OpenAI has spent hundreds of millions on math, CEO Sam Altman estimates
Altman estimates around $10 million, “maybe a little more,” went to OpenAI’s claimed Navier–Stokes solution, and says the company holds further unpublished mathematical discoveries.
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OpenAI CEO Sam Altman estimated that the company had spent hundreds of millions of dollars tackling mathematical problems, including around $10 million—“maybe a little more”—on its claimed Navier–Stokes solution.
He gave the estimates on an episode of the Cheeky Pint podcast released 29 October 2026, The Verge said. The company has released hundreds of mathematical results during October 2026.
On 8 September 2026, OpenAI claimed to have found a three-dimensional Navier–Stokes solution with a smooth external force that develops a singularity in finite time, meaning the modeled velocities grow without bound. Mathematicians speaking to The Verge criticized insufficient verification of OpenAI’s mathematical releases and said researchers were left checking the work.
Altman says the effort tested the models’ limits
Altman said OpenAI’s pursuit of mathematical problems briefly got out of control, but described the effort as deliberate and necessary to test the limits of its superintelligence (SI) models. He described an internal channel called “Model Name-Hold My Beer,” where employees tried the models on exceptionally difficult problems to see how they performed.
Asked whether OpenAI had additional mathematical discoveries beyond its released proofs, Altman said it did. He argued that major fundamental scientific discoveries should not be withheld because humanity deserves that knowledge, while acknowledging that OpenAI needs to improve how it communicates its findings.
How the Navier–Stokes result will be assessed
The Navier–Stokes equations describe fluid motion. The existence and smoothness problem asks whether their solutions exist and remain smooth, without mathematical breakdowns, in three-dimensional space under specified conditions.
In its 11 September 2026 statement, the Clay Mathematics Institute described the announced result as having “apparently” settled the problem. It pointed to its prize rules for evaluating the achievement and assigning credit.
Before a proposed solution can be considered for a Millennium Prize, it must be published in a qualifying outlet, at least 2 years must pass after publication, and it must gain general acceptance within the mathematical community. The institute describes that process as deliberately unhurried and says it will provide updates.
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