Fermat's Last Theorem has been proven since 1995. Andrew Wiles spent seven years on it, published 129 pages, and won the Abel Prize. So when Anthropic published a research post on September 4 saying Claude had completed "the first formalized proof of Fermat's Last Theorem," the framing needs some unpacking before you know what to think.

Wiles proved FLT. Claude formalized it. These are not the same thing, and the distinction is the whole point.

Formalization means converting a proof into a formal language — here, Lean 4 — that a computer proof assistant can verify step by step. Every logical gap that human referees wave through has to be explicitly closed. Every implicit assumption made explicit. Wiles's proof, plus thirty years of subsequent work filling in its dependencies, had to become code that Lean 4 would accept without protest.

That is what Tianyi Peng's group at Anthropic and Columbia University did with Claude. According to Anthropic, Claude wrote 13 million lines of Lean 4, proved 29,500 intermediate theorems, and consumed roughly 6 billion output tokens over 11 days of wall-clock time. It is the largest Lean proof ever written. The computer checked it. That is a real thing.

Source spread

• Anthropic research post — Formalizing Fermat's Last Theorem [hype] — the lab's own announcement; leads with the "first formalized proof" frame, explains the Prove2Me dependency, describes the scope of the effort
• SiliconANGLE, September 4 [builder] — contextualizes the 11-day wall-clock figure; notes the first attempt failed
• Anthropic on X [hype] — lead quote: "Checking that a major mathematical proof is correct can take years. Formalization can help." Sets the purpose statement cleanly
• AI Weekly alert [builder] — summarizes the Prove2Me dependency and parallelism structure

Pros & cons

What's real:

• The formalization is real. Lean 4 accepted the proof. This is the first time any system has produced a machine-checked end-to-end formalization of FLT, and that is a meaningful threshold to clear.
• The intermediate theorem count matters. Those 29,500 theorems represent gaps that Wiles's human-readable proof left implicit — things the math community accepted on faith that Lean would not. Claude found and closed them.
• This generalizes. If the approach works on FLT — one of the most complex proofs in recent mathematical history — it likely works on other results that haven't been formalized because the effort wasn't worth it. That is the actual unlock.

What deserves scrutiny:

• "11 days" is misleading in both directions. It's wall-clock time with several dozen agents running in parallel, burning 6 billion output tokens. A single agent did not work steadily for 11 days. This was a compute-heavy parallel job; resource cost matters for reproducibility.
• The first attempt failed. Success required adding Prove2Me, a third-party open-source tool for optimizing agent decisions in long workflows. The scaffolding is load-bearing, not incidental.
• This is not mathematical discovery. No new theorem was proved. No new territory mapped. Claude did a very hard translation job; Wiles did the math.

Samwise's take

What builders need to know

• This is the most compelling evidence to date that AI agents can complete sustained, formally verifiable tasks — not generate plausible text but produce output that a separate system can check line by line. If your product has a formal verification step, this is worth studying.
• Prove2Me is open-source. If you're building agentic workflows in domains with verification layers, it's worth examining what it does to improve agent decision quality in long-running sessions.
• The 6 billion token consumption is a cost benchmark for this class of task. Sustained parallel formal verification is not cheap at current pricing. Worth knowing before pitching this approach to anyone with a fixed compute budget.
• The "dozens of parallel agents + third-party scaffolding + iterative verification" pattern is increasingly the template for hard, long-horizon tasks. Not one smart agent but a coordinated fleet. Design your orchestration layer accordingly.
• If you work in formal methods, AI-accelerated formalization is now credibly in scope for active projects. The question is no longer "can AI do this?" but "what does it cost and what scaffolding does it need?"

Further reading

• Anthropic — Formalizing Fermat's Last Theorem — the primary source; all numbers derive from here
• Anthropic on X — announcement thread — shorter framing with good context on what formalization means
• SiliconANGLE coverage — notes the Prove2Me dependency and first-attempt failure
• AI Weekly — summary — clean short read for sharing with non-math-literate stakeholders