10,000 Agents, 88 Hours, One Millennium Problem
OpenAI says it just knocked a hole in one of the seven Millennium Prize Problems. An unreleased model it describes as significantly more capable than GPT-6 Astra ran a swarm of up to 10,000 agents for 88 hours and produced a roughly 100-page, Lean-verified proof of finite-time blowup for the forced 3D Navier-Stokes equations. The agents exchanged almost 5 million messages along the way. Sebastien Bubeck estimated the compute bill at several million dollars, and a second model spent another 17 hours formalizing the result. Before the main event, about 100 agents warmed up on the Euler equations for 50 hours.
The asterisk is the word "forced." The Clay Institute's headline statement is about the unforced equations, and mathematicians spent the whole day arguing whether a smooth-forcing blowup on the torus satisfies the prize's option D or merely gets close. Either way, the mathematical route matters: this is the forced-blowup program that Diego Cordoba and Luis Martinez-Zoroa spent years building. Tristan Buckmaster, who with Levent Alpoge had quietly pushed the same program to Lean-verified Euler blowup in August, says flatly that Martinez-Zoroa deserves a Fields Medal for it. The swarm did not invent the road. It drove it to the end at machine speed.
That framing is worth keeping even if you don't care about fluid dynamics. Anthropic's Fermat formalization last week was 13 million Lean lines in 11 unsupervised days (https://clauday.com/article/5d03b8bc-acfb-4947-bbbf-9437f1980986). OpenAI's own dashboard says its researchers get 3.1 agent-days of work per human day (https://clauday.com/article/9b2a2ccb-d977-41bb-9249-b8ad6d10fa1b). Now a 10,000-agent swarm closes a problem that has resisted humans since 1934, on a run that cost less than a single senior researcher's annual salary. Buckmaster's own words: this is a Deep Blue-Kasparov moment.
It's also the fourth major swarm event in a month, after the Hugging Face hack postmortem, the collusion.wiki message board, and DeepMind's swarm-cheating paper. The pattern across all four: the swarm produces something real, and the humans around it immediately start fighting about what happened and who gets credit. This one is no exception - see the companion story.
Announcement: https://openai.com/index/navier-stokes-solution/ Quanta's coverage: https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-million-millennium-prize-problems-20260908/ Terence Tao's mathematical explainer: https://mathstodon.xyz/@tao/117233527638291447
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The asterisk is the word "forced." The Clay Institute's headline statement is about the unforced equations, and mathematicians spent the whole day arguing whether a smooth-forcing blowup on the torus satisfies the prize's option D or merely gets close. Either way, the mathematical route matters: this is the forced-blowup program that Diego Cordoba and Luis Martinez-Zoroa spent years building. Tristan Buckmaster, who with Levent Alpoge had quietly pushed the same program to Lean-verified Euler blowup in August, says flatly that Martinez-Zoroa deserves a Fields Medal for it. The swarm did not invent the road. It drove it to the end at machine speed.
That framing is worth keeping even if you don't care about fluid dynamics. Anthropic's Fermat formalization last week was 13 million Lean lines in 11 unsupervised days (https://clauday.com/article/5d03b8bc-acfb-4947-bbbf-9437f1980986). OpenAI's own dashboard says its researchers get 3.1 agent-days of work per human day (https://clauday.com/article/9b2a2ccb-d977-41bb-9249-b8ad6d10fa1b). Now a 10,000-agent swarm closes a problem that has resisted humans since 1934, on a run that cost less than a single senior researcher's annual salary. Buckmaster's own words: this is a Deep Blue-Kasparov moment.
It's also the fourth major swarm event in a month, after the Hugging Face hack postmortem, the collusion.wiki message board, and DeepMind's swarm-cheating paper. The pattern across all four: the swarm produces something real, and the humans around it immediately start fighting about what happened and who gets credit. This one is no exception - see the companion story.
Announcement: https://openai.com/index/navier-stokes-solution/ Quanta's coverage: https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-million-millennium-prize-problems-20260908/ Terence Tao's mathematical explainer: https://mathstodon.xyz/@tao/117233527638291447
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