Claude Achieves First Machine-Checked Formalization of Fermat's Last Theorem in Lean

by Editorial Team Share Add us on Google Pierre de Fermat scribbled a note in the margin of a math textbook in 1637, claiming he had a proof that was too large to fit in the space. It took 358 years for a human to actually prove him right. Now an AI has done something arguably harder: translating that proof into language a computer can verify, line by line, with zero ambiguity. Anthropic’s Claude has produced the first complete machine-checked formalization of Fermat’s Last Theorem using Lean 4, a proof assistant that functions like a brutally honest math teacher who refuses to let you skip any steps. The formalization covers over 29,511 theorems and 1,450 definitions, all verified through Lean’s kernel without relying on axioms outside the standard Mathlib foundations. [...] Share Add us on Google by Editorial Team Pierre de Fermat scribbled a note in the margin of a math textbook in 1637, claiming he had a proof that was too large to fit in the space. It took 358 years for

"Checking that a major mathematical proof is correct can take years. Formalization — converting the mathematical reasoning into a form computer proof assistants like Lean can verify — can help. Last month, Claude completed the first formalized proof of Fermat's Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written. Fermat's Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized. We see this as a major step in [...] On September 5, 2026, Anthropic announced that Claude had completed the first fully formalized, machine-checked Lean 4 proof of Fermat's Last Theorem — a project the company says experts thought

Formalizing a proof means translating it into a language so painfully literal that a computer can verify every step on its own without entering into subjectivities. Mathematicians have been bad at policing this for a while. A 1908 German prize worth roughly $1 million to $2 million in today's money, offered for the first valid proof of the theorem, drew 621 wrong submissions in its first year alone. Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat's Last Theorem, one of… pic.twitter.com/pdT8zwlV4A — Anthropic (@AnthropicAI) September 4, 2026

## Alexander Kruel's Post ### Alexander Kruel 3h · Anthropic: "Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written.

Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written. Fermat’s Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized. We see this as a major step in the [...] Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last mo

Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer