Anthropic Announces Completion of Formalization of Fermat’s Last Theorem With Claude

Anthropic announced Sept. 4, 2026, that Claude had completed a proof of Fermat’s Last Theorem that can be verified by computer from beginning to end in Lean 4. Claude worked almost autonomously for 11 days and generated about 13 million lines of Lean code, the company said. Anthropic called it the first fully machine-verified proof of Fermat’s Last Theorem.

If Anthropic’s announcement is accurate, AI could be used not only to generate and summarize text but also for verification tasks with long chains of dependencies. For those working in mathematical research and formal verification, the implications include how work can be divided and how much the burden of checking consistency can be reduced.

What stands out in the announcement is less that Claude “proved” Fermat’s Last Theorem than that it translated an existing mathematical proof into a form that can be machine-verified in Lean 4. This is not the discovery of a new mathematical theorem, but an example of how much of the work of formalizing proofs AI can handle. The reported scale—about 13 million lines, about 30,300 theorems, and about 29,500 ultimately used—suggests that the task required not just model intelligence but also a design for dividing and integrating work while preserving long chains of dependencies. Our related article, Anthropic releases research version of standard for physical devices, covered common specifications for AI agents to safely handle laboratory equipment and manufacturing machinery. While that article examined safe interfaces for operating real-world equipment, this announcement focuses on whether long proofs can be handled without breaking them during mathematical formalization. Together, they point to Anthropic’s effort to expand the applications of agents from rigorous software-based tasks to controlling external equipment. However, it is too early to consider the two to be at the same stage of maturity. The announcement also said that in early attempts, agents lost track of their progress or could not fully use one another’s work, underscoring that operational design for tasks with long chains of dependencies remains an issue. The broader industry implication is that evaluating AI by accuracy on short benchmarks alone is no longer enough; attention is shifting to long-term state management, reuse of partial results, and the division and integration of work among multiple agents. Fermat’s Last Theorem is a symbolic example, but the approach could have practical value in fields such as proof assistance, code verification and research support, where the consistency of intermediate results is critical. Unresolved questions include how widely the method can be applied across other areas of mathematics and research and development, and the failure rates and retry costs it would incur in real-world use. See the original source for details.

In Japan, this could be relevant to research institutions working on proof assistance and formal verification, software verification, and fields related to safety checks for control systems. However, the announcement describes a research-stage example, and its applicability to practical work cannot be determined from the original source alone.