Claude Proved Fermat's Last Theorem in 11 Days — The First Computer-Checked Proof
In 1637, Pierre de Fermat scribbled a claim in the margin of his copy of Arithmetica that would torment mathematicians for 358 years: no positive integers a, b, c satisfy aⁿ + bⁿ = cⁿ for any n > 2. He added a note that the margin was "too narrow to contain" his marvelous proof.
It took until 1995 for Andrew Wiles to publish a correct proof — 129 pages, months of work, and a year-long gap when a critical error was discovered. In 1908, a prize of 100,000 German gold marks (~$1-2M today) was offered. Over 600 incorrect attempts were filed in the first year alone.
Now Claude has done it in 11 days.
What Claude Actually Did
Anthropic shared the first complete computer-checked proof of Fermat's Last Theorem. Claude worked largely autonomously to write the proof in Lean, a proof assistant that verifies mathematical reasoning algorithmically. The result:
- 13 million lines of Lean code — over 5x the size of Mathlib (the principal community library of formalized mathematics)
- 30,300 theorems proved along the way, with 29,500 used in the final proof
- 11 days from start to finish, with dozens of Claude agents collaborating — defining concepts, proving intermediate theorems, and building toward harder results
Dozens of Claude agents collaborated autonomously: some defined concepts, others proved intermediate lemmas, and those results were fed into higher-level theorems. Human input was limited to occasional high-level instructions from Anthropic researcher Tianyi Peng: "Jacobian as a scheme sounds high priority," "push the Mazur theorem to be done soon."
"THE FLT root reads Proved on the site. Historic moment (modulo re-check)."
"🏁🏁🏁 The FLT root reads PROVED on prove2me at 02:00:57Z Aug-18 (10:00:57pm ET Aug-17). Historic moment for this campaign."
Why This Matters
This isn't about one theorem. It's about what it means for how we verify mathematics.
Mathematical proofs are notoriously hard to check. Understanding a novel result deeply enough to be confident in its correctness can take months or years. Wiles' FLT proof required an intensive verification effort by multiple mathematicians — and they still found a critical gap that took him a year to fix.
Proof assistants like Lean solve this by verifying the logic algorithmically. The hard part has always been rewriting human proofs (which skip obvious steps and build on centuries of published work) into a form computers can check. The mathematical community expected the FLT formalization to take years — their planning blueprint alone runs 86 pages.
Claude completed it in under two weeks.
The Bigger Picture
Kevin Buzzard, the Imperial College mathematician who kicked off the FLT formalization effort in 2024, described it as an "extraordinary autoformalization achievement" and noted that the proof is now "multi-layered" — robust enough to be built upon.
This follows Claude's recent work on the Riemann hypothesis, which produced novel mathematics. The FLT result is different: what's novel isn't the math itself, but the verification — checking a proof as one would check a computation with a calculator.
The implications are profound. As AI produces ever more proofs, the ability to autoformalize means:
- Faster verification — the bottleneck shifts from human verification to AI formalization
- Crowdsourced correctness — any theorem can be independently checked, not just trusted because a few experts vetted it
- Accessible math — formalized proofs become searchable, composable building blocks
Claude's proof followed a simplified version of Wiles' proof by Darmon, Diamond, and Taylor. The code and results are open source on GitHub.
The margin was finally big enough.