Anthropic's Claude Formally Proves Fermat's Last Theorem

Anthropic has successfully used a multi-agent system powered by an internal research model comparable to Claude Fable 5.1 to produce the first end-to-end, computer-verified proof of Fermat's Last Theorem. Operating over an 11-day period, dozens of coordinated Claude agents generated a massive proof spanning 13 million lines of Lean 4 code. This output, which is more than five times the size of the community mathematical library Mathlib, contains 29,500 intermediate theorems. The entire process consumed approximately six billion output tokens.

To prevent the agents from losing track of the project's state, researchers from Anthropic and Columbia University utilized a coordination platform called Prove2Me. This system managed the agent swarm using a directed acyclic graph of theorem statements, separated proofs into individual files to accelerate Lean compilation, and provided natural-language descriptions of theorems so agents could locate lemmas semantically. Human intervention was kept to a minimum, consisting of occasional high-level guidance from researcher Tianyi Peng. The agents successfully navigated the complex Darmon-Diamond-Taylor exposition of Andrew Wiles's original proof, which involves Frey curves, Ribet's theorem, and Taylor-Wiles patching.

The resulting proof was verified using Lean's standard kernel and nanoda, an independent Rust-based kernel, relying solely on Lean's three standard axioms without any placeholders or escape hatches. Replicating the build from scratch requires roughly five and a half hours on a 96-core system with a 153 GB memory peak, while the independent kernel replay takes an additional 15 hours on a single core. Although the generated code is highly verbose and contains about 7 percent leftover lines from failed attempts, mathematicians like Kevin Buzzard of Imperial College London suggest this achievement transitions autoformalization from a research novelty into a practical tool for auditing mathematical literature and verifying AI-generated proofs.

In a separate, smaller test of the Prove2Me infrastructure, researchers used three personal Claude Max plans to formalize applications of the Hardy-Littlewood Circle Method. Working through the platform, these agents successfully formalized Vinogradov's Three Primes Theorem in just three days, demonstrating that the underlying coordination framework is key to unlocking these complex mathematical capabilities.