An unreleased Claude moves a Riemann zeta bound from 41.6% to 67.2%, with a proof you can check

Anthropic says an unreleased research version of Claude has improved a long-standing result in analytic number theory: the proven share of the Riemann zeta function's non-trivial zeros that lie on the critical line. The bound moved from 41.6% to 67.2%.

This is not a proof of the Riemann hypothesis. Nobody has one.

Anthropic says the model drew on decades of earlier work and, alongside a paper and an informal note for experts, produced a formally verifiable proof of the result. Two Anthropic mathematicians checked it internally. Externally, on short notice, it was checked by Brian Conrey and Dan Goldston, both well-known names in zeta-function theory.

Mainstream tech press had barely picked it up at the time of writing.

Why it matters

Machines have done clever maths for a while. The point here is that this is maths you don't have to take on faith: a proof a computer can check, not a plausible-looking write-up. Most claims about ai arrive from the people selling it. A result you can verify for yourself is a different kind of news.