# OpenAI says its AI cracked Navier-Stokes _OpenAI says an internal model more capable than GPT-6 Astra produced a Lean-checked proof that Navier-Stokes can blow up in finite time._ **Published:** 2026-09-13 **Source:** https://www.startuphub.ai/ai-news/ai-research/2026/openai-says-its-ai-cracked-navier-stokes --- We [reported September 12](https://www.startuphub.ai/ai-news/artificial-intelligence/2026/briefing-openai-openai-youtube-uber-2026-09-12-82ce) that [OpenAI](/startups/openai) was circling the Millennium Prizes with a new internal model. [The World, The Universe And Us](https://www.youtube.com/watch?v=NNIpdytGWf0) now frames the follow-up: OpenAI says it has solved the Navier-Stokes existence and smoothness problem, the 200-year-old question of whether fluid equations can blow up. The case, as laid out on [The World, The Universe And Us](https://www.youtube.com/watch?v=NNIpdytGWf0), is that the Navier-Stokes equations model flow as a continuous medium, from air over a Formula 1 car to blood through a heart. They were written in the 19th century and underpin modern simulation, but it was open whether smooth three-dimensional flow could stay smooth forever or develop a singularity and produce nonsense. [OpenAI](/startups/openai) describes the result more precisely. Its proof, produced by an internal system, **shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time**. The company says the work was done by an internal model that is **significantly more capable than GPT-6 Astra**, and that it is sharing both a writeup and a formalization in Lean. Scale is the story. The company ran a system of coordinating agents with tool use and code execution, with the group that produced the Navier-Stokes resolution involving **on the order of 10,000 concurrent agents**. The agents arrived at the resolution **about 88 hours after the first agents were launched**, with Lean formalization and verification taking an additional 17 hours via GPT-6 Astra. At a press conference the team said a customer running the same job would pay around $15 million, a figure that arrived after 2.7 million messages and about 130 billion output tokens on Navier-Stokes alone. That last number is doing a lot of work. According to The World, The Universe And Us, two researchers had been quietly pushing a stepping-stone version of the problem, the Euler equations, which drop viscosity. Tristan Buckmaster, a mathematician at NYU, and Levent Alpöge, listed as an [Anthropic](/startups/anthropic) employee, were working with that approach when rumors of progress reached [OpenAI](/startups/openai). The outlet describes [OpenAI](/startups/openai) then launching efforts on all six open Millennium Problems, later narrowing to Navier-Stokes and Euler, with Buckmaster and Alpöge publishing forced-Euler work the day before [OpenAI](/startups/openai). The Scientific American account aligns, noting the pair had been **using LLMs from [OpenAI](https://www.startuphub.ai/startups/openai)’s rival company Anthropic to parse through the mathematical possibilities** and that the final claim became a credit dispute, not just a proof. Context matters against what rivals have chosen to showcase. [Anthropic](/startups/anthropic) recently turned Claude to formal mathematics and produced a computer-checked formalization of Fermat’s Last Theorem, a project that took 11 days of autonomous work. Google [DeepMind](https://www.startuphub.ai/ai-news/ai-figures/2026/figure-demis-hassabis-scientific-discovery-vision-2026-05-11) has taken a different tack with AlphaProof, a reinforcement-learning system that trains itself to prove statements in Lean by first translating informal math into formal statements to build a large library of problems. [OpenAI](/startups/openai)’s Navier-Stokes sprint looks less like a new prover architecture and more like massive orchestration of a general LLM system thrown at an age-old analysis problem, with **around 10,000 agents** exchanging millions of messages in days. The skepticism in The World, The Universe And Us is not about the engineering. Mathematician Sébastien Bubeck, who leads [OpenAI](/startups/openai)’s math effort, described having about ten ideas to push past a scaling lull and finding that all of them worked. President Greg Brockman went further and called GPT-6 Astra an early form of artificial general intelligence. The biologists hosting the show pushed back that definitions of AGI remain woolly and that a chatbot that can crush a Millennium-adjacent proof can still fail at simple everyday tasks. [Terence Tao](/startups/terence-tao), cited by reporter Matt Sparks, put the academic worry bluntly: the system is throwing a carcass of raw meat on the table, not explaining why the theorem holds. And the why matters for the prize. Scientific American notes the crucial technicality is forcing, an often-ignored term in the Clay formulation that Córdoba and Martínez-Zoroa revived to try to break the equations. Buckmaster and Alpöge used that forcing idea to blow up Euler; [OpenAI](/startups/openai) says it pushed it to full Navier-Stokes. Some mathematicians argue a forced blow-up answers the problem as written but may not answer it as the field intuitively frames it without forcing, which would leave the Clay Mathematics Institute with a quandary over the $1 million award. [OpenAI](/startups/openai) says it does not intend to claim the prize. The outlet closes the loop by asking where this leaves science. The hosts note chatter that [OpenAI](/startups/openai) may also be aiming at the Hodge conjecture, and that mathematicians worry about role change: applied mathematicians expect to absorb tools like formal Lean checking, while pure theorists sense a nearer-term threat to how proofs are produced. The economics are already stark. If $15 million of compute can compress decades of collective effort into 88 hours, the limiting factor is not whether a model can try every path, but whether the field can still afford to ask why a path is correct. --- Original analysis from [startuphub.ai](https://www.startuphub.ai), the #1 AI startup directory.