Claude AI Completes Fermat’s Last Theorem Proof

Anthropic's Claude AI produces a complete computer-checked proof of Fermat’s Last Theorem in Lean after 11 days of largely autonomous work.

Anthropic says its Claude AI system produced what the company describes as the first complete computer-checked proof of Fermat’s Last Theorem in Lean after working largely autonomously for 11 days, according to a report shared by Cointelegraph.

The claim concerns one of mathematics’ most famous problems and the use of Lean, a formal proof assistant that allows mathematical arguments to be checked by computer. Anthropic’s reported result represents an application of an AI system to formal mathematical reasoning rather than simply generating an informal proof for human review.

Claude Worked Largely Autonomously for 11 Days

According to the information cited by Cointelegraph, Claude worked largely autonomously for 11 days to produce the formal proof.

The reported duration is a central part of Anthropic’s claim. Rather than describing a brief interaction in which a user asks an AI model to solve a mathematical problem, the report characterizes the work as an extended autonomous process in which Claude generated and developed the formal proof.

The proof was produced in Lean, meaning its validity can be checked computationally within the formal system. This distinction matters because computer-checked mathematics requires mathematical statements and logical steps to conform to the rules and definitions encoded in the proof assistant.

Fermat’s Last Theorem Put Into Formal Verification

Fermat’s Last Theorem states that there are no positive integers $x$ , $y$ , and $z$ satisfying $x^n + y^n = z^n$ for integers $n > 2$ .

The theorem was famously proved by Andrew Wiles in the 1990s, resolving a problem that had remained open for centuries. A modern formalization does not replace the historical proof. Instead, it translates the mathematical argument into a formal language that a proof assistant can verify step by step.

Anthropic’s reported achievement therefore relates to the formal verification of the theorem in Lean. The X-post-derived information does not provide details about the specific formalization used, the amount of human assistance involved beyond the statement that Claude worked largely autonomously, or whether the formalization has been independently reviewed.

AI and Formal Mathematics

The reported result highlights a specific use of artificial intelligence: generating formal mathematical reasoning that can subsequently be checked by software.

Formal proof systems impose strict requirements on mathematical arguments. A generated proof must satisfy the formal rules of the system rather than merely appear convincing to a human reader. That makes Lean-based verification materially different from evaluating a conventional AI-generated explanation.

The report does not establish that Claude independently discovered a new proof of Fermat’s Last Theorem. The claim concerns Claude producing a complete computer-checked proof in Lean after 11 days of largely autonomous work.

Anthropic’s reported result leaves the next point of interest in the details of the formalization and the extent to which the 11-day process can be independently reproduced and evaluated.

writer: Ethan Collins
Crypto Journalist
Ethan Collins reports on developments across the cryptocurrency and blockchain sector. His work covers market movements, protocol updates, regulatory changes, and emerging trends in digital assets.
He focuses on presenting complex topics in a clear and accessible manner for a broad readership.