First Complete Computer-Checked Proof of Fermat's Last Theorem Achieved

Sep 4, 2026

AI Summary

Researchers have successfully produced the first complete computer-checked proof of Fermat's Last Theorem using the Lean programming language. This achievement, completed in just 11 days, marks a significant advancement in the formalization of complex mathematical proofs and could enhance the verification process in mathematical research.

Fermat's Last Theorem states that no positive integers a, b, c satisfy aⁿ + bⁿ = cⁿ for any n > 2, a conjecture first noted by Pierre de Fermat in 1637.
The first proof of the theorem was provided by Andrew Wiles in 1995, which took months to verify.
A decade later, Jan Bergstra proposed formalizing Wiles's proof, leading to a community effort to encode it using the Lean proof assistant.
Recently, Tianyi Peng and his team at Columbia University tested the AI model Claude for formalizing FLT, resulting in a complete proof in 11 days, generating 13 million lines of Lean code and proving 29,500 intermediate theorems.
The formalization process was expected to take years, but the AI's rapid completion demonstrates the potential for formalizing large areas of mathematics.
The proof was verified using Lean's standard axioms and is now considered the largest Lean proof constructed to date.
This achievement could ease the burden of verifying new mathematical results and enhance trust in AI-generated proofs, as formalization becomes more common in mathematical research.
The project involved collaboration through Prove2Me, an open platform for formalizing mathematics, and utilized a multi-agent system to define concepts and prove theorems.
The formalization effort is part of a broader movement to integrate AI into mathematical research, with ongoing support for researchers in the field.

fermat's last theoremmathematicstheorem provingformal verification

First Complete Computer-Checked Proof of Fermat's Last Theorem Achieved

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