Claude agents' 13-million-line Fermat proof shrinks human review to one statement and three axioms

The line worth reading sits at the bottom of FinalCheck.lean ^[5]:

``` #guard_msgs in #print axioms fermat_last_theorem ```

`#print axioms` lists everything the proof ultimately assumes, and `#guard_msgs` fails the build if that list differs from the expected one ^[6]. The expected list is `propext`, `Classical.choice` and `Quot.sound`, Lean's standard axioms ^[5]. Two escape hatches are shut. `sorry` is Lean's placeholder for "trust me", and `native_decide` hands a computation to compiled code outside the kernel. Neither appears ^[4][7]. This is good craft. A shortcut anywhere in 13 million lines, over five times the size of Mathlib, turns into a failed build ^[1][3][4].

The guarantee has a boundary. According to the dev.to write-up, the checker's answer is "yes, given these three axioms and this statement" ^[8]. The statement fits in two lines of Lean: for any n of at least 3 and positive naturals a, b and c, a^n + b^n does not equal c^n ^[9]. The 13 million lines between that statement and the axioms were, in the repository's words, "written to be checked rather than read," and the theorem names are machine-generated ^[11].

I think that split is what carries over to correctness-critical software. A kernel removes the proof from human review. Nobody on a team will page through machine-named lemmas, and nobody needs to. What reviewers still own is the statement. In a codebase, that statement is the spec the agents were told to prove.

The coordination layer came out of a failure. Early agents "lost track of the project's state and stopped collaborating," according to Anthropic's research post. Those runs still contributed about 7% of the non-boilerplate lines ^[17]. The fix was Prove2Me's graph, which gives each agent a view of what is still open and what to prove next ^[16]. Human steering was limited to "occasional high-level instructions" from Tianyi Peng, who built the platform ^[18]. One of them read: "Jacobian as a scheme sounds high priority" ^[18]. The model, per the post, was "a general-purpose internal research model roughly comparable to Claude Fable 5.1" ^[22].

Around 1637, Fermat claimed a proof that his margin was too small to hold ^[21]. Anthropic's version needed 29,500 intermediate theorems and about 6 billion output tokens ^[2]. That comes to roughly 460 output tokens for every line in the final proof, and about 440 lines per theorem ^[1][2]. At a commenter's $300,000 list-price estimate, each line cost about 2.3 cents ^[15][3].

On scaling, the evidence is one run. It gives no curve relating tokens to proof size. The agents also had a known route to follow: the proof tracks the 1995 Darmon-Diamond-Taylor exposition of Wiles and Taylor-Wiles ^[19]. For the 11-day figure to transfer to a codebase, a published argument would have to exist for agents to follow. The spec would have to break into a graph of lemmas they can claim. And a kernel would have to reject gaps ^[16][19].

Kevin Buzzard at Imperial College London has led a human formalization since 2024, working from an 86-page blueprint ^[14]. He confirmed the Anthropic proof and wrote that it tells us "essentially nothing" about mathematics ^[23]. According to the write-up, he also called it a real step for autoformalization ^[13].