OpenAI's $10M Navier–Stokes proof could be redone for 1/100th the cost by 2027

OpenAI spent "order $10 million" on its claimed Navier–Stokes proof, CEO Sam Altman said on October 29 — and he expects the same result to cost about a hundredth of that within a year.

Speaking with Stripe co-founder John Collison on Stripe's Cheeky Pint podcast, Altman put a hard figure on the most expensive item in OpenAI's mathematics program. "I bet we could redo Navier-Stokes at 1/100th of the cost a year from when it was done," he said. Asked whether the savings came simply from knowing how the proof goes, he pointed instead to "smarter models and better approaches."

What did the run actually involve?

OpenAI announced the result in early September: a construction that starts with a fluid at rest, applies a smooth external force, and — according to the company — develops a singularity, with fluid speeds growing without bound in finite time while total energy stays finite. That addresses one version of the problem in the Clay Mathematics Institute's official statement, which includes externally driven fluid motion. The problem is one of seven Millennium Prize Problems selected in 2000, each carrying a $1 million prize. OpenAI said it would forgo the prize.

The scale of the run sets the cost baseline. OpenAI says roughly 10,000 copies of its internal model worked as coordinated agents, each able to run code, read a cached snapshot of the web and message the others. Launched September 1, the effort reached its result about 88 hours later, after 2.7 million messages and some 130 billion output tokens, Unite.AI reported from OpenAI's announcement. Verifying the proof in Lean, the machine-checked proof assistant, took another 17 hours.

One caveat matters for researchers tracking the result: OpenAI has published the Lean files, but a machine check of the formal statement is distinct from mathematicians accepting the result. That acceptance has not been reported.

Where would a 100-fold saving come from?

Altman framed the $10 million as the price of working without a playbook. "Look, we did let it get out of control for one week on the math. Intentionally so," he said, adding that "you don't know how far it's going to go until you try." When the run began, he said, "we understood absolutely nothing about the scaling laws of teams of agents" — whether to deploy the smartest model, more copies or fewer, longer rollouts or shorter.

His efficiency claim rests on two levers: better agent orchestration and cheaper underlying hardware. Later in the conversation he put the five-year cost of building and running a gigawatt of AI data center capacity at about $70 billion, a figure he said varies by who is counting. "I think if that number were 20 instead of 70, we should be much happier," he said — and even then, users should "still demand to get 10x better performance out of it with smarter models every year." Reaching $20 billion, he said, would require cheaper energy and squeezing out the gross-margin stacking between "melting sand" and "getting the token back."

What has OpenAI not published?

Navier–Stokes was the costliest piece of a broader effort. Collison put OpenAI's overall spending at "100s of millions of dollars of math," and Altman agreed, adding that the total "includes much more other discovery than what we have published." OpenAI has since announced results on three more problems in mathematics, computer science and physics.

Altman acknowledged tension over disclosure: "Humanity deserves fundamental knowledge. And we should not be sitting on a major fundamental science discovery," he said, adding that OpenAI is "working through that right now." Costs are already falling inside the program — later problems cost "way less" because the team "kept getting better so fast." The openai/math repository, where OpenAI posted 722 AI-generated manuscripts on October 6, says the model was posed about 4,000 problems and the average result used roughly three hours of ChatGPT Pro thinking compute.

How does Altman read the moment?

He described testing a new model in an internal channel named "Model Name-Hold My Beer," where researchers fed it "the hardest problems they could," including "people's hardest research problems from their academic career." The model, he said, was "knocking down one after the other" across many fields; he stayed up most of the night two nights running.

The excitement carried a cost. "I also had much more sadness and melancholy, and a feeling of something ending than I was expecting," Altman said. When Collison likened mathematicians' objections to dockworkers resisting port automation, Altman conceded the difference: "It's people's lives and it's something that has brought them great joy." He called the automation of discovery "just the shape of reality and nothing that anyone can stop, or should stop" — a verdict, like his 100-fold cost bet, that the coming year of published results and falling compute bills will test.