AI Agents Failed to Prove Fermat's Last Theorem. Then They Got a Shared To-Do List

说明与用途

多代理 AI 在尝试证明费马大定理时因共享状态丢失而失败。使用共享 DAG（Prove2Me）实现了协作，保存了失败尝试，并在 11 天内完成了完整的 Lean 证明。

问题

Multi‑agent systems often lose track of shared state when each agent stores progress only in its own context window, leading to duplicated work and stalled collaboration.

结果

The coordinated system produced the first end‑to‑end, computer‑checked proof of FLT in 11 days, with 13 million Lean lines and 30 k theorems, while salvaging 7 % of failed attempts into reusable work.

工作流

• 1. Define a DAG where each node is a theorem statement with explicit dependencies.
• 2. Store theorem statements and proofs in separate files linked by the DAG.
• 3. Maintain a natural‑language description for each node to enable search and reuse.
• 4. Agents pull tasks from the DAG, consult the shared state, and produce proofs.
• 5. Route all agent output through a strict mechanical verifier (Lean kernel).
• 6. Log state changes to shared storage, not to conversation history.
• 7. Human operator focuses on prioritizing high‑impact nodes rather than supervising execution.

证据

A number of Claude's initial attempts failed: while agents had some early success, they quickly lost track of the project's state and stopped collaborating effectively.

来源

The fix was Prove2Me, an open platform Peng and his Columbia collaborators designed, and it did three things: maintained a DAG, separated statements from proofs, and kept natural‑language descriptions.

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If the automatic formalization of FLT is possible now, then we have taken a big step towards automatic formalization of the modern mathematical literature.

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