{"rewrite":{"id":"r_773b90713437b04845907b6a","clusterId":"c_f90c4dc65ef826dba7cdf302","slug":"anthropic-s-claude-pushes-riemann-zeta-zero-bound-past-two-thirds","model":"deepseek-v4-flash:free","headline":"Anthropic's Claude Pushes Riemann Zeta Zero Bound Past Two Thirds","summary":"Anthropic released results from an unreleased research version of Claude attempting the Riemann hypothesis. Claude failed to prove the conjecture itself but derived a new lower bound: at least two thirds of the zeta function's nontrivial zeros lie on the critical line, with an optimized figure around 67.25 percent. The previous bound stood at roughly 41.7 percent. The human operator mainly encouraged Claude with phrases like \"keep going\" and \"believe in yourself\".","whyItMatters":"The result shows an AI model advancing an open mathematics problem largely through human encouragement rather than mathematical guidance, with the operator providing almost no technical input.","webCardHtml":"\u003cp\u003eAnthropic\u0026#39;s unreleased research version of Claude tackled the Riemann hypothesis and came away with a partial result. The model failed to prove the conjecture, but it established that at least two thirds of the nontrivial zeros of the Riemann zeta function lie on the critical line, with an optimized bound of about 67.25 percent. The prior proven figure was roughly 41.7 percent, from 2020.\u003c/p\u003e\u003cp\u003eThe unusual part is the division of labor. Jared Sumner, an Anthropic staff member, reported that his input consisted almost entirely of variations on \u0026#34;keep going\u0026#34; and \u0026#34;believe in yourself.\u0026#34; Claude initially doubted it could make meaningful progress, rejecting its own candidates before Sumner pushed it to continue. The model ran about 60 subagents over roughly a day and a half, executing 2,400 shell commands and writing hundreds of Python scripts.\u003c/p\u003e\u003cp\u003eAnthropic noted that the foundation came from recent human mathematical research, with Claude\u0026#39;s contribution being the recognition that those pieces could be combined. The result is formalized in the Lean 4 proof assistant, and the repository is public on GitHub.\u003c/p\u003e","blueskyPost":"Anthropic let an unreleased Claude loose on the Riemann hypothesis. It didn't prove the conjecture, but pushed the proven share of zeros on the critical line from ~41.7% to at least 2/3. The human's job: saying \"keep going\" and \"believe in yourself.\"","twitterPost":"Anthropic's unreleased Claude failed to prove the Riemann hypothesis but raised the proven bound on zeros on the critical line from ~41.7% to at least 2/3. The human operator mostly just told it \"keep going\" and \"believe in yourself.\"","threadsPost":null,"newsletterBlurb":"Anthropic released results from an unreleased Claude attempting the Riemann hypothesis. The model didn't prove the conjecture, but it pushed the proven share of zeros on the critical line from roughly 41.7 percent to at least two thirds. The human operator's main role was encouragement: \"keep going\" and \"believe in yourself.\"","attributionJson":"[{\"source\":\"GIGAZINE\",\"url\":\"https://gigazine.net/news/20260812-anthropic-claude-riemann-hypothesis/\",\"title\":\"AIに「そのまま続けろ！」「自分を信じろ！」と応援し続けることが人間の役目、Anthropicが未公開のClaudeによるリーマン予想解決の試みを公開\"}]","lintFlagsJson":null,"lintHits":0,"costUsd":0,"inputTokens":5990,"outputTokens":739,"status":"published","repairAttempts":0,"nextRepairAt":null,"factsAttemptedAt":1786760513,"createdAt":"2026-08-15T02:07:12.000Z","publishedAt":"2026-08-15T02:16:44.000Z","updatedAt":"2026-08-15T02:07:12.000Z"},"cluster":{"id":"c_f90c4dc65ef826dba7cdf302","canonicalTitle":"AIに「そのまま続けろ！」「自分を信じろ！」と応援し続けることが人間の役目、Anthropicが未公開のClaudeによるリーマン予想解決の試みを公開","representativeArticleId":"a_5f1be3a55d4fcc42228efed3","sourceCount":1,"writtenSourceCount":1,"writeAttempts":0,"isSolo":true,"entitiesJson":"{\"anime_titles\":[],\"manga_titles\":[],\"work_titles\":[],\"studios\":[\"Anthropic\"],\"people\":[],\"type\":\"news\",\"domain\":\"other\",\"is_roundup\":false}","contentType":"news","status":"published","firstSeenAt":"2026-08-12T11:00:00.000Z","lastSeenAt":"2026-08-12T11:00:00.000Z","updatedAt":"2026-08-15T02:16:45.000Z"},"attribution":[{"source":"GIGAZINE","url":"https://gigazine.net/news/20260812-anthropic-claude-riemann-hypothesis/","title":"AIに「そのまま続けろ！」「自分を信じろ！」と応援し続けることが人間の役目、Anthropicが未公開のClaudeによるリーマン予想解決の試みを公開"}],"entities":{"anime_titles":[],"manga_titles":[],"work_titles":[],"studios":["Anthropic"],"people":[],"type":"news","domain":"other","is_roundup":false},"keyFacts":null}