AI tool completes formal proof of ternary goldbach conjecture, identifying flaws in decades-old work

An independent developer named Charlie Reams utilized Claude Code to successfully complete a formal proof of the ternary Goldbach conjecture. This achievement resulted in the generation of 194,000 lines of Lean 4 code, with all mathematical reasoning passing stringent machine verification. During the process, the AI demonstrated exceptional analytical capability by autonomously detecting and correcting 11 significant errors within the original 2013 proof published by mathematician Harald Helfgott. These identified flaws spanned issues such as incorrect constants, invalid inequalities, data discrepancies, and confusion regarding major arc scales. By correcting these issues, researchers were able to narrow the required external assumptions for the proof from five down to just two publicly available numerical verification results. This development signals a major shift in mathematics, moving the standard for proof completion toward a fully machine-verifiable era, according to the researchers.