Claude AI Completes Fermat's Last Theorem Machine Proof in 11 Days, Called the Longest Mathematical Proof to Date
Anthropic announced that its internal research version model, roughly equivalent to Claude Fable 5.1, completed a full formal proof of "Fermat's Last Theorem" in 11 days, generating a total of 13 million lines of Lean language code, making it the longest mathematical proof to date.
Fermat's Last Theorem was proposed by French mathematician Pierre de Fermat in 1637, stating that there are no positive integer solutions for aⁿ + bⁿ = cⁿ when n is greater than 2. This conjecture was first rigorously proven by British mathematician Andrew Wiles in 1995, with a paper spanning 129 pages.
Anthropic did not make new mathematical discoveries but rather "formalized" Wiles' original proof, rephrasing and verifying the entire proof chain using the Lean proof assistant language, which can be verified line by line by computers. During this process, 30,300 intermediate theorems were verified, with 29,500 ultimately included in the complete proof, consuming about 6 billion output tokens.
The project utilized a scheduling tool called "Prove2Me" to manage the dependencies between theorems in a directed acyclic graph structure, with dozens of Claude agents working in parallel. The statements of theorems were separated from the specific proof processes to enhance compilation efficiency. The project was led by Anthropic researcher Tianyi Peng (in collaboration with Columbia University) and built upon a formalization project initiated by mathematician Kevin Buzzard at Imperial College London. It also utilized the community-maintained mathematical formalization library Mathlib and the infrastructure of the non-profit Lean FRO, referencing 106 upstream files in GitHub submissions.
Buzzard confirmed after review that the proof "does not depend on any other assumptions besides the mathematical axioms themselves," and a comparison tool confirmed that the theorem statements in the proof matched the official versions in Mathlib. The complete proof has been uploaded to GitHub for independent verification, with Buzzard calling it a "historic moment (pending verification)."
The formalization work was completed between August 7 and 18, 2026, taking 11 days. The article also mentioned that the previous formalization project led by Buzzard at Imperial College has not yet been completed since its launch in 2024, with about 7% of the final generated code belonging to previously attempted failed or duplicated parts.
Source: Public Information
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This is not the first time Anthropic has used Claude to tackle mathematical problems—earlier this July, the company’s research team revealed that Claude (then known as Fable 5) assisted in solving a mathematical conjecture that had existed for 87 years. Subsequently, a team of Nobel Prize-winning physicists used Claude to solve a decades-old mathematical problem. This formalization project of Fermat's Last Theorem continues to signal Anthropic's consistent messaging this year that "Claude possesses top-tier mathematical research capabilities," similar to how OpenAI and DeepMind have previously showcased model capabilities in the International Mathematical Olympiad and geometric theorem proofs.
The direct commercial value of such mathematical proof demonstrations is limited, but the capital significance lies in establishing verifiable, hard indicators of model capabilities that are difficult to fake—compared to scores and user evaluations, mathematical formalization proofs that can be publicly verified by independent scholars (like Buzzard) are more trustworthy for institutional investors and corporate clients. Anthropic leverages this to strengthen its differentiated positioning against OpenAI and Google DeepMind in "high-value reasoning tasks," accumulating trust assets for future pricing negotiations in high-end markets such as enterprise-level research and financial modeling.
This aligns with the capability demonstration curve seen in DeepMind's AlphaProof and AlphaGeometry, which previously achieved gold-level performances on mathematical competition problems—by making breakthroughs on human-recognized difficult and objectively verifiable intellectual tasks, they demonstrate that model reasoning capabilities have entered a new stage. The current large model industry is transitioning from "chat assistants" to "research collaboration tools," and mathematical formalization proofs are particularly easy for professional communities to objectively verify and difficult to question as "score inflation" scenarios.
Essentially, this represents a "technological substitution"—mechanistically, traditional formal verification of mathematical proofs previously required teams of mathematicians to spend years manually checking line by line (as seen in Buzzard's team project that started in 2024 and is still incomplete). In contrast, Claude compresses this work, originally measured in "man-years," into 11 days through parallel processing by dozens of agents and directed acyclic graph task scheduling. This marks the beginning of AI massively replacing mathematical labor that heavily relies on repetitive logical checks, while the core value of human mathematicians will further concentrate on proposing new conjectures and designing proof strategies in original judgment processes.
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Results that can be independently verified are worth more than scores that can be inflated.
Machines will always replace repetitive checks, leaving humans to pose questions.
The formalization completed in 11 days does not buy a mathematical breakthrough, but rather trust in capability.