Recently, a remarkable milestone was achieved in the realm of mathematics. The proof of Fermat's Last Theorem, originally completed by the renowned British mathematician Andrew Wiles in 1995, has now successfully undergone formal verification. This verification was autonomously conducted over an 11-day period by Anthropic's advanced AI model, Claude.

During this intensive process, Claude generated an astonishing volume of data, producing over 13 million lines of code and verifying more than 30,000 theorems. To manage the intricate dependencies between these theorems, the project ingeniously employed multi-agent collaboration and directed acyclic graph technology. Notably, human intervention was minimal, limited to providing only high-level guidance.

The entire verification endeavor consumed approximately 6 billion output tokens, leveraging an internal model operating at the Claude Fable 5.1 level. The Lean proof assistant, renowned for its rigorous verification mechanism, played a pivotal role in the process. It ensured the proof's purity by relying solely on three standard axioms, a testament to the system's precision and reliability.

Mathematical formalization experts have hailed this achievement as a significant breakthrough in AI-assisted mathematical research. The formalization of complex proofs, which previously demanded years of meticulous effort from mathematicians, has now been dramatically expedited by AI. The complete proof code has been made publicly accessible on GitHub, inviting scrutiny and further exploration by the mathematical community.

Anthropic has expressed optimism about the future implications of this breakthrough. They anticipate that providing formalized versions alongside traditional proofs may soon become an industry standard. This shift could potentially reduce the labor costs associated with verifying new theories, ushering in a new era of efficiency and collaboration in mathematical research.