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/.…
@anthropicai
@anthropicai on x
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…
@ben_golub
Ben Golub on x
How can they drop this kind of news on Friday, the day to drop bad news that you want to hide?!
@tszzl
Roon on x
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
@__nmca__
Nat McAleese on x
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.
@jdlichtman
Jared Duker Lichtman on x
Awesome! Kevin Buzzard had a 5-year grant to formalize the proof of Fermat's Last Theorem, but now Claude has done it in 11 days!
@alexolegimas
Alex Imas on x
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.
@nasqret
Bartosz Naskręcki on x
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…
@scaling01
@scaling01 on x
Claude wrote 13 million lines of Lean and proved 29,500 intermediate theorems over 11 days to formalize the proof of Fermat's Last Theorem
@acerfur
@acerfur on x
Credit where credit is due, nice job Anthropic this is very impressive good work
Mogens Fosgerau
Mogens Fosgerau on linkedin
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? …
Ethan Mollick
Ethan Mollick on linkedin
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. …
Leonardo de Moura
Leonardo de Moura on linkedin
I did not expect this. Anthropic just published the first complete machine-checked proof of Fermat's Last Theorem. It is written in Lean. …
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