Claude AI completed the first formalized proof of Fermat’s Last Theorem, delivering a machine‑verifiable formalization that represents the theorem in a form a computer can process for verification. The project was completed in 11 days and produced 13 million lines of code in total, all intended for line‑by‑line computer checking and constituting the first fully formalized, machine‑checkable encoding of the theorem.
Fermat’s Last Theorem posed a centuries‑old mathematical challenge, asserting that no three positive integers a, b, c satisfy an + bn = cn for any integer n greater than 2. In 1908 a German prize for the first valid proof attracted 621 wrong submissions in its first year, and that prize would be worth roughly $1 million to $2 million in today’s money. A full mathematical proof was published by Andrew Wiles, with contributions from Richard Taylor, culminating in a corrected 129‑page proof released in May 1995. The corrected publication in May 1995 is identified in the record as the real proof.
Claude AI carried out a project to formalize Fermat’s Last Theorem by translating the theorem into Lean, a language that computers can verify for formal proofs and that enables machine checking. The project produced 13 million lines of machine‑checkable code that a computer can inspect line by line, and the total work was completed in 11 days. The resulting formalized proof is described as the first of its kind and constitutes a fully formalized, machine‑checkable encoding of Fermat’s Last Theorem. The project output is intended for automated, line‑by‑line verification and represents the theorem and its supporting arguments encoded in Lean. Last month Claude completed the first formalized proof of Fermat’s Last Theorem.
In 2024 Kevin Buzzard of Imperial College London started a project to translate Andrew Wiles’s proof of Fermat’s Last Theorem into Lean, the proof‑assistant language that enables computer verification of formal proofs. The project’s outline runs 86 pages, and funding for the effort is locked in through 2029.
The work centers on formalization using proof assistants and on producing a machine‑checkable encoding of Wiles’s arguments in Lean, producing detailed formal code intended for automated checking. Related activity has involved volunteer mathematicians contributing to the formalization and verification process and other volunteers.
Claude AI completed the first formalized proof of Fermat’s Last Theorem by translating the theorem into the Lean language, producing 13 million lines of machine‑checkable code and finishing the work in 11 days. The corrected 129‑page proof published by Andrew Wiles with contributions from Richard Taylor in May 1995 remains the established mathematical proof, and Claude’s output constitutes a fully formalized, machine‑checkable encoding of the theorem produced in a proof‑assistant language.
