Science1 publisher3 min readPublished
OpenAI's 10,000 agents propose a Navier-Stokes blowup that needs an external force
OpenAI says about 10,000 AI agents produced a proposed finite-time singularity for the forced 3D Navier-Stokes equations in 88 hours. The construction fits one route the Clay rules allow and leaves unforced smoothness open, while the mathematicians whose forced-Euler work came first ask whether their Codex drafts reached the model.
The Scientist · Science desk
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What happened
- OpenAI says rumors on September 1, 2026 that two Millennium problems had been solved, later tied to that pair, prompted it to test its new model on the open problems.
- Nearly 100 agents first spent about 50 hours on an Euler-related problem, and that result persuaded OpenAI to concentrate its agents on Navier-Stokes.
- After the proposed solution arrived, OpenAI spent another 17 hours formalizing and verifying it in the Lean proof assistant.
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Why it matters
- constraint A correct proof would answer the Clay question by the forced-breakdown route, so anyone citing it as settling whether unforced flows stay smooth is claiming more than it shows.
- exposure Researchers who put unpublished drafts into a commercial coding assistant now have a test case for whether that vendor's next model can draw on their work.
- precedent How credit is divided between the model, OpenAI's steering and the adjacent human Euler work will set the standard for judging the next claimed AI proof.
- capability Other labs now have a working template for pointing thousands of coordinated agents at an open problem, pooling partial results and checking the output in Lean within days.
The external force is where precision matters. A finite-time singularity built with a smooth forcing term is one of the routes the Clay Mathematics Institute's formulation permits [2]. A correct proof would therefore answer the prize question under the prize's own rules. It would leave open the question most people mean when they cite Navier-Stokes: whether the unforced equations always stay smooth [2]. OpenAI's own word for the result is a proposed solution [1].
The scale figures come from OpenAI's report: on the order of 10,000 concurrent agents, 2.7 million messages and roughly 130 billion output tokens [3]. Spread evenly, that is about 13 million output tokens and 270 messages per agent [2][3]. From launch to the finished Lean check took about 105 hours: 88 to reach the proposed solution and 17 more to formalize and verify it [1]. All of these are inference numbers. KDnuggets' account of the report does not include a dollar cost, and training the new internal model [9] is a separate bill.
As an experiment, the design is a good one. Agents worked in groups that could communicate internally, run code and read a cached copy of the internet [14]. Codex pooled promising intermediate results from different groups and fed them into later prompts, a step OpenAI calls cross-pollination [13]. People steered it, too. Nearly 100 agents worked for about 50 hours on an Euler-related problem before OpenAI judged the result promising [11]. The company then moved agents off the other Millennium problems and onto Navier-Stokes [12], roughly a hundredfold scale-up [4]. The thing these figures don't tell you is how much of the final proof came from the model and how much from the loop that pooled its output.
The choice of problem also started with people. According to OpenAI, it heard rumors on September 1, 2026 that two Millennium problems had been solved. Those rumors, together with strong results from its new model, prompted it to test the system on the remaining open problems [9]. OpenAI later realized the rumors were connected to Tristan Buckmaster of NYU and Levent Alpöge, who works at Anthropic [10][6]. The pair had already built finite-time blowup for the three-dimensional incompressible Euler equations with smooth forcing. They used Claude and Codex, and they verified the work in Lean [7][8]. Their result did not solve Navier-Stokes [7].
Buckmaster then asked the question that decides the credit. According to him, he and Alpöge had put drafts from their project into Codex [15]. He asked OpenAI whether its new model had been trained on, or had access to, those sessions [16].
In my view, the evidence today supports a claim about a pipeline: a newly trained model, thousands of copies of it, a step that pooled their results, and a company that picked the target after hearing about human work and narrowed it after an early result [9][12]. Before anyone calls this an independent AI discovery, Buckmaster's question about his Codex sessions needs an answer [16].
What to watch
- OpenAI's answer to Buckmaster on whether its new model was trained on, or could access, the Codex sessions holding his and Alpöge's drafts.
- Checking of the proposed proof and its Lean formal statement by mathematicians outside OpenAI, and any response from the Clay Mathematics Institute.
- Whether OpenAI publishes the compute cost of the roughly 130-billion-token run alongside the training cost of the new model.