Claude produces first machine-checked Fermat proof
Anthropic says Claude worked largely autonomously for 11 days to write the first end-to-end, computer-verified proof of Fermat's Last Theorem in Lean, leapfrogging a multi-year community formalization effort.
Anthropic has published what it describes as the first complete computer-checked proof of Fermat's Last Theorem, written in the Lean proof assistant by Claude over 11 days with limited human guidance.
The work was initiated by Tianyi Peng, an Anthropic researcher whose Columbia University group builds AI formalization tools, to test whether Claude could make progress on the problem. Dozens of Claude agents defined concepts and chained intermediate results, producing computer-verifiable proofs of 30,300 theorems — 29,500 of which appear in the final proof — across 13 million lines of Lean, more than 5x the size of Mathlib, the community's principal proof library. The formalization follows a simplified version of Andrew Wiles's 1995 proof due to Darmon, Diamond and Taylor. Human input was limited to occasional high-level steering from Peng, such as "Jacobian as a scheme sounds high priority."
The result arrives against a community effort begun in 2024 by Kevin Buzzard at Imperial College London, whose blueprint for just the project's initial phase runs to 86 pages. Buzzard, shown the proof, called it an "extraordinary autoformalization achievement" that "proves Fermat's Last Theorem with no assumptions other than the axioms of mathematics," and said AI autoformalization artefacts "are now robust enough to be built upon."
Anthropic frames the contribution as verification rather than new mathematics, in contrast to recent AI work on the Riemann hypothesis. The announcement comes via the company's own research blog; it does not detail compute cost, agent scaffolding, or where the Lean code can be independently inspected.