Anthropic says Claude worked “largely autonomously” over 11 days to formalize the proof of Fermat's Last Theorem in the Lean programming language
Anthropic
Context & Ripple Effects
Anthropic had already positioned Claude as a research agent: an unreleased model made progress on a related problem during its unsuccessful Riemann-hypothesis attempt, while a separate 16-agent effort produced a Rust compiler. The new Lean result moves that arc from exploratory mathematical work to an artifact a proof assistant can verify.
That distinction matters because formalization turns a proof into code subject to machine checking, rather than relying only on a model’s mathematical prose. Public reaction focused on the implications for formal verification, though those assessments are opinion rather than independent validation.
First-order effects
Anthropic gains a high-profile demonstration that Claude can sustain an 11-day, largely autonomous workflow that produces a Lean formalization rather than only a proposed mathematical argument.
Lean users and mathematical researchers receive a computer-checkable formalization of the theorem’s proof that they can inspect and verify within the proof-assistant workflow.
Second-order effects
Anthropic’s research evaluations can place greater weight on end-to-end verified artifacts, building on its earlier multi-agent compiler project rather than judging agents solely by intermediate reasoning or code generation.
Teams applying AI to formal methods face a clearer practical benchmark: producing proof-assistant-accepted work, not merely generating plausible proofs or conjectures.
Third-order effects
If such workflows prove reproducible across problems, formal verification can become a more central layer of AI-assisted research because the output carries its own machine-checkable evidence.
The boundary between mathematical discovery and software verification would narrow, with proof assistants serving as the validation interface for longer-running research agents.
The trend: AI research agents are moving from generating mathematical ideas toward proof-carrying discovery, where formal systems verify the resulting work.
If you had told me in undergrad I'd love to see ~fully automatic formalization I would have bet against, and if you had told me that the machine doing it would have a running color commentary on the importance, I'd have thought you under the influence. https://www.anthropic.com/.…
Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat's Last Theorem, one of th…
apropos of nothing it is pretty funny in Star Trek TNG captain Picard is doing some Gentleman Science trying to prove fermat's last theorem in his free time — he claims it's been unsolved for centuries — and then it was proved one year after the show ended
Claude wrote 13 million lines of coherent Lean code to formalise Fermat's last theorem in 11 days. Large implications for formal verification as a whole.
With the caveat that I am not a professional mathematician, this result is the most significant that I have seen for the field of mathematics thus far. The ability to automate formalization is the ability to accelerate progress, whether that is done by machines or humans or both.
Fermat's Last Theorem is finally sealed. Congratulations to all the contributors, especially Kevin Buzzard and his vast team of students and post-docs who did the big part of the proof in the project https://github.com/... But the story continues because the proof is not yet form…
It will take us a while to understand the implications of this achievement. — Lots of questions. — What will research mathematicians be doing in the future? …
Hey, Claude formalized Fermat's Last Theorem. — “Fermat's Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. …