{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2026-08-23-elliptic-curve-rank-record-31/","md":"https://postcutoff.com/e/2026-08-23-elliptic-curve-rank-record-31/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-08-23-elliptic-curve-rank-record-31","date":"2026-08-23","date_precision":"day","short_title":"Claude-assisted search breaks the elliptic curve rank record","deck":"Rank 30, then 31","takeaway":"An elliptic curve over Q with rank at least 30 was reported on 20 Aug 2026 and one with rank ≥31 on 23 Aug. These broke the Elkies–Klagsbrun rank-29 record from 2024.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"ICARM: new record-breaking elliptic curve reported","url":"https://icarm.io/news/new-record-breaking-elliptic-curve-reported/","type":"official","group":"primary","domain":"icarm.io"},{"n":2,"title":"Andrej Dujella: history of elliptic curve rank records","url":"https://web.math.pmf.unizg.hr/~duje/tors/rankhist.html","type":"docs","group":"primary","domain":"web.math.pmf.unizg.hr"},{"n":3,"title":"Epoch AI open problems: elliptic curve rank","url":"https://epoch.ai/frontiermath/open-problems/elliptic-curve-rank","type":"official","group":"primary","domain":"epoch.ai"}],"official":3,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Anthropic"],"title":"Claude-assisted search breaks the elliptic curve rank record: rank 30, then 31","summary":"An elliptic curve over Q with rank at least 30 was reported on 20 Aug 2026 and one with rank ≥31 on 23 Aug. These broke the Elkies–Klagsbrun rank-29 record from 2024. The rank-31 curve has 31 explicit independent rational points, so the bound is unconditional. The ICARM record page credits Claude with L. Alpöge and A. Howell.","key_facts":["Previous record: rank ≥ 29 (Elkies–Klagsbrun, 2024); earlier ≥ 28 (Elkies, 2006)","Rank 30 on 20 Aug; rank 31 on 23 Aug 2026; first submitted under the name 'ranksunbounded'","31 independent rational points given explicitly"],"key_numbers":[],"tags":["math","number-theory","elliptic-curves","claude"],"science":{"field":"mathematics","subfield":"arithmetic geometry","problem":"How large can the rank of an elliptic curve over Q be?","result":"Explicit elliptic curve with rank at least 31, a new record.","open_since":"","ai_system":["Claude"],"human_role":"AI-assisted search with human researchers (Alpöge, Howell)","verification":{"key":"expert","label":"Expert-checked","text":"Independent points checkable by computer; listed by the rank record tables"},"status":"confirmed","shock":""},"body_md":"## What happened\n\nAI-directed searches through families of elliptic curves found new record-rank examples twice in one week.\n\n## Why it matters\n\nRank records move very rarely (2006, 2024). Two in a week signal AI's strength at large, structured searches in number theory.","disputed":[],"related":[{"id":"2026-08-12-claude-hadamard-matrices-below-2000","url":"https://postcutoff.com/e/2026-08-12-claude-hadamard-matrices-below-2000/","date":"2026-08-12","date_precision":"day","short_title":"Claude-assisted constructions complete Hadamard matrices for every order below 2000","deck":"Including 668","takeaway":"It closed a famous \"smallest unknown case\" that had stood for two decades, with an easily verified result.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":3,"official":2,"filed":"2026-09-29","updated":"2026-10-21","orgs":["Anthropic"]}],"people":[{"id":"levent-alpoge","name":"Levent Alpöge","url":"https://postcutoff.com/person/levent-alpoge/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-09-29","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-29","run":null,"sources_read":null,"updated":"2026-09-29","human_review":null,"version":{"date":"2026-10-04"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":115,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":54,"in_training_data":false},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":145,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":84,"in_training_data":false}],"short_url":null}