OpenAI says an unreleased model produced a resolution to the Navier–Stokes existence and smoothness problem, one of seven Millennium Prize Problems carrying a $1 million reward. NYU professor Tristan Buckmaster, who had spent nearly a year on related work with Anthropic researcher Levent Alpöge using Claude and Codex, rushed out his own paper alleging OpenAI's team began work only after hearing rumors of his breakthrough, and that OpenAI would not clarify whether its model had accessed his private drafts.
simonwillison.net
· 2026-09-09
OpenAI published a preprint claiming to show that the Navier-Stokes equations, which govern fluid motion, can break down under certain conditions, describing a spinning fluid system reaching infinite speed in finite time. The claim addresses part of one of mathematics' seven Millennium Prize Problems, but mathematicians have raised concerns over how the result was announced and over authorship disputes involving researchers connected to rival company Anthropic.
nature.com
· 2026-09-09
OpenAI says it used AI systems, backed by significant investment, to produce a solution to the Navier-Stokes equations, one of the seven unsolved Millennium Prize Problems in mathematics. The claim has drawn immediate pushback from rival labs and researchers who are scrutinizing whether the result truly meets the rigorous proof standards required for the prize.
wsj.com
· 2026-09-08
OpenAI says an internal AI model, more capable than GPT-6 Astra, generated a solution to part of the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. The proof demonstrates that three-dimensional incompressible fluid dynamics governed by these equations can develop a singularity—unbounded speed growth—in finite time, even from smooth initial conditions. OpenAI released both a written explanation of the proof and a formal verification built in the Lean proof assistant.
openai.com
· 2026-09-08
OpenAI claims its internal AI model, paired with 10,000 concurrent agents, solved the century-old Navier-Stokes equation, one of the seven Millennium Prize Problems worth $1 million. However, NYU professor Tristan Buckmaster says he and Anthropic researcher Levent Alpöge had been developing a nearly identical proof using OpenAI's Codex tool, and he suspects OpenAI may have drawn on their unpublished work without clear confirmation from the company.
theverge.com
· 2026-09-08
OpenAI announced that an AI model produced a Lean-verified solution to a key case of the 200-year-old Navier-Stokes equation, one of the Clay Millennium Prize problems, after running over a thousand agents for more than 50 hours at a cost of millions of dollars in compute. The announcement came shortly after mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge posted their own related advances, and Buckmaster has accused OpenAI of rushing to claim credit after learning of their progress.
wired.com
· 2026-09-08
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