OpenAI announced a proof addressing the Navier-Stokes problem, one of the Clay Mathematics Institute's Millennium Prize challenges, generated with help from an internal large language model. Mathematicians, including Luis Silvestre of the University of Chicago, argue the proof relies on introducing an external force that alters the equations into a version disconnected from real fluid behavior. Three mathematicians have since posted their own proof showing OpenAI's method cannot be extended to resolve the original, unmodified problem.
scientificamerican.com
· 2026-09-22
The Clay Mathematics Institute issued a statement noting growing momentum toward solving the Navier-Stokes Millennium Prize Problem, which concerns whether smooth, well-defined solutions always exist for the equations governing 3D fluid motion. CMI pointed to recent breakthroughs in related research, some already honored with its Clay Research Award, as evidence that a resolution could be near.
claymath.org
· 2026-09-12
OpenAI announced Tuesday that a swarm of 10,000 AI agents, run for 88 hours at a cost of millions of dollars, had found a scenario where the Navier-Stokes equations describe fluids reaching infinite velocity, effectively breaking the famous equations. NYU mathematician Tristan Buckmaster then publicly accused the company of producing a solution suspiciously similar to unpublished work he had been developing for years and was close to finishing.
futurism.com
· 2026-09-10
OpenAI announced its AI resolved a long-standing open question about the Navier-Stokes equations, one of the Clay Mathematics Institute's Millennium Prize Problems, claiming it did so within days using roughly 10,000 agents. Mathematician Tristan Buckmaster disputes the credit, saying he and Anthropic researcher Levent Alpöge had already developed the key approach before OpenAI learned of it and rushed to finish the proof over a weekend.
entrepreneur.com
· 2026-09-09
OpenAI published a paper claiming an unreleased model coordinated up to 10,000 AI agents over 88 hours to produce a formal Lean proof addressing the Navier-Stokes existence and smoothness Millennium Prize Problem. The company says the proof identifies conditions under which the equations develop a mathematical singularity, not evidence that real fluids behave impossibly. Outside mathematicians have yet to verify the claim.
techspot.com
· 2026-09-09
OpenAI announced that a swarm of roughly 10,000 coordinated AI agents, built on one of its internal models, produced a proposed resolution to the Navier–Stokes equations problem in about 88 hours. The agents worked in communicating subgroups with access to cached internet data and code execution tools, reaching their result on September 5. The Clay Mathematics Institute, which oversees the Millennium Prize Problems, has not yet verified or commented on the claim.
cnbc.com
· 2026-09-09
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 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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