Formalizing Fermat's Last Theorem

We present the inaugural computer-verified proof of Fermat's Last Theorem (FLT). Claude, an Anthropic AI, authored the proof in the Lean programming language over 11 autonomous days. This verification, devoid of any assumptions beyond basic mathematical axioms, confirms FLT's truth. Claude generated 13 million lines of Lean code and proved 29,500 intermediate theorems to arrive at this result.

Fermat initially conjectured FLT in 1637, stating that no positive integers a, b, c can satisfy a^n + b^n = c^n for any n > 2. The theorem remained unproven for centuries until Sir Andrew Wiles presented a 129-page proof in 1995, which took months to verify. To formalize Wiles's proof, mathematicians began encoding complex reasoning into computer-readable form, culminating in Kevin Buzzard's 2024 effort using the Lean proof assistant.

Claude's achievement surpasses expectations, demonstrating its capability to autonomously formalize FLT. The process involved writing 13 million lines of Lean and proving 29,500 intermediate theorems. Kevin Buzzard confirmed the proof's validity, stating that it verifies FLT without additional assumptions, building upon a simplified version of Wiles's original proof.

Claude's work not only validates FLT but also paves the way for a future where mathematical proofs can be readily checked, enhancing trust in the mathematical knowledge base.