{"slug": "claude-moves-bound-from-riemann-hypothesis-from-41-6-to-67-2", "title": "Claude moves bound from Riemann Hypothesis from 41.6% to 67.2%", "summary": "Claude, an AI model by Anthropic, improved the bound on the Riemann Hypothesis from 41.6% to 67.2% of nontrivial zeros lying on the critical line, building on recent human work by Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh, plus a 2000 paper by Bombieri. The proof, which was formalized in Lean and reviewed by Goldston, was achieved in a session that began eight days ago, with the user providing no mathematical input beyond encouragement.", "body_md": "8 days ago, while jogging, I asked Claude to solve the Riemann Hypothesis\nIt didn’t. 1.5 days later, it proved >= 67% of the zeros are on the line (prev: 41.6%)\nStill not sure what that means, but some analytic number theorists seem excited\n\n- I’d tried once before in a single session and it went nowhere. Eight days ago, when I tried again, this was the opening message:The heavy lifting was recent human work - Baluyot, Goldston, Suriajaya & Turnage-Butterbaugh, plus a Bombieri paper from 2000. Claude’s contribution was seeing they fit together. Goldston himself looked over the paper. Proof is formalized in Lean.I’m very much not a mathematician. I dropped out of high school at 16. I took about half of sophomore year geometry before dropping out. I didn’t contribute any math to the paper. I mostly just told Claude variations of “keep going” and “believe in yourself”If you paste the text below Sonnet 5 refuses to believe it but can’t say why Haiku 4.5 admits it doesn’t know Opus 5 times out after thinking for 17 minutes — THEOREM (unconditional). At least 2/3 of the nontrivial zeros of ζ with T