OpenAI has announced that it solved a notoriously difficult maths problem in just 88 hours using a swarm of roughly 10,000 AI agents. The problem, part of the Navier-Stokes equations concerning fluid movement, has lacked a proof for key aspects over the past 90 years. But with enough bots and a hefty electricity bill, apparently anything is possible.

On Tuesday, the ChatGPT-maker revealed that it had focused a group of AI bots on the Navier - Stokes existence and smoothness problem, a conundrum so stubborn that it's one of the Clay Mathematics Institute's Millennium Prize problems, which come with a $1m reward for the first solver. The company called its solution a "milestone" and proof that AI tools are improving quickly - though, notably, it hasn't yet been independently verified or accepted by the institute.

Here's the timeline: At the end of August, OpenAI started training a new internal model that showed a knack for maths. Last week, on 1 September, the company heard rumors that two Millennium Prize problems had been resolved, so it set thousands of AI bots to work on some remaining ones. By 5 September - roughly 88 hours later - it had a solution to the Navier - Stokes problem, which sits at the heart of turbulence, a phenomenon still not well understood by humans. The bots exchanged nearly 3 million messages and burned through 130 billion output tokens (the lines of text and code an AI model produces) on Navier-Stokes alone. At OpenAI's own pricing, that effort would have cost about $10m (£7.3m).

The solution reportedly resolves two of the four statements in the proof that the Millennium Prize demanded. But OpenAI isn't claiming the prize. "Our goal in releasing this result is to report on the substantial progress of our AI models," the company said. "We do not intend to claim the Millennium Prize for this result." Which is convenient, since the prize is worth $1m and they've already spent $10m on compute.

Naturally, controversy has erupted. Tristan Buckmaster, a mathematics professor at New York University, claims he and Levent Alpöge, a mathematician at OpenAI rival Anthropic, were also working on the problem using OpenAI's Codex tool. Buckmaster says that on 3 September, he learned that "information about our progress had been passed to OpenAI." He went public with emails exchanged with OpenAI, alleging that the company didn't start its Navier-Stokes work until after learning of Buckmaster and Alpöge's progress. "The alternative is to let a sequence of announcements say something I know to be false," he said.

OpenAI responded by congratulating the "concurrent work" of Buckmaster and Alpöge, calling it "remarkable." The company insists it hadn't seen any of their work until it was released publicly and that no user data was accessed. But in a fine print worthy of a spy novel, OpenAI added: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." In other words: your AI homework might not just be graded - it could be used to solve the world's hardest maths problems without you ever getting the credit.