OpenAI claims its AI system cracked part of a math problem that has stumped experts for 90 years. And it did it in less than four days.

The problem is called the Navier-Stokes existence and smoothness problem. And it deals with fluid motion. 

Scientists use equations to describe that motion. But for decades, nobody could fully prove certain parts of those equations always work.

It’s one of seven Millennium Prize Problems. The Clay Mathematics Institute created this list years ago. 

Solve one, and you win $1 million. Only one problem on the list has ever been solved. That’s how tough these problems are.

OpenAI Solution

Late in August, OpenAI started training a brand new AI model. Right away, researchers noticed something: this model was really good at math.

Then something interesting happened. OpenAI heard rumors that two Millennium Prize problems had already been cracked by someone else. 

That news apparently lit a fire under the team. So OpenAI put its new model to work; the company deployed roughly 10,000 AI agents. Each one worked somewhat independently, tackling pieces of the problem. 

Together, these AI agents exchanged nearly 3 million messages. That’s a staggering number.

They also produced 130 billion output tokens, which is basically the total amount of text and code the system generated while working through the problem.

Within 88 hours, OpenAI says its bots had found a partial solution.

Incomplete Solution

Here’s an important detail. The Millennium Prize requires proof of four separate statements to fully solve the Navier-Stokes problem.

OpenAI’s system only resolved two of those four. So this isn’t a full solution, but it’s progress. Real progress, according to OpenAI, but not a finished proof.

The company was upfront about that. OpenAI stated plainly that it does not plan to claim the Millennium Prize for this result. 

Instead, the company framed this as proof of how fast its AI models are improving. That was the whole point of releasing the news.

Costs

Speed isn’t cheap. OpenAI estimated that running this many AI agents for that many hours would cost around $10 million, based on standard pricing for its top-tier models.

That’s a massive price tag for one math problem. But for a company like OpenAI, it’s also a demonstration. 

A show of what’s possible when you throw computing power at a hard question.

Fair Play

Not long after OpenAI shared its results, Tristan Buckmaster, a math professor at New York University, spoke out. 

He said he had been working on the same problem alongside Levent Alpöge, a mathematician who works for Anthropic, a rival AI company.

Buckmaster and Alpöge had been using OpenAI’s coding tool, called Codex, throughout their research process. 

Then Buckmaster said he learned that details about his and Alpöge’s progress had somehow made their way to OpenAI. 

According to Buckmaster, this happened before OpenAI even started its own Navier-Stokes work.

Buckmaster said he hadn’t fully reviewed OpenAI’s proof yet. But he felt he needed to speak up anyway.

OpenAI’s Response 

OpenAI responded, calling Buckmaster and Alpöge’s work “remarkable.”

OpenAI also pushed back on the timeline concerns. The company said it never viewed any of their research through private channels. 

According to OpenAI, the first time anyone there saw the work was when it went public. There was one careful admission, though. 

OpenAI acknowledged it couldn’t fully rule out the possibility that some de-identified data, pulled from how Buckmaster and Alpöge used OpenAI’s own products, may have indirectly helped train its models.

Still, OpenAI insisted the two proofs are different. Not just in approach, but in what they actually prove.