Anthropic has published a landmark research paper detailing the complete machine verification of Fermat's Last Theorem using the formal proof language Lean 4. Released on September 4 and 5, 2026, under the title 'Formalizing Fermat's Last Theorem in Lean', the paper marks an extraordinary advance in automated mathematics and formal verification. Rather than relying on large teams of human mathematicians to encode logical steps by hand over many years, an autonomous multi-agent system executed the entire formalization pipeline. The artificial intelligence agents worked continuously over multiple days to construct an unbroken chain of verified deductions without manual steering.
The technical scope of the project highlights the unprecedented scaling capabilities of coordinated agent architectures. Operating across an 11-day timeframe, the autonomous multi-agent setup produced approximately 13 million lines of formal Lean code. Throughout this execution, the agents resolved more than 30,000 intermediate lemmas via the specialized proof environment Prove2Me. The system decomposed complex proof structures into granular subgoals, tested alternative hypotheses, and iteratively resolved syntax and proof errors directly against the Lean compiler.
Anthropic explicitly noted that the paper does not present a new mathematical discovery of the theorem itself. The historic proposition that no three positive integers satisfy the equation x^n plus y^n equals z^n for any integer exponent greater than two was originally solved by British mathematician Andrew Wiles in 1995. However, Wiles' landmark paper spanned hundreds of pages of advanced algebraic geometry, creating an enormous barrier for manual translation into interactive theorem provers. Anthropic's agents bridged this divide by converting the dense theoretical framework into an airtight, machine-verifiable representation.
The integrity of the machine-generated artifact has already been acknowledged by senior leaders in the formal mathematics community. Professor Kevin Buzzard of Imperial College London, who led the ongoing human collaborative effort to formalize the theorem in Lean, reviewed the output and verified the validity of the proof chain. The mathematical community has followed the announcement closely, as the multi-agent system finished within 11 days a task that human academic working groups had estimated would take years of laborious coding. Buzzard's endorsement resolves doubts regarding the consistency of the 13-million-line formal codebase.
The milestone signals a decisive shift from standard generative models toward closed-loop, verifiable symbolic reasoning systems. While conventional large language models are susceptible to factual hallucinations in open domain prose, pairing generative intelligence with rigorous proof checkers like Lean 4 enforces strict logical guarantees. Every mathematical step must be verified deterministically by the system before it is incorporated into the formal codebase. This successful demonstration points toward broad utility in mission-critical software verification, microprocessor design, and automated scientific discovery.