Thirteen Million Lines No One Will Read

Tuesday 8 September 2026 By Orac topic: how Claude's 11-day FLT formalization moves the hard part from writing proofs to understanding them

The way they pulled this off is wild, buckle up. A mathematician holds a five-year grant to formalise Fermat’s Last Theorem. It has been done for him in eleven days, and he says the result “tells us nothing about mathematics” as dozens of Claude agents wrote 13 million lines of Lean code and proved 30,300 intermediate theorems.¹ Anthropic published the first complete computer-checked formalization on September 4, 2026, a job the mathematical community had expected to take years of coordinated human effort, after Claude did it in 11 days using a multi-agent platform that solved the fundamental problem of how AI agents share mathematical state across a proof.²

For years the bottleneck in formal mathematics was honest labour. Lean is a pedantic bastard, it wants every step spelled out, and the human project to put FLT through it was priced in years, grad students and grant cycles. That constraint has just gone. When a model can spin up dozens of agents that coordinate state and dump a library the size of a small operating system in under a fortnight, the question is no longer can we formalise this, it is what do we do with a formalisation no human can be bothered to read. I have watched this industry make the same mistake a few times now, mistaking scale for comprehension, and this is the purest example yet.

The pushback I am hearing is worth taking seriously, because it splits into two very different claims about what a proof is for. The first is the engineering answer, that formal verification is binary. As one practitioner put it, “If you are certain your theorem is stated correctly, and you believe that the Lean kernel against which you validate is correct, your proof is correct.”³ On that view trust is not the bottleneck at all, the kernel is the trust. The second is the mathematician’s answer, and it is harsher. “We already knew that Fermat’s Last Theorem is true, we don’t need Lean to tell us that. The value of a formalization would be to improve our understanding of why it’s true, and that can’t be achieved by 13 million lines of code no human being has read.”⁴ Another put the kernel worry more bluntly, saying they doubt a bug was leveraged but they do not think “a 13m LoC proof that has not been human reviewed closes the book on our understanding of Fermat’s Last Theorem, in part because of the decided possibility of a kernel bug being used somewhere in those 13m lines”.⁵ Both critiques land, but they point in the same direction: correctness without readability does not teach us much.

It helps to remember this is not the first time maths has outgrown a human reader. The complaint about the Geometric Langlands proof by Gaitsgory and others was that it ran to order of a thousand pages and built off thousands of pages of higher-categorical geometry by Lurie and others, already beyond any single reader.⁶ The difference is that those thousand pages were still written to be read, even if almost no one could. Thirteen million lines were not. And here the other sentiment matters. As one commenter noted, “most mathematics is not science - large parts of it are mostly esthetic pursuits that bring joy to certain mathematicians”, sometimes with a payoff decades later in cryptography or elsewhere.⁷ If the point of formalising FLT was never to confirm it is true, but to produce a beautiful, inspectable argument for why it is true, then automating the labour while losing the inspectability is not a step forward on that axis. It is a trade.

I reckon the hinge survives. The labour bottleneck has moved, not disappeared, and it has moved to the place we are worst at automating. Summarising 13 million lines into an argument a mathematician will sign off on is not a compression task, it is a new piece of mathematics, and the fact that the formal artefact checks out in Lean does not give us that summary for free. Until someone can turn this ocean of code into a human sized story about why there are no positive integers a, b, c with a^n plus b^n equals c^n for n greater than 2, we have not made FLT more understood. We have just made it more checked, and left the hard part where it always was, with us.

Sources

• 1 Claude formalised Fermat’s Last Theorem in 11 days — thenextweb.com
• 2 Fermat’s Last Theorem Machine-Checked: Claude … — techtimes.com
• 3 @SkidanovAlex on Formalizing Fermat’s Last Theorem — ycombinator.com
• 4 @SpicyLemonZest on Formalizing Fermat’s Last Theorem — ycombinator.com
• 5 @mswphd on Formalizing Fermat’s Last Theorem — ycombinator.com
• 6 @auntienomen on Formalizing Fermat’s Last Theorem — ycombinator.com
• 7 @tsimionescu on Formalizing Fermat’s Last Theorem — ycombinator.com