Claude Proves Fermat's Last Theorem for the First Time with Tsinghua Talents

A landmark claim, and what “proved” means here

Anthropic’s new claim is extraordinary, but it needs to be read precisely: Claude has not discovered a brand-new human mathematical route that replaces Andrew Wiles’s 1995 breakthrough; it has produced what Anthropic describes as the first complete end-to-end, computer-checked formal proof of Fermat’s Last Theorem in Lean [1]. That distinction matters. Fermat’s Last Theorem was already proved by Wiles, with Richard Taylor helping repair the crucial gap, and the theorem has been accepted by mathematicians for decades. The new step is that an AI system has turned the logical architecture of that proof tradition into machine-checkable code, so that a proof assistant can verify the chain of reasoning line by line [1].

According to Anthropic, Claude worked largely autonomously for 11 days and wrote 13 million lines of Lean code while producing 30,300 computer-verifiable theorems, 29,500 of which were used in the final proof [1]. The company says the finished formalization was checked by Lean, used only Lean’s three standard axioms, and was also compared against Mathlib’s statement of Fermat’s Last Theorem [1]. TechNewsReel, summarizing the announcement, described the result as the first complete computer-checked proof of the theorem and emphasized that the output was generated by Claude over an 11-day period [3].

The theorem itself is simple to state and historically enormous: for any integer exponent greater than 2, there are no positive integers a, b and c satisfying aⁿ + bⁿ = cⁿ [1]. Fermat wrote the claim around 1637, and generations of mathematicians tried to prove it until Wiles’s proof was accepted in 1995 [1]. That long history is why the latest development is being treated less as a new theorem and more as a potential turning point for computational proof methods.

The Tsinghua link: Tianyi Peng and the Yao Class

The Chinese technology outlet 36Kr Europe highlighted the role of Tianyi Peng, describing him as a top talent from Tsinghua University’s Yao Class who studied there from 2013 to 2017 before pursuing doctoral work at MIT and later working as an assistant professor at Columbia Business School and as a researcher at Anthropic [2]. In Anthropic’s own account, Peng is the researcher whose Columbia group builds tools for AI formalization and who set out to test whether Claude could make progress on formalizing Fermat’s Last Theorem [1].

That background is more than a biographical note. The result was not simply a chatbot being asked to “prove Fermat.” Anthropic describes a structured research workflow in which dozens of Claude agents collaborated to define mathematical concepts, prove intermediate results and build toward harder statements [1]. Peng’s team used Prove2Me, an open collaborative platform for formalizing mathematics, to organize the project and prevent the agents from losing the state of a very large proof [1]. 36Kr framed the work as a breakthrough in which “top talents” from Tsinghua’s Yao Class stepped into one of the most symbolic achievements in modern AI-assisted mathematics [2].

The human contribution was therefore strategic rather than line-by-line manual proof-writing. Anthropic says human input was limited to occasional high-level instructions, including directions about prioritizing the Jacobian variety as a scheme and advancing Mazur’s theorem [1]. That is a major part of the story: Claude supplied the scale and the code, but the scaffolding, project management and mathematical guidance came from researchers who knew how to make a proof assistant, a theorem library and an LLM-agent system work together.

Why Lean and formalization matter

Formalization means translating a mathematical proof into a language that a proof assistant can check mechanically. In this case the language was Lean, a system used in modern formal mathematics projects [1]. Human mathematical writing relies on expertise, convention and omitted “obvious” steps; Lean requires every logical step to be explicit enough for a kernel to verify. That makes formalization powerful but brutally demanding.

Anthropic notes that the community expected the formalization of Fermat’s Last Theorem to take years, and that an existing blueprint for an initial phase of the project alone ran to 86 pages [1]. Claude’s 11-day result, if it stands up to continuing scrutiny, changes the perceived cost curve. It suggests that large language models, when embedded in the right infrastructure, may be able to convert major portions of modern mathematical literature into checkable form far faster than previously assumed.

The size of the output is also central. Anthropic says Claude’s 13 million lines of Lean made the proof more than five times the size of Mathlib, the principal Lean mathematical library on which the theorem builds [1]. That is both impressive and awkward. It demonstrates scale, but it also means the proof is not a compact human exposition. For mathematicians, the point is not that the AI wrote elegant prose; it is that the Lean kernel accepted the relevant formal statements.

This is why Anthropic and outside commentators are emphasizing verification rather than discovery. A formal proof can reduce uncertainty in places where traditional peer review is stretched by complexity. TechNewsReel argued that such machine-readable proof work could reduce the burden on human referees and help identify errors in the broader body of mathematical literature [3]. That argument echoes Anthropic’s own claim that autoformalization may help mathematicians keep up as AI-generated proofs become more common [1].

Prove2Me as the hidden infrastructure

Anthropic’s account makes clear that the early attempts did not work smoothly. The company says initial Claude agents lost track of project state and failed to collaborate effectively; those failed efforts contributed about 7% of the non-boilerplate lines in the final proof [1]. The turnaround came when the project moved to Prove2Me, which maintained a directed acyclic graph of theorem statements, separated statements from proofs to speed compilation, and kept natural-language descriptions to help agents search and reuse earlier results [1].

That is an important lesson for the next generation of AI mathematics. The breakthrough was not just “a smarter model.” It was a system: a general-purpose internal research model comparable to Claude Fable 5.1, a Claude Code-based multi-agent harness, Prove2Me’s collaborative proof graph, Lean as the verifier, and Mathlib as a foundation [1]. In other words, the achievement points toward AI as an engineering layer around formal mathematics, not merely as a replacement for mathematicians.

The social reaction has reflected that nuance. Zeli’s Hacker News-linked summary framed the news as Claude’s 11-day formal proof “passing computer verification,” and highlighted that the proof followed a simplified version of Wiles’s proof with only high-level human guidance [4]. 36Kr, meanwhile, emphasized the internet’s shock at the speed and scale of the result, including the claim that the process consumed around six billion output tokens [2].

What remains to be checked

Even a machine-checked proof is not magic. Anthropic’s claim depends on trust in the Lean kernel, the correctness of the formal statement being proved, the imported mathematical library and the broader verification tooling [1]. The company says a comparator confirmed that the theorem statement matches Mathlib’s own statement of Fermat’s Last Theorem [1]. That is crucial because one recurring concern in formal mathematics is not whether the machine checked a statement correctly, but whether the formal statement captures the theorem humans think it captures.

There is also the question of readability. A 13-million-line proof is not something the mathematical community can absorb like a journal article. It is closer to infrastructure: a massive artifact that can be compiled, checked, searched and gradually audited. Anthropic itself says a formalized proof should not replace a human-understandable exposition [1]. The future may therefore be hybrid: human papers for explanation, machine-checkable code for certainty, and AI agents for the labor-intensive middle layer.

The result also does not imply that Claude can now solve every major open problem. Fermat’s Last Theorem already had a known proof. The achievement was translating, organizing and verifying an existing proof path at unprecedented speed. That is still a huge milestone, because much of modern mathematics depends on long chains of prior work that are trusted through expert consensus. If AI can formalize those chains at scale, it could make the foundations of research more inspectable.

A real breakthrough, but not the end of mathematics

The most careful reading of the announcement is also the most interesting one. Claude did not make Fermat’s Last Theorem true; Wiles’s proof already did that. Claude appears to have made the theorem machine-checkable at a scale and speed the community did not expect [1]. With Tianyi Peng and the Prove2Me infrastructure, the project shows how elite human mathematical judgment and AI agent labor can combine to attack the bottleneck of formal verification [1][2].

For 8news.ai readers, the significance is not only that an iconic theorem has entered the AI era. It is that the mechanics of trust in mathematics may be changing. If future papers arrive with a readable proof and a verified Lean artifact, referees could spend less time hunting for hidden gaps and more time judging meaning, novelty and conceptual value. The Tsinghua-linked Claude project is therefore best understood as a proof about proofs: a demonstration that AI may help mathematics become more checkable, more collaborative and perhaps more reliable [1][3].

Developments

1. Claude Proves Fermat's Last Theorem for the First Time with Tsinghua Talentseu.36kr.com · Sep 5, 2026, 1:40 AM UTC · 10/10

Sources from the last 72 hours

1. [1]Formalizing Fermat's Last TheoremSep 4, 2026, 12:00 AM UTC
2. [2]Just now, Claude has proved Fermat's Last Theorem for the first time, and the top talent from the Yao Class of Tsinghua University has stepped in.Sep 5, 2026, 1:16 AM UTC
3. [3]Anthropic's Claude Completes First Computer-Checked Proof of Fermat's Last TheoremSep 4, 2026, 12:00 AM UTC
4. [4]Claude's 11-day proof of Fermat's Last Theorem passes computer verificationSep 4, 2026, 12:00 AM UTC

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