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

Описание и применение

Многопользовательские ИИ‑агенты, пытавшиеся доказать теорему Ферма, потерпели неудачу из‑за потери общего состояния. Использование общей DAG‑схемы (Prove2Me) позволило координировать работу, сохранить результаты неудачных попыток и завершить доказательство за 11 дней.

Задача

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.

Результат

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.

Рабочий процесс

• 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.

Доказательства

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.

Источник

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.

Источник

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

Источник