What's this about?
An Anthropic staffer told an unreleased research version of Claude to "take a real stab at the Riemann hypothesis" — arguably the most famous unsolved problem in math. Claude didn't solve it (nobody has since 1859), but while trying, it improved a *related* known result: the proven lower bound on what fraction of the zeta function's "zeros" sit on the critical line, pushing it from a decades-old 41.6% up to 67.2%. Crucially, Claude also produced a machine-checkable proof in Lean, and human experts (including outside number theorists Brian Conrey and Dan Goldston) validated it.
What exactly is the "Riemann hypothesis"?
The Riemann zeta function is a mathematical object whose "zeros" (inputs where it equals zero) secretly encode how prime numbers are distributed. The Riemann hypothesis conjectures that all these important zeros line up on one specific vertical line. Proving it would unlock a huge amount of other math — it carries a $1M prize and has stood 167 years. Nobody proved the whole thing here; instead, mathematicians have long chipped away at proving that *at least some percentage* of the zeros are on the line. Claude raised that guaranteed percentage — real, incremental progress on a frontier problem, not a solution.
What's the community saying?
- "Just tell it to keep going" — Thariq (trq212) and others noted the result came partly from persistence and compute allocation, not a magic prompt — the human had to decide the problem was worth the tokens.
- What does 67.2% even mean? — jarredsumner admitted he wasn't sure of the significance; number theorists in the thread explained it's a respected, hard-won type of bound, not a gimmick.
- Formal proof is the trust anchor — the Lean-verified proof got singled out as the thing that makes this credible rather than a plausible-sounding hallucination.