10,000 Decentralized Agents Crack Navier-Stokes Millennium Problem in 4 Days

Background: Navier-Stokes Millennium Problem

The Navier-Stokes equations describe fluid motion and are fundamental to fields from aircraft design to weather forecasting. A core mathematical question — whether a smooth three-dimensional fluid flow can develop a singularity (infinite velocity) in finite time — has remained open for nearly 90 years. In 2000, the Clay Mathematics Institute listed it as one of seven Millennium Prize Problems, each carrying a $1 million reward.

OpenAI's Announcement and Altman's Revelation

On September 8, 2024, OpenAI publicly disclosed a research breakthrough: an internal model constructed a mathematical proof showing that under smooth external forcing, an initially stationary, smooth fluid can form a singularity in finite time while keeping total energy finite. The proof resolves cases C and D of the formal problem statement. OpenAI released the paper and Lean formalization files simultaneously.

At the ADIPEC 2026 energy conference in Abu Dhabi on November 2, Sam Altman revealed the scale and nature of the research effort behind this result. The work was performed by approximately 10,000 agents driven by the yet-to-be-released next-generation GPT model. These agents operated continuously for about 88 hours (4 days) , exchanging 2.7 million messages and generating roughly 130 billion tokens .

Decentralized Agent Collaboration Process

Altman emphasized the system had no hierarchy and no central manager . Each agent could independently explore research directions, share progress, and decide next steps based on accumulated findings. The experiment began on September 1, 2024. Researchers tasked different agent groups with exploring distinct mathematical problems and proof paths. Agents could read cached internet information and execute code.

As the research progressed, a breakthrough on a related Euler equation problem provided new clues for Navier-Stokes. The team then redirected more compute toward the latter. OpenAI used Codex to aggregate intermediate findings from various agent groups and feed valuable discoveries back to other groups, accelerating the collective effort.

During the experiment, the underlying model underwent a further training upgrade, and the agents were updated accordingly. The final agent count reached ~10,000. After the core mathematical exploration phase, GPT-6 Astra spent an additional 17 hours formalizing and verifying the proof in the Lean theorem prover.

Cost and Future Projections

In an October 29, 2024 podcast with Stripe co-founder John Collison, Altman disclosed that OpenAI spent approximately $10 million on this single research project, possibly slightly more. He predicted that by September 2027, OpenAI could replicate the same work at about 1% of the current cost , driven by smarter models and improved research methodologies.

Implications for Next-Generation GPT

Altman's disclosure suggests the next GPT's capabilities extend beyond single-model reasoning to orchestrating massive, decentralized agent swarms that collaboratively solve complex scientific problems. The system demonstrated a complete AI-assisted research pipeline: problem decomposition, parallel exploration, result aggregation, and formal verification.

However, Altman has not announced a specific model name, release date, or whether end users will directly access the 10,000-agent collaboration framework.

Reference: Altman's ADIPEC 2026 talk (YouTube timestamp https://www.youtube.com/watch?v=2YWfVGpVtvc&t=332s), OpenAI's September 8 announcement, and X post by Hesamation (https://x.com/Hesamation/status/2117261058650112105).