Unreleased Claude Model Advances Century-Old Riemann Hypothesis Bounds

Anthropic details how an unreleased Claude model advances mathematical bounds on the unsolved Riemann hypothesis. The model failed to solve the core $1M problem but unexpectedly increased the proven lower bound for zeros on the critical line from 41.6% to 67.2%. Over a day and a half, the system coordinated 60 subagents to run 2,400 shell commands and write hundreds of Python scripts. Anthropic researchers burned through 31 million output tokens for the attempt, overcoming the model's initial failures by prompting it with phrases like "keep going" and "believe in yourself." Two human mathematicians and a standard validation tool formally verified the resulting proof.