{
  "schema_version": 1,
  "id": "evt-2013-odd-order-coq",
  "slug": "odd-order-theorem-coq",
  "title": {
    "en": "Coq completes a machine-checked formal proof of the Odd Order Theorem",
    "zh-CN": "Coq 完成奇数阶定理的机器检查形式证明"
  },
  "dates": {
    "event": "2013-07-22",
    "first_public_claim": "2013-07-22",
    "paper_release": "2013-07-22",
    "artifact_release": null,
    "independently_verified": null,
    "added_to_chronicle": "2026-09-15",
    "last_updated": "2026-09-15"
  },
  "event_types": [
    "formalization",
    "proof"
  ],
  "significance": {
    "tier": "H2",
    "rationale": {
      "en": "The six-year Coq formalization of the Feit–Thompson Odd Order Theorem demonstrated that proof assistants could sustain a deep research-level argument while simultaneously building reusable libraries across finite group theory, algebra and number systems.",
      "zh-CN": "历时六年的 Feit–Thompson 奇数阶定理 Coq 形式化展示了证明助手能够承载深层研究级数学论证，并同时建设有限群论、代数和数系等可复用形式库。"
    }
  },
  "mathematical_novelty": {
    "type": "formalization_of_known_result"
  },
  "interfaces": [
    "formal",
    "symbolic"
  ],
  "claim": {
    "en": "The ITP 2013 paper reports a complete constructive formalization of the Feit–Thompson Odd Order Theorem in Coq, relying only on the axioms and rules of Coq's foundational framework.",
    "zh-CN": "ITP 2013 论文报告在 Coq 中完成 Feit–Thompson 奇数阶定理的完整构造性形式化，其证明只依赖 Coq 基础框架中的公理与规则。"
  },
  "summary": {
    "en": "The project formalized the theorem together with a substantial mathematical library spanning group theory, linear algebra, Galois theory and real/complex algebraic numbers.",
    "zh-CN": "项目在形式化定理本身的同时，建立了覆盖群论、线性代数、Galois 理论及实/复代数数的大规模数学库。"
  },
  "why_it_matters": {
    "en": "It raised the demonstrated scale and depth of machine-checked research mathematics and strengthened the library infrastructure later available to automation and AI systems.",
    "zh-CN": "它显著提高机器检查研究数学所展示的规模与深度，并强化了后来可供自动化与 AI 系统使用的形式库基础设施。"
  },
  "ai_role": {
    "level": "human_ai_collaboration",
    "description": {
      "en": "Human authors constructed the formal proof while Coq checked every formal inference under its foundational rules.",
      "zh-CN": "人类作者构造形式证明，Coq 按其基础规则检查每一步形式推理。"
    }
  },
  "human_contribution": {
    "description": {
      "en": "The collaboration formalized the mathematics, engineered reusable libraries and developed proof methodology and tooling needed for the large project.",
      "zh-CN": "协作团队形式化数学内容、建设可复用形式库，并开发大型工程所需的证明方法与工具。"
    }
  },
  "systems": [
    "coq"
  ],
  "organizations": [
    "microsoft-research",
    "inria"
  ],
  "people": [
    "georges-gonthier",
    "jeremy-avigad"
  ],
  "problems": [
    "odd-order-theorem"
  ],
  "methods": [
    "formalization",
    "proof-checking",
    "mathematical-library"
  ],
  "verification": {
    "evidence_level": "E2",
    "status": "paper_released",
    "formal_assurance": "machine_checked",
    "history": [
      {
        "date": "2013-07-22",
        "status": "paper_released",
        "evidence_level": "E2",
        "note": {
          "en": "The peer-reviewed ITP paper documents the complete Coq formalization; machine checking reflects Coq verification and does not mean Chronicle independently replayed the full development.",
          "zh-CN": "ITP 同行评议论文记录了完整 Coq 形式化；machine_checked 表示由 Coq 完成验证，并不表示 Chronicle 独立重放全部工程。"
        }
      }
    ]
  },
  "sources": [
    {
      "id": "itp-odd-order-2013",
      "tier": "S1",
      "type": "paper",
      "title": "A Machine-Checked Proof of the Odd Order Theorem",
      "url": "https://doi.org/10.1007/978-3-642-39634-2_14",
      "primary": true,
      "published_date": "2013-07-22",
      "accessed_at": "2026-09-15"
    }
  ],
  "artifacts": [],
  "relationships": {
    "predecessors": [],
    "successors": [],
    "related": []
  },
  "timeline": {
    "featured": true,
    "significance": "primary"
  },
  "tags": [
    "odd-order-theorem",
    "coq",
    "formalization",
    "machine-checked-proof"
  ],
  "editorial": {
    "created_at": "2026-09-15",
    "last_reviewed": "2026-09-15",
    "reviewers": [
      "Charlie-Wang-03"
    ]
  },
  "corrections": []
}