Claude Pushes Unsolved Math: Riemann Zeta Bound Raised from 41.6% to 67.2%

Claude raised the lower bound on the proportion of Riemann zeta-function zeros lying on the critical line from 41.6% to 67.2% — a problem tied to the unsolved Riemann Hypothesis (1859, $1M prize). The model consumed 31 million tokens, coordinated 60 subagents that executed 2,400 commands, wrote hundreds of Python scripts, and downloaded 54 arXiv papers. Claude initially generated 650 ideas — all dead ends; the breakthrough came through an unconventional approach involving a function space with a quadratic form.

Two Anthropic mathematicians reviewed the result, which was then formally verified in Lean — the proof was approved by experts Brian Conrey and Dan Goldston. AI is now pushing the boundaries of mathematical knowledge in areas where humans have been stuck for decades: breakthroughs no longer emerge from a single mind, but from a swarm of agents sifting through millions of possibilities — and that fundamentally changes the model of scientific discovery.