaneously engaged on the problem, with access to cached internet data and code execution. Some agents were given formulations leading to a proof, while others were tasked with finding a counterexample.

Plagiarism Accusation

NYU mathematics professor Tristan Buckmaster accused OpenAI of using his and Levent Alpege's work without credit. Buckmaster said he and Alpege had worked on the problem for a long time, uploading their work to OpenAI's Codex service. He claimed that shortly after rumors of the AI's success, the model reached the same conclusions. Buckmaster said he asked whether the model was trained on their Codex sessions and received no answer. OpenAI denied deliberately accessing user logs but acknowledged that anonymous user data could have entered its training set.