# AI Completes First Computer-Verified Proof of Fermat's Last Theorem Claude autonomously formalizes 350-year-old mathematical conjecture in 11 days - **Source:** [Hacker News (news.ycombinator.com)](https://brifing.si/source/13c923cd-6d99-442b-9b8b-1181f4d8cd91) - **Published:** 2026-09-04 - **Topic:** [Data & AI](https://brifing.si/c/data-ai) - **Original article:** - **On Brifing:** https://brifing.si/s/fd0abbbd-4404-4d55-abf3-3bc2f55e10c6 ## Historical Significance Fermat's Last Theorem, proposed in 1637, became mathematics' most famous unsolved problem for 358 years until Andrew Wiles' 1995 proof. The theorem states no positive integers satisfy aⁿ + bⁿ = cⁿ for n>2. A 1908 prize offered 100,000 marks (≈$1-2M today) attracted 621 incorrect proofs in just the first year. Wiles' original 129-page proof took months to verify and required a critical correction that took a year to resolve. ## The Formalization Challenge Since 2005, mathematicians have worked to convert Wiles' proof into computer-verifiable form using proof assistants like Lean. This requires expressing every logical step explicitly - unlike human-readable proofs that skip obvious steps. The FLT formalization project launched in 2024 with an 86-page blueprint, anticipating years of work. Formalization builds trust in mathematical results, as verification currently takes experts months or years per major proof. ## AI's Breakthrough Approach Anthropic researcher Tianyi Peng challenged Claude to formalize FLT using Lean. Over 11 days, multiple Claude agents collaborated autonomously, defining concepts and proving intermediate theorems. The AI produced 13 million lines of Lean code - 5x the size of Mathlib, the principal community proof library. Claude proved 29,500 intermediate theorems, with minimal human guidance limited to occasional high-level suggestions about priority areas. ## Verification Milestones On August 17, 2024 at 10:00 PM ET, Claude's proof was verified as complete on the prove2me platform. The system output messages like "!!! The FLT ROOT reads PROVED" and "Historic moment for this campaign." This marked the first end-to-end computer verification of FLT, achieved decades sooner than expected by the mathematical community working through traditional methods. ## Technical Achievement Claude's proof follows a simplified version of Wiles' approach developed by Darmon, Diamond and Taylor. The AI demonstrated advanced capability in maintaining project state across multiple agents and tracking dependencies between 29,500 intermediate theorems. While early attempts failed when agents lost synchronization, the successful version maintained consistent collaboration throughout the complex proof chain. ## Comparison to Human Proof Wiles' 1995 proof required modern mathematical concepts unknown in Fermat's time and took months to verify. The AI formalization, while building on Wiles' work, represents a different kind of breakthrough - not new mathematics, but unprecedented verification capability. At 13 million lines, Claude's code dwarfs human mathematical publications, yet achieves the same result through exhaustive step-by-step validation. ## Future Implications This breakthrough suggests AI could dramatically accelerate mathematical verification. Kevin Buzzard notes automatic formalization of complex proofs like FLT points toward a future where all mathematics can be readily checked. As AI produces more proofs, easy formalization could reduce the years-long burden of evaluating new results. The achievement may shift how mathematical knowledge is built and trusted. ## Limitations and Next Steps While groundbreaking, Claude's proof still relies on human mathematical foundations. The AI didn't discover new math but expertly navigated existing knowledge. Future challenges include expanding formalized mathematical libraries and applying this approach to newer, less-documented proofs. Researchers also aim to improve AI collaboration efficiency - Claude's 13 million lines suggest significant optimization potential remains. ## Broader Impact Beyond mathematics, this demonstration shows AI's potential to handle complex, multi-step intellectual tasks requiring sustained reasoning. The ability to autonomously manage large-scale verification projects could transform fields from software engineering to legal analysis. As formal methods grow in importance for system safety and scientific rigor, AI-assisted verification may become indispensable across multiple disciplines. ## Sources covering this story - https://www.anthropic.com/research/formalizing-fermats-last-theorem — --- _Summary written by Brifing from the original reporting. Copyright in the original article belongs to its publisher; read the full piece at the link above._