Anthropic AI 'formalizes' proof of Fermat's last theorem in just 11 days (www.nature.com)

Anthropic AI has achieved a groundbreaking milestone by using its AI chatbot Claude to formalize the proof of Fermat's Last Theorem in just 11 days. This theorem, famously stated by Pierre de Fermat in 1637 and proven by Andrew Wiles in 1994, posits that there are no whole numbers x, y, and z that satisfy the equation \(x^n + y^n = z^n\) for \(n > 2\). Claude generated a computer-verified proof spanning an impressive 13 million lines, a task anticipated to take humans a decade. This accomplishment not only showcases the potential of AI in mathematical reasoning but also hints at its ability to validate and possibly challenge established mathematical knowledge. The significance of this achievement is profound for the AI and ML community, as it demonstrates AI's growing role in formalizing complex mathematical proofs, translating them into rigorous computer code, and enhancing the efficiency of mathematical research. Experts like Kevin Buzzard emphasize that the successful formalization of Fermat's Last Theorem sets a new benchmark, suggesting that if AI can tackle such a complex proof, it may soon be capable of addressing a wide range of mathematical inquiries, potentially revealing errors in previously accepted results. The development marks a pivotal moment in integrating AI with advanced mathematical inquiry, raising the prospect of AI as a transformative tool in both verifying and innovating mathematical understanding.