Claude increases the bound for the unproven Riemann zeta function from 41.6% to 67.2%.

Claude improved the lower bound of the percentage of Riemann zeta function zeros on the critical line from 41.6% to 67.2%, which relates to the famous Riemann Hypothesis (1859, $1M prize). It took 31 million tokens, 60 subagents executing 2,400 commands, hundreds of Python scripts, and 54 arXiv papers downloaded. Initially, it produced 650 ideas, all of which were wrong, but finally succeeded with an unexpected method related to the quadratic form in the function space.

This solution has been checked by two Anthropic mathematicians and has been formally verified in Lean (approved by experts Brian Conrey and Dan Goldston). With the help of AI, we are exploring the frontier of human knowledge in some fields that humans have been working on for decades without success. We are seeing the birth of new discoveries, not from individual geniuses, but from a group of agents exploring among millions of options, changing our understanding of the way science is done.