Anthropic has reported the autonomous formalization of the proof of Fermat's Last Theorem using Claude. The model completed in just 11 days a task that the mathematical community, led by Kevin Buzzard, had previously projected would take years to verify. For the first time, Andrew Wiles's 129-page proof from 1995 has been translated into machine-verifiable code without human proof engineers.
During the process, Claude generated 13 million lines of code in the Lean formal proof language—five times the volume of the entire Mathlib repository. The autonomous agents formulated and proved 29,500 intermediate lemmas along the way, consuming 6 billion output tokens. After verification, Buzzard himself acknowledged the result as flawless: the system relied strictly on fundamental mathematical axioms, eliminating all hidden assumptions.
This breakthrough proves that reasoning architectures have reached an operational level where hallucinations and logical gaps are filtered out directly by formal verification syntax. Translating highly complex, multi-page mathematical reasoning into rigorous, verifiable code paves the way for the autonomous auditing of mission-critical software, compilers, and smart contracts, where logic errors can easily cost millions.