AI Formalizes Famous Theorem
Claude AI Model Rapidly Translates Fermat’s Last Theorem Into Computer-Verifiable Code
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The project was led by Peng Tianyi, a Tsinghua Yao Class alumnus and assistant professor at Columbia Business School, with Claude operating largely autonomously and receiving only limited high-level human input.
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Fermat’s Last Theorem states that the equation xⁿ + yⁿ = zⁿ has no positive-integer solutions when n is greater than 2. Pierre de Fermat wrote the conjecture in 1637 alongside the famous claim that he had found a proof but lacked enough space to record it.
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The formalization was difficult because Wiles’s proof is highly compressed and omits explanations that a computer needs; moreover, a single erroneous Lean statement can invalidate all later statements that depend on it.
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The theorem’s original proof attracted intense historical interest: after the Göttingen Academy of Sciences offered a prize in 1908, it reportedly received 621 incorrect proofs in the first year alone.
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Formalizing the proof makes it easier to share and removes the possibility of undetected human checking errors, because Lean verifies the logical dependencies automatically rather than relying solely on manual review.
Anthropic's Claude AI completed the first computer-verifiable formalization of Fermat's Last Theorem in just 11 days, a task experts expected to take years Tech Times. The project generated 13 million lines of code and 30,300 theorems — the largest Lean proof ever produced. Claude did not discover a new proof, but translated mathematician Andrew Wiles's famous 1995 solution into Lean, a programming language that allows computers to check every logical step Hoka News.
The breakthrough shows AI's power to assist with complex mathematics while reducing human errors In Shorts. Peng Tianyi, a Columbia Business School assistant professor and Tsinghua Yao Class alumnus, led the project with Claude operating largely on its own and receiving only limited high-level guidance. Formalizing the proof makes it easier to share and removes the risk of undetected checking mistakes, since Lean automatically verifies logical dependencies rather than relying on manual review BigGo Finance.
A 358-Year-Old Problem Finally Checkable by Machine
Pierre de Fermat wrote his famous conjecture in 1637: the equation xⁿ + yⁿ = zⁿ has no positive-integer solutions when n is greater than 2. Fermat claimed he had found a proof but lacked space to write it down Tech Times. The unsolved theorem fascinated mathematicians for centuries. When the Göttingen Academy of Sciences offered a prize in 1908, it received 621 incorrect proofs in the first year alone 36kr.
Andrew Wiles finally solved it in 1995, but his proof was highly compressed and omitted explanations that computers need to verify each step Tech Times. A single erroneous statement in Lean can invalidate all later statements that depend on it, making formalization extremely difficult. Claude's speed — completing the work in 11 days — demonstrates how AI can handle this painstaking translation work far faster than human mathematicians working manually In Shorts.
How Claude Turned Proof into Perfect Computer Code
Lean is a formal proof assistant — a programming language designed to let computers check mathematical arguments step by step Hoka News. Claude took Wiles's dense, human-written proof and translated it into Lean statements. Each claim had to be linked to earlier statements so the computer could verify the logic from start to finish.
The result: 13 million lines of code and 30,300 theorems In Shorts. This is the largest Lean proof ever built. The scale shows just how many small logical pieces Wiles's original proof contained. Claude handled this complexity with minimal human guidance, receiving only high-level direction from Peng Tianyi and his team BigGo Finance.
Why Machine-Checking Matters for Mathematics
Traditionally, mathematicians review proofs by reading and checking them manually. Errors can slip through. With Lean, the computer verifies every logical dependency automatically, eliminating undetected human mistakes Finance BigGo. The formalized proof is also easier to share and build upon, since other researchers can run it on any machine that supports Lean.
This achievement does not mean AI discovered a new solution or proved something Wiles missed. Instead, it shows AI excels at the grinding, error-prone work of translation and verification Tech Times. For mathematics, that is powerful. As more classic theorems get formalized, mathematicians gain tools that reduce mistakes and speed up their most tedious work 36kr.
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