Fermat’s Last Theorem formalised in Lean
On 4 September 2026 Anthropic published what it called the first complete computer-checked proof of Fermat’s Last Theorem in Lean: Claude, working largely autonomously, wrote it in 11 days, 13 million lines of Lean. It is a formalisation of Wiles’s 1995 proof, not new mathematics. The repository says Lean’s kernel, the Comparator tool and a second kernel (nanoda) accepted it, with only the three standard axioms.
Why it matters
A project of this size was expected to take years (a community effort led by Buzzard has run since 2024); here it closed in 11 days. Anthropic itself stresses that what is new is verification, not mathematics. State of the claim: claimed and formalised; Buzzard’s review is given in Anthropic’s words.
State of the claim. Claimed: Anthropic’s post "Formalizing Fermat’s Last Theorem" of 4 September; read in full. Formalised in Lean: the repository github.com/anthropics/fermats-last-theorem (created 4 September 14:21 UTC, last push 24 September); its README: Lean 4.33.1, Mathlib v4.33.0, 60,475 modules built; Comparator v4.33.0 says "Your solution is okay!"; a second kernel, nanoda 0.4.13 (the authors made four small changes, which by their account neither add, remove nor weaken a typing rule), accepted an export of 1,052,234 declarations with no errors; no module contains axiom, sorry or native_decide; only propext, Classical.choice, Quot.sound. The build took 5 h 32 min and Comparator 14 h 46 min on the authors’ machine. The pass did not build the repository. The README states a limit too: no tool can check that each intermediate theorem means what its name suggests. PROOF-PATH.md, in its section on the exact strength of the named steps, says the named classical theorems (Mazur, Langlands–Tunnell, modularity lifting, Wiles, Ribet) are proved in the strength the argument needs, not in general; the statement proved is Mathlib’s FermatLastTheorem. 106 files contain material from the Imperial College project (Buzzard) and flt-regular. Checked by people: Anthropic quotes Kevin Buzzard saying the proof "proves Fermat’s Last Theorem with no assumptions other than the axioms of mathematics" and thanks him for reviewing it; his own text was not found. No dispute was found in what was read. The AI’s role. Tianyi Peng, an Anthropic researcher whose group at Columbia builds formalisation tools, set out to test it; human input was limited to occasional high-level instructions; Claude worked with dozens of agents on the Prove2Me platform, about six billion output tokens of "a general-purpose internal research model roughly comparable to Claude Fable 5.1". What the record does not claim: that anything new was proved about Fermat’s theorem; that Buzzard’s project is finished; that the pass built the proof.