Claude formally verifies Fermat's Last Theorem in 11 days

Overview

Updated 5 days ago

Fermat's Last Theorem waited 358 years for a proof. Andrew Wiles supplied one in 1995. In August 2026, Anthropic's Claude AI produced a computer-verified version of that proof in 11 days, writing 13 million lines of Lean code and proving 29,500 intermediate theorems along the way.

The mechanics matter more than the headline. Claude didn't discover new mathematics; it formalized Wiles's known proof, converting it into a form a computer can check line by line. That conversion has historically been mathematics' slowest step—a funded Imperial College London project to do for FLT what Claude just did was budgeted until 2029.

Why it matters

Verification is mathematics' slowest step. If AI can check FLT in 11 days, new proofs will be checked at machine speed.

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Key Indicators

11 days

Days Claude worked autonomously

From run start to the closing theorem card marked proved.

13 million

Lines of Lean code written

Over five times the size of Mathlib, the community proof library it builds on.

29,500

Intermediate theorems proved

Roughly 30,000 theorem cards in the dependency tree, each with a machine-checked proof.

129 pages

Length of Wiles's 1995 proof

The human proof Claude formalized, verified over months of painstaking work.

Voices

Curated perspectives — historical figures and your fellow readers.

Ever wondered what historical figures would say about today's headlines?

People Involved

Tianyi Peng

Anthropic researcher and Prove2Me designer

Led the Claude formalization attempt

Kevin Buzzard

Professor of pure mathematics, Imperial College London

Leads the competing human formalization project, now effectively overtaken

Andrew Wiles

Mathematician, proved Fermat's Last Theorem in 1995

Author of the proof Claude formalized

Organizations Involved

Anthropic

AI Company

Produced the formalization with Claude

AI company that developed Claude, the model that produced the 11-day formalization of Fermat's Last Theorem.

Lean 4 and Mathlib

Proof assistant and community library

Infrastructure the proof builds on

Lean 4 is a proof assistant, a computer program that checks mathematical arguments line by line. Mathlib is its community library of formalized mathematics.

Imperial College London FLT project

Academic research project

Ongoing human-led formalization effort, now overtaken by Claude

Funded project, budgeted at 934,000 GBP to 2029, to formalize Fermat's Last Theorem in Lean by human effort.

Prove2Me

Software platform

Orchestrated the multi-agent work

Open collaborative platform for formalizing mathematics, designed by Tianyi Peng's group at Columbia University.

Timeline

1637 September 2026

6 events Latest: 7 days ago

Tap a bar to jump to that date

September 2026
Independent recheck begins
Latest Verification

Team recompiles all 29,511 theorem cards from source, confirming the three-axiom build.
7 days ago
Anthropic announces completion
Announcement

13-million-line Lean proof with no placeholders; Buzzard posts 'Anthropic has beaten me to it.'
September 4th, 2026
August 2026
Claude's run begins on Prove2Me
Milestone

After earlier multi-agent attempts failed, the run routes work through Prove2Me.
August 24th, 2026
2024
Human formalization begins
Milestone

Imperial College London project and flt-regular start formalizing FLT in Lean.
2024
1995
Wiles publishes his proof
Historical

Andrew Wiles publishes the 129-page proof, verified over subsequent months.
1995
1637
Fermat jots the theorem in a margin
Historical

Pierre de Fermat claims a proof exists but doesn't write it down.
1637

Scenarios

Claude's FLT proof enters Mathlib

Possible Resolves by Q2 2027

Discussed by: Lean FRO, Mathlib maintainers

Anthropic's proof is too sprawling for Mathlib's standards, over five times the library's size and mostly machine-written. If Anthropic works with the Lean community to de-duplicate it, the deep theorems (Mazur, Ribet level-lowering, the 3–5 switch, R=T) become reusable community assets, shortening every future formalization that needs them.

Independent verification confirms the proof tree

Likely Resolves by Jan 31, 2027

Discussed by: Lean FRO comparator tool, Anthropic's own recheck

Anthropic says it recompiled all 29,511 theorem cards from source off-platform and ran two third-party checking tools. The result stands formally if external mathematicians independently rebuild and check the full proof tree, confirming no unproved placeholders and only Lean's three standard axioms.

AI formalizes a theorem humans never proved

Uncertain Resolves by Q2 2028

Discussed by: Kevin Buzzard, Tianyi Peng, automation skeptics

Buzzard notes Claude's work adds nothing mathematically, since it formalizes Wiles's known route. The open test is whether the technique transfers to genuinely new mathematics, an AI proof of an unproven result or a new simpler proof of FLT. That would mark the real break, turning autoformalization from a verification tool into a discovery engine.

Historical Context

3 moments from history that rhyme with this story — and how they unfolded.

1976

Four Color Theorem (1976)

Kenneth Appel and Wolfgang Haken used a computer to check 1,936 configurations and prove the map theorem. It was the first major theorem that depended on a computer, and mathematicians debated for years whether a proof no human could check by hand counted as proof.

Then

The theorem was eventually accepted, but the controversy forced mathematicians to confront the role of computation.

Now

It opened the door to computer-assisted proof, which is now routine in combinatorics.

Why this matters now

The same doubt attached to computer-generated math now follows AI-generated proofs, though Lean's line-by-line checking removes any question about gaps.

2003–2014

Flyspeck / Kepler Conjecture (2003–2014)

Thomas Hales's 1998 proof of Kepler's conjecture about sphere packing was rejected by reviewers who could not verify it. The Flyspeck project spent 11 years formalizing the proof in machine-checkable form, confirming it with certainty.

Then

Flyspeck succeeded in 2014 after more than a decade of coordinated human effort.

Now

It showed that formal verification of a deep result, while possible, was slow enough to scare off most mathematicians.

Why this matters now

Human formalization of Hales's theorem took 11 years. Claude formalized a deeper theorem in 11 days, a reduction in time of three orders of magnitude.

2021–2022

Liquid Tensor Experiment (2021–2022)

Field medalist Peter Scholze challenged the Lean community to formalize one of his theorems as a stress test. A team of volunteers completed the work in about a year, and Scholze reported the result strengthened his confidence in the mathematics.

Then

The proof was accepted and became a landmark demonstration of modern proof assistants.

Now

It showed that frontier mathematics was within reach of formalization, but only with substantial expert human labor.

Why this matters now

A theorem Scholze considered formalization-worthy took a year of human work. FLT, a far deeper result, was formalized by AI agents in under two weeks.