How 750 Claude Agents Cracked Fermat's Last Theorem's Hardest Step in Lean

01 Why Allocate 75% of Agents to One Problem?

Fermat's Last Theorem states that no three positive integers satisfy a^n + b^n = c^n for integer n > 2. Wiles proved it in 1995. Anthropic used an early version of Fable 5.2 to reproduce a proof that Lean can verify step by step. Lean requires every definition, condition, and inference to be written in a machine-checkable form, unlike human readers who can fill in gaps.

The experiment provided 60 propositions to prove, including the final theorem and 59 intermediate milestones. Also supplied: a brief hint of the classical proof path, definitions used, and 47 previously formalized lemmas. The team had to complete the missing derivations.

At start, assistants were divided across propositions, 16–17 per group, and asked to estimate difficulty. After ~27 minutes, three propositions were proved, but assistants judged 47 others too hard for the budget. The lead paused those and concentrated effort on the remaining 10. Within ~70 minutes, those 10 were done, and assistants returned to the hard set.

By hour 18, most remaining work centered on the Langlands–Tunnell theorem and its downstream propositions — a critical link in Wiles' proof. Finishing peripheral tasks could not bypass this bottleneck. The lead reassigned ~750 assistants to this single step. The "<1%" estimate came from the agent originally responsible for that theorem; by then available hands and completed work had changed dramatically.

02 1,000 Agents Start, Claude Builds Five Tables

Reassigning people is only step one. A newly moved assistant must know the existing proof plan, who is working on which step, and which results are reusable. If this information stays scattered in individual contexts, late joiners duplicate work. Anthropic's September trial hit this problem: agents made initial progress but gradually lost sync with overall project state, and collaboration broke down. The team then adopted the math collaboration platform Prove2Me to centralize task and dependency management.

This time, Anthropic gave the team a shared Postgres database, a Git repository, one lead, and 999 assistants with initial assignments. Each agent works in its own sandbox. Within 10 minutes, the Fable lead created five tables in the database: announcements, task assignments, shared notes, subtask claims, and delivered work records.

An assistant receives a task, checks the group's proof plan in the notes table, claims a subtask in the subtask table, writes a Lean proof, runs local verification, commits via Git, then updates the database status. Thus others see whether a piece is taken and can locate the exact commit. Database tracks progress, Git stores deliverables, the checker judges proof validity.

Task distribution evolved: initially group leads broke plans into subtasks; later ordinary assistants also created new tasks, and idle assistants could claim across groups. By hour 5.6, 73 assistants had created 756 tasks, only 16 by leads. The lead still directs bulk reassignment, but how to further split a task is increasingly decided by assistants facing concrete difficulties.

03 How One Problem Expands to 2,418 Tasks

750 assistants working simultaneously relies on unpacking proof dependencies. The Langlands–Tunnell group lead first outlined 10 work directions . An assistant claims one; if it's too large, they split it into smaller propositions, register them in the subtask table, and others pick them up. This recursive splitting produced a task tree of 2,418 tasks with maximum depth 10 .

Example: You are proving proposition A and discover it needs lemmas B and C. You first write "if B and C hold, then A holds". Two other assistants prove B and C. If proving B needs further lemmas, split again. Thus work that was sequential in the derivation chain can run in parallel. At final acceptance, every premise must have a verified proof to close the chain.

A hidden effort: when splitting, the assistant must specify the sub-proposition precisely — under what conditions it holds, which step will use it. Too coarse, and the next assistant cannot proceed; incomplete conditions, and the upper layer cannot connect. Each split requires deciding what to delegate so the result still fits the original derivation.

At hour 28.4, Langlands–Tunnell was proved. ~18 minutes later, at hour 28.7 , the full Fermat's Last Theorem proof passed Lean checking. The 2,418 count is the total tasks generated during this multi-layer splitting.

04 60 Propositions, Only 54 Done — Why Submit?

At experiment end, the team had proved 54 of the original 60 propositions . The remaining 6: 5 were alternative routes later deemed unnecessary, 1 was abandoned. The final theorem passed because the actual proof path's required derivations were all connected.

This makes "progress" concrete. Two tasks each occupy one line in the list, but their weight in delivery differs completely. Finishing an alternative proposition merely adds a possible route; proving the key theorem unlocks all downstream work. The hour-18 reassignment targeted exactly this dependency. While it remained unresolved, no amount of delivery from other groups could complete the final proof.

The same release also gave Opus 5.5 's curve. With ~1,000 agents, Opus reached 26% at hour 18 (per official chart), then after restoring from checkpoint ran 12 more hours with little advance. Both models ran once. The public retrospective details Fable's scheduling and splitting, explaining how that team finished. Why Opus stalled, and how much each of the 750 assistants contributed, need more controlled comparisons.

05 Moving This Method Out of Math: What Step Is Hardest?

For engineering teams, the most transferable practice is separating tasks, artifacts, and acceptance . In a software migration, work can be split by interface or module, letting different agents submit changes independently, then using contract tests and integration tests to verify they run together. If an interface is still changing, parallel changes around it may require rework at integration — just like sub-lemmas in a proof. The clearer the agreed conditions at handoff, the easier for the receiver to work independently.

Math tasks have a uniquely favorable condition: the proposition to prove can be stated extremely precisely, and Lean provides a uniform checking standard. In business analysis, several agents might each retrieve numbers but use different revenue definitions, time windows, or data scopes. To combine those results into one conclusion, the team must first agree on definitions and evidence standards . Only such agreements can be checked, making post-split results composable.

The Fermat experiment makes this vivid. The lead can summon 750 assistants at once, but what actually gives every assistant something to do is the team breaking the hard problem step by step into verifiable, handoff-able pieces. When the proof finally closes, the deliverable is a complete derivation chain ; the number of tasks completed is just an intermediate metric.