Primary source AIArticle·11 October 2026·5 min read

OpenAI Claims to Have Solved Navier–Stokes With 10,000 AI Agents

An internal model more powerful than GPT-6 Astra reportedly demonstrated in 88 hours that fluid equations can "blow up": an announcement as dizzying as the race that triggered it.

ShareWhatsApp X LinkedIn Facebook

Save to my selection

OpenAI Claims to Have Solved Navier–Stokes With 10,000 AI Agents

Source : OpenAI · OpenAIView original ↗

In brief

OpenAI has published a proof, generated by an internal system of agents, establishing that a 3D incompressible fluid, initially at rest and subjected to a smooth force, can develop a finite-time singularity. This would resolve, in the negative, one of the Clay Institute's seven Millennium Prize Problems, backed by a Lean formalization. The company is not claiming the prize and presents the result as a signal about the speed of AI progress.

🍺 Bar-stool version

For 90 years, mathematicians have wondered whether water could, in theory, start spinning infinitely fast. OpenAI unleashed 10,000 AIs on the question over a long weekend, and the answer is yes: a vortex that stretches like spaghetti until it breaks the equations. The best part is that the whole thing started from a rumor that Anthropic had gotten there first, which technically makes the greatest math breakthrough of the century a story about neighborly jealousy. If confirmed, the question is no longer whether AI can do math, but how much time mathematicians have left to peer-review it.

Key takeaways

1
OpenAI claims to have proven that a 3D incompressible fluid, starting at rest with a smooth external force and finite energy, can see its velocity diverge in finite time, establishing statements "C" and "D" of the Clay Institute's official formulation.
2
The solution takes the form of a vortex that spirals inward and stretches "like spaghetti," with the central region shrinking and accelerating while keeping finite energy.
3
The proof comes from an internal model that has been training since August 28, described as "significantly more capable than GPT-6 Astra."
4
The group that found the solution involved roughly 10,000 simultaneous agents; the solution arrived on September 5, about 88 hours after launch, followed by 17 hours of Lean formalization via GPT-6 Astra.
5
Along the way, the system solved the blow-up problem for the unforced Euler equations with nearly 100 agents in about 50 hours, which redirected the effort toward Navier–Stokes.
6
The operation was launched after a rumor linked to Levent Alpöge (Anthropic) and Tristan Buckmaster (NYU), who had actually solved the forced Euler problem; OpenAI credits them with priority on that result.
7
Total cost: 4.9 million messages and about 300 billion output tokens, including 2.7 million messages and 130 billion tokens for Navier–Stokes alone.

A 90-Year-Old Problem

The Navier–Stokes equations apply Newton's second law to fluids, treated as a continuous medium rather than a collection of molecules. They are used to design airplanes, forecast weather, or study blood flow.

The open question: can a 3D incompressible fluid, starting from perfectly smooth motion, develop a "singularity," meaning velocities that grow without bound in finite time, despite viscosity's tendency to smooth everything out?

Jean Leray showed in 1934 the existence of solutions in a generalized sense, without being able to guarantee that they remain smooth. In 2000, the Clay Mathematics Institute made it one of its seven Millennium Prize Problems.

The Result: Yes, the Equations Can Break

According to OpenAI, its system produced an analytical proof and a Lean formalization showing that a fluid initially at rest, subjected to a smooth force and maintaining finite energy, can form a finite-time singularity. This is therefore a disproof of global regularity, corresponding to the Clay's statements "C" and "D."

The construction relies on a vortex that spirals inward while elongating. The whole difficulty is that the blow-up must arise from the fluid's own dynamics, not from an infinite force injected by hand.

Concretely, acceleration, pressure gradients, momentum transfer, and viscosity must all become enormous while precisely canceling each other out, so that the external force stays smooth while the velocity diverges.

The Method: An Army of Agents and a Weekend

On September 1, rumors circulated about two Millennium Prize Problems being solved. OpenAI then launched its new internal model on all the still-open Millennium Problems, plus a few other high-impact problems.

The setup: coordinated groups of agents, with access to a cached version of the internet and code execution, each group receiving a different variant of the statement (proof via "A" and "B," disproof via "C" and "D").

A surprise came from a problem considered "easier": the blow-up for Euler without viscosity or forcing, solved by nearly 100 agents in about 50 hours. OpenAI then redirected resources to Navier–Stokes, fed the agents this result, updated the model along the way, and used Codex to cross-pollinate the best ideas between groups.

The solution landed on Saturday, September 5, about 88 hours after launch. Lean verification took an additional 17 hours with GPT-6 Astra.

The Race With Anthropic

The initial rumor concerned Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, an NYU professor. Believing they also held a Navier–Stokes solution, OpenAI contacted them on September 6 to propose a joint announcement.

It turned out they had solved, using an internal Anthropic model, the forced Euler problem. OpenAI acknowledges their priority on that result and notes that its own Euler proof, without forcing, is different.

Notably, OpenAI says it investigated and confirmed that Buckmaster's Codex prompts over the previous two months could not have influenced its system in any way, including through training, and that no user data was consulted.

The Message Behind the Announcement

OpenAI states it does not intend to claim the Millennium Prize. The stated goal is to inform the world about the pace of AI progress and what to expect from upcoming models.

The company speaks of a "new period" of AI progress and says it wants to understand this model before going further, even if that means making more deliberate choices about the pace of advancement.

“The solution is a vortex, a spinning swirl of fluid, that spirals inward and gets increasingly elongated, like spaghetti.”

“We do not intend to claim the Millennium Prize for this result.”

“This is not a culmination, but rather a snapshot in time, of progress on AI development.”

Why it matters

If the proof holds, it's a historic shift: for the first time, an AI system would have settled a Millennium Prize Problem, and in days rather than decades. The Lean formalization is the strongest part of the case, since it makes verification mechanical, but it doesn't exempt the community from checking that the formalized statement exactly matches the Clay's formulation; that's where the result's credibility will be decided. The narrative itself is telling: a race launched over a rumor about a competitor, colossal resources (300 billion tokens, 10,000 simultaneous agents) mobilized in a single weekend, and a defensive paragraph about a rival researcher's Codex prompts that alone raises questions about the boundary between customer data and R&D. Finally, the cautious tone of the conclusion about the "pace" of progress sounds as much like a warning as a show of strength: a model still in training doing this is at least as worrying as it is impressive.

#openai #mathematics #agents #lean #anthropic #research

Original source

On the Navier–Stokes Millennium Prize Problem

OpenAI

Open the article ↗

For you

Put it to work on your sources.

Free: a month of articles and three sources of your own. Pro: the whole archive and your sources, from €8/month.

Create my account →

For your team

The same machine, on your topics.

A space in your colours, your watch angles, your curators. Pilot open to three companies.

Request pilot access →