Anthropic, a research company specializing in artificial intelligence, has made a significant breakthrough by using its AI system, Claude, to create a fully computer-checked version of a famous mathematical proof known as Fermat's Last Theorem. The theorem was first proposed by the mathematician Pierre de Fermat in 1637, and it wasn't until 1995 that mathematician Andrew Wiles provided the first complete proof, which spanned 129 pages. This new achievement marks the first time an AI has fully formalized such a complex mathematical proof without direct human coding. Formalizing a proof involves translating its logical steps into code that computers can verify automatically, ensuring there are no errors in the reasoning. Anthropic expected the project to take several years, as mathematicians typically estimate, but Claude completed the task in just 11 days with minimal human intervention. The final proof consists of 13 million lines of code written in Lean, a specialized programming language used by mathematicians for formal proofs. Along the way, the AI proved approximately 30,300 theorems, using 29,500 of them in the final version. Human input was limited to high-level guidance, rather than direct coding. The completed proof is significantly larger than Mathlib, the primary proof library used by the mathematical community, being over five times longer. Kevin Buzzard, a mathematician at Imperial College London, praised the achievement, noting that it proves Fermat's Last Theorem using only the axioms of mathematics. He also highlighted that the proof includes autoformalized elements from various branches of mathematics, such as algebra and number theory, and that the AI's output is now robust enough to serve as a foundation for future research. Anthropic attempted the formalization multiple times before succeeding, with earlier efforts contributing about 7% of the final proof. This accomplishment follows closely on the heels of another breakthrough by Anthropic, where they detailed a new insight into the Riemann zeta function, a mathematical object central to the famous Riemann Hypothesis. Meanwhile, rival AI research lab OpenAI has also made progress, using its Astra model to solve classic problems posed by mathematician Paul Erdős and to make advances in theoretical computer science. Anthropic’s success was aided by an open-source tool called Prove2Me, which helps AI agents make efficient decisions during complex research tasks. The company has also expanded access to its AI for mathematicians working on formalization projects, offering research credits and grants to support further exploration. Despite the rapid pace of this achievement, the 11-day timeline underscores the immense effort required to fully formalize complex mathematical proofs, even with today’s most advanced AI systems.