{
  "schema_version": 1,
  "id": "evt-2023-funsearch-cap-set",
  "slug": "funsearch-mathematical-discovery",
  "title": {
    "en": "FunSearch reports new cap-set constructions with LLM-guided program search",
    "zh-CN": "FunSearch 通过 LLM 引导的程序搜索报告新的 cap set 构造"
  },
  "dates": {
    "event": "2023-12-14",
    "first_public_claim": "2023-12-14",
    "paper_release": "2023-12-14",
    "artifact_release": null,
    "independently_verified": null,
    "added_to_chronicle": "2026-09-10",
    "last_updated": "2026-09-10"
  },
  "event_types": [
    "discovery",
    "system"
  ],
  "significance": {
    "tier": "H1",
    "rationale": {
      "en": "The Nature paper demonstrated an LLM-based search loop producing improved constructions for an established extremal-combinatorics problem, making it a useful early reference point for AI-assisted mathematical discovery.",
      "zh-CN": "Nature 论文展示了基于 LLM 的搜索闭环在一个既有极值组合问题上产生改进构造，是 AI 辅助数学发现的重要早期参照点。"
    }
  },
  "mathematical_novelty": {
    "type": "new_result"
  },
  "interfaces": [
    "informal",
    "numeric"
  ],
  "claim": {
    "en": "FunSearch found cap-set constructions exceeding previously known constructions in finite-dimensional and asymptotic settings, and also found improved heuristics for online bin packing.",
    "zh-CN": "FunSearch 在有限维与渐近情形中找到超过此前已知结果的 cap set 构造，并在在线装箱问题上找到改进启发式算法。"
  },
  "summary": {
    "en": "Google DeepMind paired a pretrained language model with an evaluator and evolutionary program search. The resulting system searched over executable programs rather than directly emitting final mathematical answers.",
    "zh-CN": "Google DeepMind 将预训练语言模型、评估器与进化式程序搜索结合，让系统搜索可执行程序，而不是直接生成最终数学答案。"
  },
  "why_it_matters": {
    "en": "The result supplied a concrete, checkable example of LLM-generated code participating in a search process that improved the known solution landscape of an established mathematical problem.",
    "zh-CN": "该结果提供了一个可检查的具体案例：LLM 生成的代码参与系统化搜索，并改进了一个既有数学问题的已知解空间。"
  },
  "ai_role": {
    "level": "ai_primary_human_verified",
    "description": {
      "en": "The language model generated candidate programs inside an automated evolutionary loop, while deterministic evaluators selected and scored candidates.",
      "zh-CN": "语言模型在自动化进化搜索闭环中生成候选程序，确定性的评估器负责筛选与评分。"
    }
  },
  "human_contribution": {
    "description": {
      "en": "Researchers designed the search procedure and evaluators, chose the mathematical tasks and representations, interpreted the discovered programs, and authored the scientific analysis.",
      "zh-CN": "研究人员设计搜索流程与评估器，选择数学任务和表示方式，解释发现的程序，并完成科学分析。"
    }
  },
  "systems": [
    "funsearch"
  ],
  "organizations": [
    "google-deepmind"
  ],
  "people": [
    "alhussein-fawzi",
    "bernardino-romera-paredes"
  ],
  "problems": [
    "cap-set-problem",
    "online-bin-packing"
  ],
  "methods": [
    "large-language-models",
    "evolutionary-search",
    "program-search"
  ],
  "verification": {
    "evidence_level": "E2",
    "status": "paper_released",
    "formal_assurance": "none",
    "history": [
      {
        "date": "2023-12-14",
        "status": "paper_released",
        "evidence_level": "E2",
        "note": {
          "en": "Peer-reviewed Nature article and official institutional announcement were public.",
          "zh-CN": "经同行评审的 Nature 论文与机构官方公告已公开。"
        }
      }
    ]
  },
  "sources": [
    {
      "id": "nature-funsearch-2023",
      "tier": "S1",
      "type": "paper",
      "title": "Mathematical discoveries from program search with large language models",
      "url": "https://www.nature.com/articles/s41586-023-06924-6",
      "primary": true,
      "published_date": "2023-12-14",
      "accessed_at": "2026-09-10"
    },
    {
      "id": "deepmind-funsearch-2023",
      "tier": "S2",
      "type": "official_announcement",
      "title": "FunSearch — Making new discoveries in mathematical sciences using Large Language Models",
      "url": "https://deepmind.google/blog/funsearch-making-new-discoveries-in-mathematical-sciences-using-large-language-models/",
      "primary": false,
      "published_date": "2023-12-14",
      "accessed_at": "2026-09-10"
    }
  ],
  "artifacts": [],
  "relationships": {
    "predecessors": [],
    "successors": [],
    "related": []
  },
  "timeline": {
    "featured": true,
    "significance": "primary"
  },
  "tags": [
    "mathematical-discovery",
    "combinatorics",
    "program-search",
    "llm"
  ],
  "editorial": {
    "created_at": "2026-09-10",
    "last_reviewed": "2026-09-11",
    "reviewers": [
      "Charlie-Wang-03"
    ]
  },
  "corrections": []
}