Claude's Fermat run failed until the agents got a to-do list

On September 4, @AnthropicAI posted that Claude had completed the first formalized proof of Fermat's Last Theorem. The post opens with the reason anyone should care: "Checking that a major mathematical proof is correct can take years." Formalization, meaning translating a proof into something a computer can check line by line, is the known fix. It has just been too slow to do at any real scale.

The run took 11 days. Anthropic says it produced roughly 13 million lines of Lean, proved 30,300 theorems along the way, and burned about six billion output tokens. Lean checked the result against its standard axioms.

Kevin Buzzard at Imperial College London, who leads the human project that has been formalizing this same theorem, reviewed the work. @sammcallister posted his assessment, which called it an "extraordinary autoformalization achievement, which Anthropic researchers say only took 11 days."

Nobody discovered new mathematics here

Andrew Wiles proved Fermat's Last Theorem in 1995. What happened last week was translation: an existing proof, written the way mathematicians write for other mathematicians, got converted into code a proof checker can verify mechanically. Anthropic says so plainly in its own writeup.

That still matters. Peer review of a proof this size takes years of expert attention, and experts are scarce. If machines can do the formalizing, a whole category of verification work gets cheap. Buzzard's take, in the post above, is that this points toward doing the same thing to the broader mathematical literature.

The part worth an owner's attention

The first attempt failed.

Anthropic ran this with a standard multi-agent setup to start, the same general shape you would get pointing Claude Code at a big project. The agents made early progress and then came apart. They piled up local context, lost track of which pieces were already proved, and started duplicating each other's work. That is a bookkeeping failure, not a reasoning one.

What fixed it was Prove2Me, an open platform out of Columbia University that keeps a dependency graph of every theorem statement and who is working on what. Every agent reads from the same live list, so nobody re-proves something already finished and nobody wanders into a corner that connects to nothing.

The model did not change and neither did the task. What separated a dead run from 13 million lines of verified Lean was a shared source of truth sitting outside the agents.

My honest read

The press counted lines of code, but the interesting result here is about infrastructure rather than intelligence. A swarm of capable agents with no shared memory does worse than a handful of agents that can see each other's work.

The skeptics have a fair point too. Thirteen million lines is more than five times the size of Mathlib, the community library it draws on, and it takes far longer to compile. No human read it; the checker did. That is acceptable for a proof, because the checker is the authority. It is much less acceptable in other kinds of work, and it shoves the bottleneck from writing to reviewing, which is where a lot of AI output is already stacking up.

Why this shows up in ordinary businesses

Strip out the mathematics and you have a problem most owners already know from staffing. Three capable people working the same job without a shared list will duplicate half of it and drop the other half. Hiring a fourth person makes it worse. One list everybody writes to makes it better.

AI tools fail the same way, for the same reason. A shop running one assistant for quotes and another for follow-up, with no shared record between them, ends up with a pile of confident, contradictory work. The customer who already booked gets a text asking if she wants to book. The estimate goes out twice with different numbers on it.

So before you add another tool, it is worth asking where the shared list actually lives. Often it turns out to be a CRM you already pay for that nobody writes to. Occasionally there is no list at all, and finding that out is the whole project.

If you want a second set of eyes on how work moves through your business, New Face Design does a free process audit. We map what happens between a lead coming in and a job getting paid, then tell you which gaps are worth closing and which ones are fine left alone.