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 The result has not been peer-reviewed or accepted by the Clay Mathematics Institute, which oversees the Millennium Prize.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 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 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
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