Quick answer
Anthropic has published what it describes as the first complete computer-checked proof of Fermat's Last Theorem. The company says dozens of Claude agents, coordinated through a Claude Code-based harness and the Prove2Me platform, produced the Lean formalization largely autonomously over 11 days. The public artifact contains about 13 million lines of Lean and 29,511 theorem pages, and Anthropic reports that it was accepted by Lean's kernel, the Lean Comparator, and a second kernel called nanoda. This is a formalization of established mathematics derived from the Wiles and Taylor-Wiles proof path, not a new elementary proof of Fermat's theorem. The workflow used roughly six billion output tokens from an internal research model comparable to Claude Fable 5.1, so it is not evidence that an ordinary chat session can reproduce the result.
Anthropic says Claude completed the formalization in 11 days
Anthropic says dozens of Claude agents worked largely autonomously for 11 days to turn an established proof of Fermat's Last Theorem into Lean code that a proof assistant can check. The agents produced about 13 million lines of Lean and proved tens of thousands of intermediate results. Human mathematical input was limited to occasional high-level prioritization from Anthropic researcher Tianyi Peng, according to the company. The result is an official Anthropic research claim supported by a public proof artifact; it is not an independent benchmark of Claude's general mathematical ability.
Sources: Anthropic, Anthropic on GitHub
The result formalizes Wiles's proof rather than replacing it
The project did not discover a new elementary proof of Fermat's Last Theorem. Anthropic says the formalization follows a simplified account of the Frey-Serre-Ribet-Wiles and Taylor-Wiles argument and adapts earlier work from the Imperial College London FLT project, flt-regular, and Mathlib. The novelty is that the entire chain has been expressed in a form that proof-checking software can evaluate from end to end. A readable mathematical exposition is still valuable because a kernel checks logical validity, not whether every generated name or explanation conveys the intended mathematical idea clearly.
Sources: Anthropic, Anthropic on GitHub
Prove2Me gave the agents a shared map of the proof
Anthropic reports that early attempts stalled when agents lost track of the project's state and stopped collaborating effectively. The successful run used Prove2Me to represent theorem dependencies as a directed acyclic graph, separate statements from proofs for faster compilation, and attach natural-language descriptions that made results easier to search and reuse. A Claude Code-based multi-agent harness then assigned work across that graph. This suggests that orchestration, shared state, and reusable intermediate results were central to the outcome, rather than model prompting alone.
The public artifact documents three layers of checking
The repository pins Lean 4.33.1 and Mathlib v4.33.0. Its default FinalCheck target is designed to fail unless the Fermat theorem depends on exactly Lean's three standard axioms and avoids shortcuts such as sorry, native_decide, unsafe declarations, or added axioms. Anthropic also reports that Lean Comparator confirmed the proved statement matches Mathlib's statement and that nanoda, an independent Rust implementation of a Lean kernel, checked more than one million declarations without errors. These checks make the logical artifact reproducible under the stated toolchain, while still requiring trust in the kernels, build environment, and checking tools.
Sources: Anthropic on GitHub
Independent reproduction requires unusually large compute
The repository provides build and verification commands, but its published resource estimates put a full reproduction beyond a typical laptop. Anthropic reports that its build used 96 jobs, peaked at 153 GB of memory, and took about five and a half hours; the Comparator run took nearly 15 hours and peaked at 230 GB. The working tree can require tens of gigabytes of disk plus hundreds of gigabytes of generated C files. Readers can browse the generated proof pages locally, but should distinguish reviewing the artifact from rerunning every verification step.
Sources: Anthropic on GitHub
The run used an internal model and about six billion output tokens
Anthropic says the workflow consumed about six billion output tokens from a general-purpose internal research model roughly comparable to Claude Fable 5.1. That description does not identify the system as the public Fable 5.1 product, and the company does not claim a single consumer conversation can repeat the 11-day run. The result therefore says more about a heavily scaffolded, parallel research workflow than about what an individual Claude subscriber should expect from an ordinary prompt.
Sources: Anthropic
The practical lesson is to pair AI-generated proofs with formal checks
Formal proof systems can make large AI-assisted mathematical outputs easier to audit because the final logical chain must pass a small trusted kernel. They do not automatically make the proof concise, readable, or scientifically useful. For teams experimenting with theorem proving, the transferable pattern is to define an exact target, track dependencies explicitly, preserve reusable intermediate lemmas, pin the toolchain, and publish verification instructions alongside the result. Human experts still need to assess attribution, exposition, and whether the formal statements capture the intended mathematics.
Sources: Anthropic, Anthropic on GitHub
This research result does not add a model to Chat AI
Anthropic's publication describes an internal research workflow, not a new public model release or a Chat AI integration. Chat AI's verified model directory should be used for current catalog availability; this article does not claim that the internal system behind the formalization can be selected there. Chat AI availability is therefore not applicable to this story.
Frequently asked questions
What readers usually ask
Did Claude prove Fermat's Last Theorem for the first time?
No. Andrew Wiles and Richard Taylor completed the accepted mathematical proof in the 1990s. Anthropic says Claude produced the first complete end-to-end formalization that a computer proof assistant can check.
What does computer-checked mean in this project?
The proof was encoded in Lean, whose kernel checks that each logical step follows under the permitted axioms. The repository also documents checks with Lean Comparator and the independent nanoda kernel.
How autonomous was Claude during the formalization?
Anthropic says dozens of agents worked largely autonomously for 11 days, with occasional high-level instructions from a human researcher. A multi-agent harness and Prove2Me coordinated the shared proof graph.
Which Claude model produced the proof?
Anthropic describes it as an internal general-purpose research model roughly comparable to Claude Fable 5.1. It does not say the public Fable 5.1 product ran the full workflow.
Can I verify the proof myself?
The code and commands are public, but the documented full build and independent checks require substantial memory, disk space, and time. The repository also includes generated HTML pages for browsing the proof without rerunning everything.
Is the model used for this proof available in Chat AI?
No availability claim applies. The work used an internal Anthropic research system, and the publication does not announce a new model integration for Chat AI.
Evidence