Anthropic's Claude AI formalizes Fermat's Last Theorem in 11 days

AI completes years-long mathematical verification task in days

Anthropic has successfully created a formalized, machine-verifiable proof of Fermat's Last Theorem using its Claude AI system. A team of AI agents completed the complex translation work in just 11 days, confirming the validity of mathematician Andrew Wiles's proof from the 1990s.

The achievement represents a significant milestone in automated mathematical verification. Formalizing a proof means converting it into precise logical code that computers can independently check for correctness—a process that eliminates ambiguity and ensures no steps contain hidden errors.

Fermat's Last Theorem states that no three whole numbers a, b, and c can satisfy the equation aⁿ + bⁿ = cⁿ when n is a whole number greater than 2. While the theorem itself is simple to state, it remained unsolved for over 350 years after Pierre de Fermat posed it in the 17th century. Fermat famously claimed to have discovered a proof but noted it was too large to fit in the margin of his textbook.

Andrew Wiles finally proved the theorem in 1995 after years of intensive work. His proof, however, was written in traditional mathematical language—rigorous by human standards but not in the formal logical syntax that computers require for verification.

Why it matters

The speed of this formalization has major implications for mathematical research and AI capabilities. Converting complex proofs into machine-checkable code typically requires years of painstaking work by human experts. Anthropic's AI agents compressed this timeline by orders of magnitude, suggesting that AI could soon accelerate the verification of new mathematical discoveries and help identify errors in existing proofs. For AI companies, the achievement demonstrates advanced reasoning capabilities that extend beyond pattern matching into formal logical verification—a key requirement for systems that need to provide guarantees of correctness.

Accelerating mathematical verification

The 11-day timeline stands in sharp contrast to previous expectations. Mathematical formalization projects often span years because they require translating intuitive mathematical arguments into explicit logical steps that leave no room for interpretation. Every assumption must be stated, every inference justified according to strict rules.

By automating this process, AI systems could help mathematicians verify new results more quickly and build libraries of machine-checked proofs that serve as reliable foundations for further work. The approach also opens possibilities for AI to assist in discovering new proofs by exploring formal logical spaces more systematically than humans can.

New Scientist first reported these details about Anthropic's formalization of Fermat's Last Theorem.