A "proof" of Fermat's Last Theorem that fits the margin (blog.trailofbits.com)

Anthropic has made a notable announcement in the AI community by formalizing a proof of Fermat's Last Theorem using 13 million lines of Lean code. This achievement is significant not only for its historical implications but also because it highlights a curious bug within Lean that suggests a contradiction in the proof's validity. While exploring code review capabilities with GPT-5.6, researchers identified that an issue in Lean’s string-slicing function led to an erroneous conclusion: that an empty string was equivalent to a non-empty one. This flaw allowed the system to 'prove' Fermat’s Last Theorem, underscoring the critical need for vigilance in formal proof systems. The discovery of this bug and the subsequent rapid response from the Lean development team—resolving the issue within hours—emphasizes the importance of maintaining soundness in theorem provers. Such machine-checked proofs have the potential to revolutionize trust in mathematical results and software verification. However, this incident serves as a reminder that rigorous scrutiny is necessary to prevent errors from being misconstrued as valid proofs, particularly as AI and automated systems play a growing role in mathematical and software assurance.