{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2023-12-14-funsearch-cap-sets/","md":"https://postcutoff.com/e/2023-12-14-funsearch-cap-sets/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":"2023-12-14-funsearch-cap-sets","date":"2023-12-14","date_precision":"day","short_title":"FunSearch: an LLM finds new cap-set constructions, the first LLM discovery in open maths","deck":null,"takeaway":"FunSearch (Nature, Dec 2023) paired a code LLM with an automated evaluator in an evolutionary loop.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"Mathematical discoveries from program search with large language models (Nature)","url":"https://www.nature.com/articles/s41586-023-06924-6","type":"paper","group":"primary","domain":"nature.com"},{"n":2,"title":"GitHub: google-deepmind/funsearch","url":"https://github.com/google-deepmind/funsearch","type":"code","group":"primary","domain":"github.com"},{"n":3,"title":"Ernest Davis: comment on FunSearch","url":"https://cs.nyu.edu/~davise/papers/FunSearchComment.pdf","type":"discussion","group":"reactions","domain":"cs.nyu.edu"}],"official":2,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Google DeepMind","University of Wisconsin–Madison"],"title":"FunSearch: an LLM finds new cap-set constructions, the first LLM discovery in open maths","summary":"FunSearch (Nature, Dec 2023) paired a code LLM with an automated evaluator in an evolutionary loop. It found a cap set of size 512 in dimension 8 (previous best 496) and better lower bounds on the asymptotic cap-set capacity. It also found bin-packing heuristics beating first-fit and best-fit.","key_facts":["Cap set in F_3^8 of size 512, beating the previous record of 496","Improved lower bound on cap-set capacity via new admissible sets","Outputs are programs, so humans can read how the construction works","Co-author: mathematician Jordan Ellenberg"],"key_numbers":[],"tags":["math","combinatorics","llm","evolutionary-search","cap-set"],"science":{"field":"mathematics","subfield":"extremal combinatorics","problem":"Cap set problem: largest subsets of F_3^n with no three points on a line","result":"Largest known cap set in dimension 8 (512 vs 496) and improved capacity lower bound.","open_since":"","ai_system":["FunSearch (PaLM 2 / Codey)"],"human_role":"Humans wrote program skeleton and evaluator; LLM-driven search autonomous","verification":{"key":"peer-review","label":"Peer-reviewed","text":"Peer-reviewed in Nature; constructions verified computationally"},"status":"confirmed","shock":"First time an LLM-based system produced a verifiably new result on a well-known open combinatorics problem."},"body_md":"## What happened\n\nDeepMind evolved short Python programs that construct cap sets, with an LLM proposing program mutations and a scorer keeping the best.\n\n## Why it matters\n\nIt was the direct ancestor of AlphaEvolve and showed that LLMs' mistakes don't matter when outputs can be automatically checked.","disputed":[],"related":[{"id":"2025-05-14-alphaevolve","url":"https://postcutoff.com/e/2025-05-14-alphaevolve/","date":"2025-05-14","date_precision":"day","short_title":"AlphaEvolve: Gemini-powered agent discovers new algorithms","deck":null,"takeaway":"A concrete example of LLM-based systems making novel discoveries and improving the infrastructure that trains them — an early form of recursive improvement.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":4,"official":4,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Google DeepMind"]}],"people":[],"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":null,"in_training_data":true},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":null,"in_training_data":true},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":null,"in_training_data":true},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":null,"in_training_data":true}],"short_url":"https://postcutoff.com/s/funsearch-llm-finds-new"}