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How Claude Formalized Fermat’s Last Theorem in Lean in 11 Days
Anthropic says Claude agents formalized an existing Wiles style proof of Fermat’s Last Theorem in Lean in 11 days, generating about 13 million lines of code and 29,500 theorems used in the final chain. The reported breakthrough depended on coordinating dozens of agents through Prove2Me, which tracked theorem depende...
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Key takeaways
- Anthropic says Claude agents formalized an existing Wiles style proof of Fermat’s Last Theorem in Lean in 11 days, generating about 13 million lines of code and 29,500 theorems used in the final chain.
- The reported breakthrough depended on coordinating dozens of agents through Prove2Me, which tracked theorem dependencies and helped the system divide a huge formalization into workable tasks.
- Lean can check the encoded derivation rigorously, but mathematicians still need to assess whether formal definitions faithfully capture the intended informal mathematics.
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openai.comCreate a landscape editorial hero image for this Studio Global article: How did Anthropic’s Claude reportedly produce the first end-to-end Lean-verified formal proof of Fermat’s Last Theorem in 11 days—including. Article summary: Anthropic says Claude did not discover a new proof of Fermat’s Last Theorem (FLT); it formalized an established Wiles-style proof in Lean so that a proof assistant could check every encoded logical step. The reported ach. Topic tags: general, general web, user generated. Style: premium digital editorial illustration, source-backed research mood, clean composition, high detail, modern web publication hero. Use reference image context only for broad subject, composition, and topical grounding; do not copy the exact image. Avoid: logos, brand marks, copyrighted characters, real person likenesses, fake screenshots, UI text, readable text, watermarks, charts with fak
Anthropic reported on September 4, 2026 that Claude had produced what it describes as the first complete, end-to-end computer-checked Lean proof of Fermat’s Last Theorem (FLT). The striking result was not the discovery of a new route through number theory. Rather, it was the conversion of an established proof strategy into a formal artifact that Lean can verify step by step. 15
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The crucial distinction: formalization, not discovery
Fermat’s Last Theorem states that there are no positive integer solutions to
[
a^n + b^n = c^n
]
for integers (n > 2). Pierre de Fermat wrote the claim in the 17th century, and Andrew Wiles’s proof—completed with Richard Taylor—settled it in the 1990s. 10
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Claude’s work does not replace or supersede that mathematics. It reportedly formalizes a presentation of the Wiles strategy by Henri Darmon, Fred Diamond, and Richard Taylor, following a route that includes Frey curves, Ribet’s theorem, and Taylor–Wiles patching. 3 In plain terms, the system translated a proof already accepted by mathematicians into Lean 4, a language in which every required inference must be stated precisely enough for software to check.
That distinction matters. A new proof would introduce new mathematical ideas; a formalization makes an existing argument machine-checkable. Both are difficult, but they are different achievements.
What Claude reportedly built
Anthropic says the work took 11 days of largely autonomous operation. The project generated roughly 13 million lines of Lean code and proved about 30,300 theorems, with approximately 29,500 intermediate results used in the final proof dependency chain. 15
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Reports describe the codebase as more than five times the size of Mathlib, Lean’s major community-maintained mathematics library. 8
9 That scale helps explain why this was not simply a matter of asking one model to write a proof in a single session. The central challenge was project coordination: identifying prerequisites, preserving completed work, and ensuring that thousands of formal statements fit together.
How a multi-agent system tackled the proof
The reported workflow used dozens of Claude agents alongside Prove2Me, an open collaborative platform developed by Tianyi Peng and Columbia collaborators. 3
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Early attempts reportedly ran into a familiar limitation of agentic systems: individual agents could make local progress but lacked a reliable shared view of the overall project. Prove2Me addressed that problem by maintaining a directed acyclic graph of theorem goals and dependencies. This allowed agents to:
- identify which missing lemmas blocked higher-level goals;
- select useful subproblems that could be worked on in parallel;
- record and reuse completed results; and
- retain project-level structure even when individual agents had limited working memory.
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This coordination layer appears to be the key technical lesson. The system’s accomplishment was not only generating Lean syntax; it was managing a vast network of interdependent formal tasks until a complete chain reached the target theorem.
Human involvement was reportedly limited chiefly to high-level prioritization rather than supplying the detailed formal proofs themselves. 15
4 That makes the project a notable example of agents operating over a long horizon while being guided by a shared representation of the work.
What Lean verification guarantees—and what it does not
Lean’s role is essential. Once the formal proof is expressed in Lean, the proof assistant checks whether the target theorem follows from the encoded definitions, imported results, and its accepted foundational axioms. Anthropic’s reported result was checked in this sense, rather than being accepted because an AI or a human reader found a prose argument persuasive. 15
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That is a powerful form of verification: an omitted logical step cannot be waved through as “obvious” if Lean cannot establish it.
But formal checking has a boundary. Lean verifies the formal statement and derivation that it is given. Mathematicians must still evaluate whether the chosen definitions accurately represent the intended objects, whether the formal theorem matches the informal claim, and whether the overall formalization is understandable and maintainable. 3 Machine checking strengthens mathematical review; it does not make expert judgment unnecessary.
Why mathematicians see a milestone
Kevin Buzzard, who has been involved in community efforts to formalize FLT, characterized the project as an “extraordinary autoformalization achievement.” Reports on his reaction emphasize that the result adds no new mathematics to Wiles’s proof, but demonstrates the potential to formalize substantial bodies of modern mathematical literature. 13
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The immediate implication is practical: formalization can make long, technically dense arguments more resistant to hidden gaps and easier to reuse as dependable infrastructure. A formally checked result can become a building block for later work without requiring every subsequent researcher to re-audit every low-level inference.
The broader implication is about the shape of AI mathematics. Earlier systems often focused on proposing ideas, solving individual problems, or filling isolated proof gaps. This project suggests that coordinated agents can also undertake large-scale formal engineering: breaking down a mathematical program, constructing its dependency graph, and producing a machine-checked result at a scale that would ordinarily demand extensive human collaboration. 2
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A major result with an important caveat
The most accurate takeaway is neither “AI proved Fermat’s Last Theorem” nor “nothing happened.” Wiles’s argument remains the intellectual foundation of the proof. Yet translating that argument into an end-to-end Lean artifact of this size, in the reported time frame, is a substantial advance in automated formalization. 3
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Its long-term value will depend on independent inspection, the usability of the generated library, and whether similar systems can formalize other difficult results while preserving semantic fidelity. If they can, proof assistants may become not just final checkers for elite mathematical results, but increasingly normal tools for constructing, reviewing, and maintaining them.
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What is the short answer to "How Claude Formalized Fermat’s Last Theorem in Lean in 11 Days"?
Anthropic says Claude agents formalized an existing Wiles style proof of Fermat’s Last Theorem in Lean in 11 days, generating about 13 million lines of code and 29,500 theorems used in the final chain.
What are the key points to validate first?
Anthropic says Claude agents formalized an existing Wiles style proof of Fermat’s Last Theorem in Lean in 11 days, generating about 13 million lines of code and 29,500 theorems used in the final chain. The reported breakthrough depended on coordinating dozens of agents through Prove2Me, which tracked theorem dependencies and helped the system divide a huge formalization into workable tasks.
What should I do next in practice?
Lean can check the encoded derivation rigorously, but mathematicians still need to assess whether formal definitions faithfully capture the intended informal mathematics.