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

Experiment Overview

On November 10, Anthropic released Claude Fable 5.2 and Mythos 5.2 and disclosed a formalization experiment targeting Fermat's Last Theorem. Using an early version of Fable 5.2, the team aimed to reproduce a proof that Lean could verify step by step. The experiment provided 60 propositions — the final theorem plus 59 intermediate milestones — along with a brief classical proof sketch, required definitions, and 47 previously formalized lemmas.

Initial Task Allocation and Early Progress

Agents were divided into groups of 16–17 per proposition and asked to estimate difficulty. Within 27 minutes , three propositions were proved, but agents judged 47 others too hard for the budget. The manager shelved those and focused on the remaining 10, which were all completed within 70 minutes . Agents then returned to the harder problems.

Bottleneck at the Langlands–Tunnell Theorem

By hour 18, most unfinished work centered on the Langlands–Tunnell theorem, a critical dependency in Wiles's proof. The manager reassigned approximately 750 agents to this single step. The agent originally responsible had estimated a less than 1% chance of finishing on time, but the expanded workforce and accumulated context changed the outlook.

Coordination Infrastructure: Five Shared Tables

To avoid the coordination failures seen in earlier September trials, Anthropic gave the team a shared Postgres database, a Git repository, one manager, and 999 assistants. Within 10 minutes the manager created five tables: announcements, task assignments, shared notes, subtask claims, and delivered work records. Agents read the plan from notes, claim subtasks, write Lean proofs locally, verify them, commit via Git, and update the database. This separation — database tracks progress, Git stores artifacts, Lean checker validates correctness — became the backbone of collaboration.

Dynamic Task Decomposition into 2,418 Tasks

The Langlands–Tunnell group leader initially outlined 10 work directions . As agents claimed pieces and discovered gaps, they recursively split tasks into smaller lemmas, registering each in the subtask table. This produced a task tree of 2,418 tasks with a maximum depth of 10 layers. The key pattern: an agent proves "if B and C hold then A holds", while others prove B and C independently, enabling parallel work on a sequential proof chain. Each split required precise statement of conditions and usage to ensure later composition.

Completion and the Meaning of "Progress"

At 28.4 hours the Langlands–Tunnell theorem was proved; 18 minutes later (hour 28.7) the full Fermat's Last Theorem proof passed Lean checking. Of the original 60 propositions, 54 were proved . The remaining 6 included 5 unused alternative routes and 1 abandoned item. The experiment showed that "progress" is not uniform: proving a critical dependency unlocks downstream work, while completing optional branches adds little to the final goal.

Comparison with Opus 5.5

Under the same ~1,000-agent setup, Opus 5.5 reached only 26% completion by hour 18 and made little further progress after a 12-hour resume. The public retrospective details Fable's scheduling and decomposition, explaining how that team finished; Opus's specific failure modes and the marginal contribution of each of the 750 agents remain open questions.

Lessons for Engineering Teams

The most transferable practice is separating tasks, artifacts, and acceptance criteria . In software migration, for example, work can be split by interface or module, with agents submitting changes verified by contract and integration tests. Unstable interfaces cause rework, just as underspecified lemmas break proof composition. Mathematics benefits from precise propositions and a single checker (Lean); business analysis lacks such rigor — teams must first agree on definitions, metrics, and evidence standards before parallel results can be combined. The Fermat experiment illustrates that massive parallelism only becomes productive when the problem is decomposed into verifiable, handoff-ready units, culminating in a complete derivation chain rather than a mere task count.

References

Anthropic model release with Fable and Opus comparison curves

Claude engineering retrospective on task tree and scheduling

Anthropic September Fermat formalization report

The Verge model release coverage