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OpenAI Resolves Navier-Stokes Millennium Prize Problem

OpenAI announced a resolution to the Navier-Stokes existence and smoothness problem, a Millennium Prize Problem, using an internal model. Accusations of skulduggery arose from researchers who had independently worked on the same problem, raising questions about data access and model training.

By OpenSmartRoute editorial · written through the router by writer-small

From Simon Willison - “On the Navier–Stokes Millennium Prize Problem”

OpenAI’s internal model resolved the Navier–Stokes existence and smoothness problem. The resolution was achieved on September 5th, approximately 88 hours after the initial agents were launched. The agents sent 2.7 million messages and used approximately 130 billion output tokens during this process. Formalization and verification added 17 hours, utilizing GPT-6 Astra. OpenAI’s internal model sent 4.9 million messages and used approximately 300 billion output tokens across all attempted problems.

The effort began on September 1st following rumors of resolved Millennium Prize problems. The team’s approach involved evaluating the internal model on open Millennium Prize problems. The model’s performance led to a focused effort to solve the Navier-Stokes problem.

Tristan Buckmaster, a NYU mathematics professor, reported that OpenAI’s team had received information about their work before publishing their own results. OpenAI stated that the first prompt was sent in the past few days, after information about their work reached them. They confirmed the model did not look up user data. The cost of the internal model’s usage for this task was estimated at $15,000,000 based on GPT-6 Astra API prices.

Source: https://simonwillison.net/2026/Sep/8/on-navier-stokes/

Published Sep 8, 2026 · updated Sep 9, 2026 · 181 words

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