750 AI Agents, 2,418 Tasks: How Anthropic Formalized Fermat's Last Theorem in Lean

Why Allocate Three-Quarters of the Team to a Single Problem?

Fermat's Last Theorem states that no three positive integers satisfy a^n + b^n = c^n for integer n > 2. Andrew Wiles proved it in 1995. Anthropic used an early version of its Fable 5.2 model to reproduce a proof along the existing mathematical path that could be stepwise verified by Lean . Unlike human readers who can fill in omitted steps, Lean requires every definition, condition, and inference to be written in a machine-checkable form.

The experiment provided the team with 60 propositions to prove , including the final theorem and 59 intermediate milestones. Also supplied were a brief hint of the classical proof path, definitions used by the propositions, and 47 previously proven lemmas from earlier formalization work. The team had to complete the missing proofs to reach the final conclusion.

At startup, the manager assigned assistants to each proposition in groups of 16–17 and asked each group to estimate task difficulty. After about 27 minutes , three propositions were already proven, but assistants judged another 47 too hard to finish within the budget. The manager shelved those difficult tasks and concentrated effort on the remaining 10 propositions . Within ~70 minutes, those 10 were completed, and assistants returned to the previously shelved hard problems.

Around hour 18 , most remaining work centered on the Langlands–Tunnell theorem and its downstream propositions — a critical link in Wiles's proof. Finishing a few easy peripheral tasks could not bypass this bottleneck. The manager reassigned approximately 750 assistants to focus on the single step blocking final delivery. The earlier “<1% chance of on-time completion” estimate came from the agent responsible for that theorem; by this point both available manpower and completed work differed significantly from the start.

One Thousand Agents Start: Claude First Creates Five Tables

Reassigning people was only the first step. A newly assigned assistant needs to know the existing proof plan, who is working on which step, and which results can be reused. If this information stays scattered in individual contexts, late joiners easily duplicate work. Anthropic's September pilot hit this problem: agents made initial progress but gradually lost track of overall project state, and collaboration broke down. The team later adopted the mathematical collaboration platform Prove2Me to centralize task and dependency management.

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

An assistant receiving a task first checks the notes table for the group's proof plan, then claims a piece of work in the subtask table. After writing a Lean proof and passing local checks, it submits code via Git and updates the database status. This way, other assistants can see whether a piece of work is taken and locate the exact commit. The database tracks progress, Git stores deliverables, and the checker judges proof correctness.

As work advanced, task distribution evolved. Initially, team leads broke plans into subtasks. Later, ordinary assistants also created new tasks, and idle assistants could claim work across teams. By hour 5.6 , 73 assistants had created 756 tasks , only 16 of which were created by leads. The manager could still concentrate manpower, but how to further split a task was increasingly decided by the assistants encountering concrete difficulties.

How Does One Problem Yield 2,418 Tasks?

The ability for 750 assistants to work simultaneously relied on exposing the proof's dependency structure. The Langlands–Tunnell team lead first outlined 10 work directions . An assistant claiming one direction who found it too large would break it into smaller propositions, register them in the subtask table, and let others pick them up. This recursive splitting produced a task tree of 2,418 tasks with a maximum depth of 10 layers .

For example, if you are proving proposition A and discover it needs lemmas B and C, you can first write “if B and C hold, then A holds” . Two other assistants then prove B and C separately. If proving B requires further lemmas, the decomposition continues. Thus, work that originally lay on a single sequential chain can be partially parallelized. At final verification, the premises must still have valid proofs to close the whole chain.

A subtle but significant effort lies in task splitting: the assistant must specify the sub-proposition precisely — under what conditions it holds and which step will use it. Too coarse a split leaves the next assistant stuck; incomplete conditions mean a delivered subtask may not connect to the upper layer. Every split requires careful thought about what to delegate and how to ensure it fits back into the main derivation.

At hour 28.4 , the Langlands–Tunnell theorem was proven. About 18 minutes later (hour 28.7) , the final Fermat's Last Theorem proof passed Lean checking. The 2,418 count represents the total tasks generated during this multi-layer decomposition.

Only 54 of 60 Propositions Proven: Why Submit Anyway?

When the experiment ended, the team had proven 54 of the original 60 propositions . Of the remaining 6, five were alternative routes that turned out unnecessary, and one was abandoned. The final theorem passed verification because the actual proof path adopted had all its required derivations connected.

These numbers make “progress” concrete . Two tasks may each occupy one line in the checklist, yet their weight in delivery can differ completely. Finishing an alternative proposition merely adds an optional route; proving a critical theorem unlocks all downstream work. The hour-18 resourcing decision targeted exactly this dependency. While that dependency remained unresolved, no amount of delivery from other groups could complete the final proof.

The same release materials also showed a curve for Opus 5.5 . Under a similar ~1,000-agent setup, Opus reached 26% at hour 18 (per official charts), and after restoring from a checkpoint and running 12 more hours, progress barely moved. Each model ran once. The public retrospective details Fable's scheduling and decomposition process, explaining how that team finished. The specific reasons Opus stalled, and how much each of the 750 assistants contributed, require more controlled comparisons to determine.

Applying This Approach Beyond Mathematics: What Is the Hardest Step?

For engineering teams, the most transferable lesson is separating tasks, artifacts, and acceptance criteria . In a software migration, for instance, 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 cause rework at integration — just like sub-lemmas in a proof. The clearer the agreed-upon conditions at handoff, the easier it is for the next party to start independently.

Mathematical tasks enjoy a particularly favorable condition: the propositions to be proved can be stated extremely precisely, and Lean provides a unified 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 a single conclusion, the team must first agree on definitions and evidence standards . Only such agreements can be checked, giving the post-decomposition outputs a chance to fit together.

The Fermat's Last Theorem experiment makes this problem vivid. A manager can summon 750 assistants at once, but what actually gives every assistant something useful to do is the team's step-by-step decomposition of the hard problem into hand-off-able, verifiable units of work . When the proof finally closes, the deliverable is a complete derivation chain ; the number of tasks completed is merely an intermediate metric.

References:

Anthropic model release with Fable and Opus comparison curves

Claude engineering retrospective and task tree/scheduling details

Anthropic September Fermat's Last Theorem formalization report

The Verge model release coverage