OpenAI, Navier-Stokes, and the problem that goes beyond mathematics

On September 8, 2026, OpenAI published something far more serious than another benchmark with colored bars: it claimed to have a solution to the existence and smoothness problem of Navier-Stokes, one of the Millennium Problems.

This is one of those stories where "an AI solved a math problem" falls way too short.

The company put roughly 10,000 simultaneous agents to work for about 88 hours. In the process related to Navier-Stokes, they exchanged 2.7 million messages and produced approximately 130 billion output tokens. They then did additional formalization and verification with Lean using GPT-6 Astra.

And even with all that, I would still avoid saying that Navier-Stokes "is now officially solved."

What problem OpenAI tried to solve

The Navier-Stokes equations are used to describe the motion of fluids.

Water flowing through a pipe, air around an airplane, atmospheric currents, or even the behavior of blood are all related to them.

The equations work. The mathematical problem is deeper.

For decades, people have been trying to prove whether, starting from certain perfectly normal conditions in three dimensions, their solutions always remain sufficiently regular or can reach a point where some quantity blows up and the model stops behaving smoothly.

The latter is called a singularity.

OpenAI claims to have proven precisely that this singularity can appear in finite time.

Its official publication on Navier-Stokes includes both an explanation of the proof and a formalized version using Lean.

10,000 agents are not 10,000 open ChatGPTs

Here's another interesting part.

OpenAI didn't put one enormous question into a chat hoping a 160-page answer would come out.

It used groups of coordinated agents that tested different paths. Some could consult a stored copy of the Internet, run tools, and share results with each other.

Then the useful findings from different groups were cross-referenced to continue exploring the most promising routes.

The scale gives an idea of where this is heading:

To me, this matters more than the name of the model.

We're moving from asking an AI for answers to giving it a problem, the ability to explore, tools, coordination, and enough resources to pursue it for days.

That looks a lot more like assembling a research team than using a chatbot.

The result still needs to pass a human test

This is where it's worth slowing down the headline a bit.

The Clay Mathematics Institute maintains specific rules for recognizing the solution to any of its Millennium Problems.

A proposal must be published in a medium that meets its requirements, at least two years must pass since publication, and it must also gain general acceptance within the mathematical community.

The official rules of the Clay Mathematics Institute are quite clear on that point.

Lean helps enormously because it allows formal verification of parts of a proof. But a computer-formalized proof and the official recognition of a Millennium Problem are different processes.

So the correct phrasing for now is: OpenAI claims to have found a solution.

That would already be gigantic if it survives scrutiny from specialists.

And then the authorship problem showed up

The story gets quite a bit more uncomfortable when the work of other mathematicians comes into play.

Diego Córdoba and Luis Martínez-Zoroa had been developing since 2023 a strategy based on a vorticity cascade: structures at increasingly smaller scales that amplify the behavior of the next ones until they produce a singularity.

Later Tristan Buckmaster and Levent Alpöge continued working on a related direction and made important progress.

According to Buckmaster, during the project they used AI tools intensively, including Codex, and introduced drafts of their unpublished research there.

Later OpenAI heard rumors about that progress.

The company itself acknowledges that its operation to attack the Millennium Problems began on September 1, after hearing those rumors.

Four days later, its agents had arrived at the solution to Navier-Stokes.

It's a coincidence that was inevitably going to raise questions.

OpenAI denies having read their work, but there's an important phrase

OpenAI's public stance is quite specific.

The company states that neither its researchers nor the agents accessed Buckmaster and Alpöge's work before it was published, and that no specific information from those users was used to solve the problem.

So far everything seems quite clear.

But a much more interesting nuance immediately emerges: OpenAI says that, although it considers it unlikely, it cannot rule out that de-identified data derived from the use of its products may have previously helped improve its models.

That nuance is huge.

It doesn't prove that OpenAI took these mathematicians' research. Buckmaster doesn't claim to have proof that it happened either.

But the mere impossibility of ruling it out raises a question that goes far beyond Navier-Stokes.

What does it mean to work with unpublished information inside an AI?

Let's think about software development.

You're designing a new architecture for a client. You paste documentation, technical decisions, fragments of a still-confidential specification, and several of your own ideas into an AI tool because you need help analyzing them.

Six months later, something similar shows up in another context.

How would you prove a connection exists?

You probably couldn't.

In mathematics the problem becomes even more delicate because a correct idea can represent years of professional career, academic publications, and international recognition.

That's why I think the OpenAI case is going to accelerate a conversation we already needed to have.

Before using any AI service with truly important information, we should know, at the very least:

• whether our conversations can be used to improve models;
• what controls can prevent it;
• how long they're stored;
• who can access them;
• what happens with derived or de-identified data;
• and what guarantees exist when we're talking about intellectual property that hasn't been published yet.

It doesn't mean stopping using AI.

It means treating it like we treat any other external service we hand sensitive information to.

We also need to share credit better

There's another easy mistake to make: telling this story as "AI versus mathematicians."

That's not how it happened.

Behind the mathematical route there are years of human work. Córdoba and Martínez-Zoroa developed fundamental ideas. Buckmaster and Alpöge built on them using AI tools as well. OpenAI then brought enormous computational capacity to bear on the problem.

The interesting question stops being who won.

It's how much science changes when a good human idea can be explored simultaneously by thousands of artificial agents.

That's where I do see an important shift.

Finding a promising direction can still be extraordinarily difficult. But once it's located, testing thousands of variants, connecting results, and formalizing proofs starts to become a type of work that machines can compress brutally.

A year versus 88 hours sounds spectacular.

Although those 88 hours wouldn't exist in a vacuum.

What I take away

I'm left with four fairly concrete points.

First: if the proof withstands scrutiny from the mathematical community, we're looking at one of the most important scientific results produced with the help of artificial intelligence.

Second: architecture matters as much as the model. Thousands of coordinated agents can change the scale of the problems an AI is capable of tackling.

Third: using commercial tools for unpublished research, proprietary code, or intellectual property requires seriously reviewing their data policies.

Fourth: we'll have to redefine what authorship means when a human idea, an AI tool, and thousands of agents take part in different parts of a discovery.

Conclusion

A few years ago we were debating whether ChatGPT could correctly solve an operation or write code that compiles.

This week we're debating who deserves credit for a possible solution to one of the Millennium Problems.

The distance between those two conversations is enormous.

It still remains to be verified that OpenAI's proof is accepted, and that process won't be quick. But even if a major error appeared in the proof tomorrow, the experiment has already made something quite clear: AI systems are entering frontier scientific research.

And with them come problems that can't be fixed by increasing the number of parameters.

Authorship, privacy, attribution, and trust also have to scale.