Altman says OpenAI spent about $10 million on its claimed proof for the Navier-Stokes fluid equations and hundreds of millions of dollars on mathematics overall, with more results than it has published

Altman says OpenAI spent about $10 million on its claimed proof for the Navier-Stokes fluid equations and hundreds of millions of dollars on mathematics overall, with more results than it has published

An episode of the Cheeky Pint podcast released on October 29 features host John Collison in conversation with OpenAI CEO Sam Altman.

On September 8, OpenAI announced that its agents had proved that, in the Navier-Stokes equations, a fluid subjected to a suitably chosen smooth external force reaches unbounded velocity in finite time. According to its report, about 10 thousand agents (copies of the model running simultaneously) searched for a solution for 88 hours and generated about 130 billion tokens (fragments of text). LisanBench, a project that compares language models, estimated the cost of those tokens at OpenAI’s retail prices: about $6.5 million for the tokens the agents generated, and $10–40 million including the tokens they read.

Collison asked how much this kind of mathematics costs. Altman replied: “On the order of $10 million… for Navier-Stokes, I think… Maybe a little more.” The average cost of the other proofs was “much less,” Altman explained, because the team learned quickly. On October 6, OpenAI released more than 700 manuscripts; by its estimate, the average result took three hours of ChatGPT Pro computation. Collison put OpenAI’s total spending on mathematics at “hundreds of millions of dollars.” Altman agreed, saying that the sum covered “many more discoveries than we have published.”

Collison remarked that once a researcher spends a billion on mathematics, someone will have to ask them to slow down. Altman replied: “We let this get out of control for one week, on mathematics. Deliberately… You don’t know how far it will go until you try.” While working on Navier-Stokes, the company did not know which model to use for the agents, how many copies to run, or how long to let them work: “We understood absolutely nothing about the scaling laws for teams of agents.” It now understands “a little,” and Altman is confident that each year it will find a way to make its use of compute ten times more efficient. Collison asked when optimization would begin. Altman replied: “I think we’re already doing it.” Altman was willing to bet that a year after the proof, OpenAI could repeat the Navier-Stokes result “at one hundredth of the cost” (about $100 thousand), using smarter models and better methods.

Collison asked whether there were results beyond the 700 proofs. Altman replied: “Yes. Of course.” Asked when those results had been obtained, he began discussing a “real tension”: “Humanity deserves fundamental knowledge. And we should not sit on a major fundamental scientific discovery.” He said this outweighed scientists’ interests: much of their career success and enjoyment of life comes from making discoveries. If OpenAI continues making such discoveries or begins making them in other sciences, “we have more than an obligation” to find an arrangement that gives the world the knowledge and scientists the best possible future: “We’re working on that now.” On October 26, OpenAI announced that groups of scientists would examine its results in algorithms and physics, and acknowledged that choosing who gets involved first “creates an information asymmetry.”

Collison saw mathematicians’ discontent as a normal response: the dockworkers’ union had also objected to port automation. Altman asked himself, “Why do I feel differently about this?” He then described a weekend when employees gave a new model the hardest problems they had encountered in their scientific careers, and it “knocked them down one after another. Across all kinds of fields.” He barely slept for two nights out of excitement, but the sadness and sense that something was ending were “much greater than I expected.”