NYU mathematician Tristan Buckmaster alleges OpenAI accelerated its own Navier-Stokes work after learning a rival team using Anthropic's Claude was nearing a solution, and suspects OpenAI's Codex tool may have drawn on his team's draft sessions. Buckmaster says he was offered two credit-sharing arrangements, both of which he rejected, including one that would have excluded his collaborator Levent Alpöge from a paper. OpenAI researcher Sebastien Bubeck and CEO Sam Altman have publicly disputed parts of Buckmaster's account, and OpenAI says it won't seek the $1 million prize tied to the problem.
engadget.com
· 2026-09-08
OpenAI says an unreleased internal AI model, running roughly 10,000 autonomous agents, produced a proof addressing the long-unresolved Navier-Stokes existence and smoothness problem within about 88 hours. The effort began after the company heard rumors that two Millennium Prize problems had been cracked elsewhere, prompting it to test the model on outstanding mathematical challenges. The result has not been peer-reviewed or accepted by the Clay Mathematics Institute, which oversees the Millennium Prize.
bbc.co.uk
· 2026-09-08
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had been developing a nearly identical proof using OpenAI's Codex tool, and he suspects OpenAI may have drawn on their unpublished work without clear confirmation from the company.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
OpenAI announced on 8 September that its latest AI model produced a proof showing that the Navier-Stokes equations, which model fluid motion, can break down and predict a fluid reaching infinite speed in finite time. This addresses one of the seven unsolved Clay Mathematics Institute Millennium Problems, which carries a $1 million prize for a full solution. OpenAI researchers say they focused their AI on this problem after hearing that two academic mathematicians were close to solving related aspects.
nature.com
· 2026-09-08
Terence Tao posted a paper showing that a modified, 'averaged' version of the three-dimensional Navier-Stokes equations can develop a finite-time singularity, even though this modified equation preserves the same energy identity and function-space bounds as the real equations. Earlier blowup examples for Navier-Stokes-like systems either lacked the energy identity or required five or more dimensions; Tao's construction is the first to combine three dimensions, the energy identity, and finite-time blowup.
terrytao.wordpress.com
· 2026-09-05
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