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Claude formally verifies Fermat's Last Theorem in 11 days

Claude formally verifies Fermat's Last Theorem in 11 days

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Anthropic's machine-checked Lean proof follows Wiles's 1995 argument

2 days ago: Independent recheck begins

Overview

Updated 2 hours 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.

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People Involved

Organizations Involved

Timeline

1637 September 2026

6 events Latest: 2 days ago
Tap a bar to jump to that date
  1. Independent recheck begins

    Latest Verification

    Team recompiles all 29,511 theorem cards from source, confirming the three-axiom build.

  2. Anthropic announces completion

    Announcement

    13-million-line Lean proof with no placeholders; Buzzard posts 'Anthropic has beaten me to it.'

  3. Claude's run begins on Prove2Me

    Milestone

    After earlier multi-agent attempts failed, the run routes work through Prove2Me.

  4. Human formalization begins

    Milestone

    Imperial College London project and flt-regular start formalizing FLT in Lean.

  5. Wiles publishes his proof

    Historical

    Andrew Wiles publishes the 129-page proof, verified over subsequent months.

  6. Fermat jots the theorem in a margin

    Historical

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

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.

Sources

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