Technology & Science
OpenAI says internal system found Navier–Stokes solution, pending independent review
The company said an internal model coordinated thousands of agents on the proposed solution, while a public dispute over credit and the use of AI in frontier mathematics followed.
Executive summary
- The claim: OpenAI says an internal system produced a proposed solution to the Navier–Stokes existence-and-smoothness problem, one of the Millennium Prize Problems.[1]
- The qualification: The result is OpenAI's claim and has not yet completed independent mathematical review, so it should not be treated as a settled resolution of the prize problem.[1][2]
- The method: OpenAI said the effort used a multi-agent system powered by an unreleased internal model, with roughly 10,000 concurrent agents in the group that produced the proposed resolution.[1]
- The dispute: The announcement prompted a public dispute involving NYU mathematician Tristan Buckmaster over parallel work, research credit and whether product-use data could have informed OpenAI's work; OpenAI disputed that its recent Codex prompts could have influenced the system.[1][2]
OpenAI says an unreleased internal model produced a proposed solution to the Navier–Stokes existence-and-smoothness problem, one of the Clay Mathematics Institute's Millennium Prize Problems. The company released an analytical proof and a Lean formalization, but the claimed result has not yet completed independent mathematical review.[1][2]
The Navier–Stokes equations describe fluid motion and are used in fields including aerodynamics, weather forecasting and blood-flow modeling. The longstanding mathematical question asks whether smooth three-dimensional fluid motion can develop a finite-time singularity. OpenAI says its proposed construction shows such a singularity while retaining finite energy.[1]
OpenAI said the system used an internal model it described as significantly more capable than GPT-6 Astra. It said the agent group that produced the proposed resolution involved on the order of 10,000 concurrent agents, reached a result about 88 hours after the effort began, and was followed by Lean formalization and verification.[1]
The announcement also intensified debate about priority and AI-assisted research. NYU mathematics professor Tristan Buckmaster said he and Anthropic mathematician Levent Alpöge had been working on related questions and raised concerns about OpenAI's parallel effort, according to TechCrunch.[2]
OpenAI said its researchers and agents did not see their work before it became public. In a later update, the company said Buckmaster's Codex prompts from the preceding two months could not have influenced the internal system used for the result; the company said the proofs and the specific Euler results differed.[1]
The claim arrives as the leaders of major frontier labs have called for greater caution around capability advances. OpenAI said it was studying what the result indicates about the pace of AI progress and how to guide future advances, while Anthropic CEO Dario Amodei has argued that capability gains should be paced so evaluation and safety work can keep up.[1][3]