Claude's Fermat proof: the task graph did the coordinating

Anthropic ran dozens of Claude agents at one of the hardest formalization problems in mathematics and got a machine-checked proof out the other side in eleven days. The headline is the theorem. The part worth stealing is how the agents avoided tripping over each other: a shared task graph that every agent read from and wrote to.

What actually happened

Per Anthropic's write-up, a team of Claude agents produced a complete, machine-checked proof of Fermat's Last Theorem in Lean 4 — around 13 million lines of Lean, 30,300 theorems proved with 29,500 used in the final proof, over five times the size of Mathlib, Lean's main library. It burned roughly 6 billion output tokens from a general-purpose internal research model Anthropic describes as roughly comparable to Claude Fable 5.1. Human mathematical input was limited to occasional high-level nudges.

The coordination layer was Prove2Me, an open platform built by Tianyi Peng and collaborators at Columbia. It holds a directed acyclic graph of theorem statements: a claim can be stated with a natural-language description before it is proved. An agent that needs a lemma looks it up, uses it as a black box, and moves on. Another agent proves it later. Lean checked the logic mechanically, and a comparator confirmed the final statement matched Mathlib's definition of FLT. Anthropic notes about 7% of non-boilerplate lines came from attempts that failed. As Kevin Buzzard, who has led the human formalization effort, put it: Anthropic got there first.

Why multi-agent orchestration matters for your business

Most teams that try parallel agents get mud. Five agents edit the same files, three solve the same subproblem, and someone spends the afternoon reconciling it by hand. The instinct is to blame the model and buy a bigger one.

That is not what happened here. The agents were coordinated by an artifact outside any of them: a graph of named, described, individually verifiable units of work, plus a checker that says pass or fail with no argument. Interface first, implementation later, machine-verified at the boundary. Swap "theorem" for "function," "endpoint," or "migration" and you have a plan for your own repo.

Concretely: before you fan out, write the interfaces — signatures, schemas, contract tests — and register them somewhere every agent can read. Let an agent depend on a stub that does not exist yet. Make the pass/fail check cheap and automatic, because six billion tokens of output is only useful if something other than a human is reading it. And budget for waste: 7% of the winning proof came from dead ends, which is a rounding error when the checker catches them for free.

Sources: Anthropic, SiliconANGLE, Xena Project.