Claude formalizes Fermat's Last Theorem in 11 days
Anthropic agents autoformalized a massive math proof in 11 days, proving AI can now rigorously verify complex human logic.
Research · Source: Hacker News
What happened
Anthropic researchers used Claude to formalize Fermat's Last Theorem into the Lean programming language. The AI worked largely autonomously over 11 days. It generated a staggering 13 million lines of code to complete the task. The original proof by Andrew Wiles ran 129 pages, and a human formalization effort started in 2024 was expected to take years. Claude finished it in less than two weeks.
The system relied on a multi-agent harness and an open collaborative platform called Prove2Me. Prove2Me maintained a directed acyclic graph of theorem statements. This kept the AI agents on track and allowed them to work in parallel without losing memory context. Early attempts failed when agents lost track of state and stopped collaborating. The successful run consumed roughly six billion output tokens from an internal model comparable to Claude Fable 5.1.
The final output was verified by the Lean proof assistant using only the three standard axioms of mathematics. Claude successfully proved 29,500 intermediate theorems to reach the final goal. Human input was limited to occasional high-level steering from researcher Tianyi Peng. The resulting proof is over five times the size of Mathlib.
Key facts
- 11 days — Time it took Claude to formalize the proof
- 13 million — Lines of Lean code written by Claude
- 29,500 — Intermediate theorems used in the final proof
- 6 billion — Output tokens consumed by the internal research model
- 5x — Size of Claude's proof compared to Mathlib
Why it matters
Mathematical verification is a massive bottleneck. Human peer review for complex proofs takes years and still leaves room for critical errors. By automating formalization, we can instantly check math exactly like we check code compilation. This turns a slow and subjective human process into a fast and objective computational one.
The second-order effect is a massive acceleration in AI-generated mathematics. AI models are producing more purported proofs than ever before. If AI can generate novel math, humans cannot possibly review it all manually. Autoformalization means AI models can now rigorously check their own work. This creates a closed-loop system where AI proposes and mathematically proves new discoveries without human bottlenecks. We can scale mathematical discovery without sacrificing trust.
For builders
Build domain-specific agent scaffolds
Anthropic succeeded because they used Prove2Me to manage state via a directed acyclic graph. Raw models lose context quickly on long tasks. Structured scaffolding allows agents to collaborate on massive projects without degrading. Builders who create these specialized harnesses will capture massive value.
Consumer AI plans are enough
Anthropic formalized Vinogradov's Three Primes Theorem in three days using just three consumer Claude Max subscriptions. You do not need massive compute clusters to achieve breakthrough results. Smart architecture and collaborative platforms beat raw compute for complex reasoning tasks.
Automated verification markets
The ability to autoformalize logic opens doors for automated auditing tools beyond pure math. Startups can build products that translate complex legal, financial, or engineering logic into formal languages. Companies paying expensive human auditors will eagerly adopt software that mathematically guarantees correctness.
My take
I have been saying that scaffolding is where the real magic happens. Claude did not achieve this alone. It needed a directed acyclic graph to keep its memory intact and coordinate multiple agents. Stop waiting for a god model to solve your problems. Start building robust infrastructure around the models we already have today.
Original reporting: Hacker News. This is my rewrite and opinion.