{"id":"anthropic-science/riemann-zeta","url":"https://www.anthropic.com/research/riemann-zeta","tags":["riemann-hypothesis","zeta-function","number-theory"],"score":0,"title":"Claude has improved on a longstanding lower bound for the fraction of zeros of the Riemann zeta function that satisfy the Riemann hypothesis","source":"anthropic-science","authors":["Anthropic"],"reviews":0,"subject":"math.NT","summary":"An unreleased Claude model improved the lower bound for the fraction of zeroes of the Riemann zeta function that satisfy the hypothesis, raising it from 41.6% to 67.2%.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":3,"published":"2026-08-10","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2609.02882","date":"2026-09-02","kind":"web","site":"arXiv.org","text":"We obtain a new, conceptually simpler, unconditional proof that more than $67.25\\%$ of the non-trivial zeros of the Riemann zeta function are simple and on the critical line, and that at least $83.62\\%$ of the non-trivial zeros are distinct. Our approach also yields two new unconditional estimates…","added":"2026-11-04","title":"A new proof that more than $2/3$ of the zeros of the Riemann zeta function are simple and on the critical line","author":"Youness Lamzouri","record":"arxiv/2609.02882"},{"url":"https://mathoverflow.net/questions/516206/reliability-of-anthropics-lean-verifications","date":"2026-10-20","kind":"web","site":"mathoverflow.net","text":"This morning appeared on arXiv a very nice paper by Arias de Reyna entitled \"Human exposition of Claude's 2/3 theorem on the zeros of zeta\" which does exactly what the title says (I am eagerly waiting for a similar paper for quasi-RH). I was struck by the following paragraph: \"As it's written, [1]…","added":"2026-11-04","title":"Reliability of Anthropic's Lean verifications","author":"Henri Cohen"},{"url":"https://mathoverflow.net/a/516219","date":"2026-10-20","kind":"web","site":"mathoverflow.net","text":"Without looking at the details of this specific case, I can describe the typical scenario. A \"flagship theorem\" is (allegedly) proved (by AI models, let's say). Some natural-language proof is produced. The statement of the flagship theorem is formalized in Lean. A Lean proof of the formalized…","added":"2026-11-04","title":"Answer to: Reliability of Anthropic's Lean verifications","author":"Timothy Chow"}]}