Learning more about Claude's mathematical capabilities

Claude, prompted by an Anthropic staff member, significantly advanced the Riemann Hypothesis by increasing the provable lower bound for the fraction of zeros of the Riemann zeta function satisfying the hypothesis from 41.6% to 67.2%. After 650 initial failed attempts, Claude, coordinating about 60 subagents, ran 2,400 shell commands and wrote hundreds of Python scripts, performing thousands of numerical checks. The staff member's encouragement helped Claude overcome initial skepticism and achieve this breakthrough.