Anthropic's Fermat swarm failed until a theorem graph told the agents what to do next

The check ran on a 96-core machine, and it was not quick. Buzzard measured the repository at 13.4 million lines, more than five times the size of Mathlib, and reports that it takes nearly twenty times as long to compile ^[17]. Twenty over five is four, so each line of this proof costs roughly four times what a line of the community library costs to verify ^[22]. That is the standing bill for anyone who wants to build on the artifact rather than admire it. It is also not the artifact Buzzard's grant was buying. The proof follows the 1995 exposition of Wiles by Darmon, Diamond and Taylor, not the modern route his project has been formalising ^[15]. The most instructive part of Anthropic's write-up is the run that failed. Agents made early progress, then lost track of the project's state and stopped collaborating, and those dead runs still supplied around 7% of the non-boilerplate lines in the finished proof ^[9]. The repair was not a stronger model. It was Prove2Me, an open platform built by Anthropic researcher Tianyi Peng with collaborators at Columbia University, which maintains a graph of theorem statements so an agent can see what to attempt next, splits statements and proofs into separate files to speed compilation, and keeps a plain-language description of each statement so finished work can be found and reused ^[10]. Wrap that in a multi-agent harness on Claude Code and the same models closed the job inside a fortnight ^[11]. The human steering that survives in Anthropic's account is fragments: "Jacobian as a scheme sounds high priority", and "Push Mazur to be done soon" ^[12]. Teams often assume the bottleneck is model capability and plan to wait for the next release. Anthropic's account undercuts that: the weights were identical, the run failed and then succeeded, and a shared state artifact was the only thing that changed. Then the money, which is where the comparison gets loose. Buzzard's project has £1m over five years, an average of £200,000 a year ^[7][21]. Anthropic says the run consumed about six billion output tokens from an internal research model it calls roughly comparable to Claude Fable 5.1 ^[8], and at the $50 per million output tokens Fable 5.1 lists, six billion is $300,000 ^[13], or about 2.2 cents per line of Lean ^[23]. No invoice was raised, the model was internal, and a lab's own inference costs it less than list price, so this is the only public arithmetic rather than a price ^[14]. Buzzard wonders in print whether Anthropic spent more than he was given ^[7]. That is a pound grant measured against a dollar illustration, and everyone quoting him is making the same comparison. On soundness: Lean has had bugs found in it recently, and an agent determined enough could in principle exploit one to prove anything ^[18]. After his own inspection, and OpenAI models' review of the Lean codebase finding no soundness issues in the version used, Buzzard's summary is that a hack finishing the job is extremely unlikely ^[20]. Whether this transfers to your own long-horizon agent work turns on two things. The first is whether anything can reject bad output before a human reads it; Lean compiles or it does not, and a comparator confirmed the theorem proved matches the statement in Mathlib ^[16]. The second is whether there is a durable artifact the agents read to pick their next task and write back to when they finish. With both in place, the result is 13 million lines and a mathematician willing to compile them. With a checker but no shared state, the result is the first run: real output that never assembled into a proof, contributing that 7% salvage.