OpenAI Solved the Math but Nobody Is Happy: The Navier-Stokes Fight

Fireship's September 11 Code Report tells the week's strangest science fight: OpenAI announced that an in-house model had solved the Navier-Stokes equations. According to the company, around 10,000 agents worked for 88 hours and produced 300 billion tokens. That is the frame reported by the BBC and the Guardian; the bill, per TechCrunch, equals $22.5 million of compute at current rates.

The object of the fight dates back to the 1800s: French engineer Claude Navier first turned fluid motion into equations, and decades later Irish mathematician George Stokes fixed and completed the work. The resulting Navier-Stokes equations are roughly F=ma for fluids: you feed in current speed and pressure, and they tell you how the fluid moves a moment later. Engineers have trusted these equations for nearly 200 years — hurricane forecasts, airplane wing designs, and simulations of blood pumping through vessels all rest on them. But for mathematicians trust is not enough; they demand proof.

The unanswered question is plain: can these equations ever break — can a fluid's speed blow up to infinity at some point? The question was so hard that in 2000 the Clay Mathematics Institute named it one of seven Millennium problems with $1 million on its head. Claiming the money takes one of two paths: proving the equations never break, or exhibiting a single case where they do.

One of the few who cared is NYU math professor Tristan Buckmaster, who won the Clay Research Award in 2019 for work on these very equations. Last year he teamed up with Levent Alpoge, a mathematician working at Anthropic. Leaning harder on Claude Code and Codex in August, the pair sped up, and on August 15 they made the simplified Euler equations fall apart. It was not the million-dollar problem, but it was the closest anyone had ever come.

What follows is the video's central claim: in late August, while training a new model, OpenAI decided to hand it every unsolved Millennium problem at once and watch what happened. Within weeks the company announced a Navier-Stokes proof — using, the video says, the exact novel method Buckmaster and Alpoge had spent a year pouring into Codex.

On September 3 Buckmaster emailed OpenAI to ask what was going on, and that Sunday he spoke by phone with the researcher running the project. Per Buckmaster's four-page statement, he was first told the model had been given only the problem statement; as the call went on it emerged that the whole team had worked on it, that the prompt was written with Codex, and that the effort had started days earlier upon hearing rumors of his work. Whether the model had been trained on his Codex sessions went unanswered; the company says no user data was accessed.

Buckmaster further claims he was offered two options: publish the Euler result first and then be credited in OpenAI's proof as the man who came closest, or write the Navier-Stokes paper himself while leaving Alpoge — an Anthropic employee — off it. He says that when he refused both and threatened to go public, the reply was to ask why he would ruin his career. OpenAI disputes this account; Sam Altman says everyone on his side acted with integrity and that Buckmaster was the one making threats.

On Tuesday morning Buckmaster and Alpoge posted three proofs plus the four-page statement; that afternoon OpenAI posted its own solution with a blog post insisting the proofs differ significantly. The next day rumors spread that the company is close to verifying yet another Millennium problem. The most level-headed comment came from Terence Tao: when even loose talk about unfinished work can summon fleets of agents eager to publish first, mathematicians will simply stop sharing ideas, undoing centuries of open science.