{"version":"2026-10-19.boundary.1","asOf":"2026-10-19","month":"2026-10","domain":{"id":"math","title":"数学 · 推导与证明","summary":"数值答案、几何构造、机器可检证明和自然语言研究证明需要不同验收；竞赛突破不能代表整个数学职业。","frontierId":"F07","sourceIds":["BS02","BS03"],"terms":[{"term":"形式化 / Lean","definition":"把问题与条件写为机器可检查的逻辑命题；Lean检查所写命题的证明，人检查它是不是原问题。"},{"term":"CoT / pass@k","definition":"CoT是先生成推理步骤；Pass@K表示在指定评测标准下生成K个候选，至少一个通过的题目比例。M01的答案Pass@K核对最终答案，CoT-Pass@K另由模型裁判检查过程；两者都不等于形式证明内核通过。"},{"term":"自然语言核对器","definition":"用模型检查候选论证的语言流程，可能漏错；与严格规则的证明内核不同。"},{"term":"复数标量乘法","definition":"一次复数与复数相乘的算术操作计数；不能直接当成实数乘法次数或程序运行时间。"}]},"focusTask":"M03","caseStudy":null,"caseOptions":[],"tasks":[{"id":"M03","domainId":"math","title":"为形式化命题搜索机器可检证明","input":"用逻辑语言写出的命题、库与环境版本。形式化是把问题及条件写成计算机可逐步核查的语言；Lean是这种证明检查工具。","output":"可由内核检查的证明文件","human":"检查所写形式命题是否正是原问题，核对假设与自然语言含义","acceptance":["固定Lean环境重放通过","不额外假定结论，不用未完成证明占位","自然语言与形式命题一致"],"relation":"形式化已提供命题的证明搜索；不等于自动选题及发表研究","workTaskId":null,"actualCoverage":null}],"events":[{"id":"M03-2024","taskId":"M03","availableAt":"2024-07-25","eventDate":null,"dateBasis":"按该条支持材料的公开日期进入时间轴；不是实验统一发生日","title":"形式证明扩展到多种竞赛命题","kind":"benchmark","mode":"bounded","result":"AlphaProof完成2道代数与1道数论题；配合AlphaGeometry2，共4/6题、28/42分。","aiRole":"人在形式化后，系统搜索证明；AlphaProof完成2道代数与1道数论题。","config":"专家先形式化；AlphaProof使用Lean；系统部分题耗时最长3天","metric":"组合系统的竞赛分；不是AlphaProof单独4/6","meaning":"系统可搜索机器可检证明，但自然语言与形式命题的转换仍由人承担。","limit":"不能拿组合成绩当Lean工具通用成功率。","sourceIds":["BM04"],"comparison":"任务/配置或指标不同，不计算统一增长率","supersedes":null,"actualCoverage":null,"measurementWindow":null},{"id":"M03-2025","taskId":"M03","availableAt":"2025-04-30","eventDate":null,"dateBasis":"按该条支持材料的公开日期进入时间轴；不是实验统一发生日","title":"开放证明模型可按预算测量","kind":"benchmark","mode":"bounded","result":"DeepSeek-Prover-V2-671B CoT在miniF2F-test：pass@1为61.9%，pass@32为82.4%，pass@8192为88.9%。","aiRole":"开放模型为已形式化命题生成机器可检证明；结果随候选预算改变。","config":"671B、先生成推理步骤（CoT）；Lean 4.9.0证明检查环境；论文采用并再次修订的miniF2F-test共244题，每题最多8192候选。数学库与环境沿论文说明，本页未核对具体commit。","metric":"给定样本预算下至少一份机器可检证明的题目比例","meaning":"证明搜索可委派给开放模型；预算与核验环境需要一起交接。","limit":"88.9%不是一次调用准确率；题集有修订，不与原始题集或IMO年度得分直接连线。","sourceIds":["BM06"],"comparison":"任务/配置或指标不同，不计算统一增长率","supersedes":null,"actualCoverage":null,"measurementWindow":null}],"sources":[{"id":"BM04","title":"AlphaProof与AlphaGeometry 2：IMO2024","url":"https://deepmind.google/blog/ai-solves-imo-problems-at-silver-medal-level/","publishedAt":"2024-07-25","kind":"竞赛结果","locator":"人工形式化说明；4/6题与28/42分","limit":"4.5小时×两场是学生制度；系统耗时最长3天，不是同时间预算","family":"imo-deepmind","readAt":"2026-10-14","readingScope":"本轮直接阅读所列原文位置；未复跑实验","dateBasis":"页面标示发布日期或固定预印本v1页首日期","status":"active"},{"id":"BM06","title":"DeepSeek-Prover-V2首稿","url":"https://arxiv.org/html/2504.21801v1","publishedAt":"2025-04-30","kind":"研究基准","locator":"§3及§3.1 Experimental Results；表1（671B CoT/候选预算）、表2（题目类别）；附录C题集修订。","limit":"671B CoT的88.9%为pass@8192；82.4%为pass@32，61.9%为pass@1；不是首试成功率","family":"BM06","readAt":"2026-10-14","readingScope":"本轮直接阅读所列原文位置；未复跑实验","dateBasis":"页面标示发布日期或固定预印本v1页首日期","status":"active"},{"id":"BS02","title":"数学推理综述","url":"https://arxiv.org/html/2506.08446v1","publishedAt":"2025-06-10","kind":"综述","locator":"§3推理组成；§4方法；§5–6局限","limit":"综述用于任务框架与机制，不回填更早年份的已知成绩","family":"BS02","readAt":"2026-10-14","readingScope":"本轮直接阅读所列原文位置；未复跑实验","dateBasis":"页面标示发布日期或固定预印本v1页首日期","status":"active"},{"id":"BS03","title":"自动形式化综述","url":"https://arxiv.org/html/2505.23486v1","publishedAt":"2025-05-29","kind":"综述","locator":"formalization定义；评测/语义对齐讨论","limit":"机器核查形式命题不保证与自然语言原问题等价","family":"BS03","readAt":"2026-10-14","readingScope":"本轮直接阅读所列原文位置；未复跑实验","dateBasis":"页面标示发布日期或固定预印本v1页首日期","status":"active"}],"scope":"全模块16个代表任务切片；当前聚焦1个M03；不是完整职业清单或任务覆盖比例。","actualCoverage":null,"knowledgeRule":"主轴按原始材料公开日期；实验/上线时点另列。历史空白仅表示本次未收录证据；后来的质疑不偷偷改写早期结果。","method":{"coverage":"覆盖的含义：在指定输入、环境和验收下，材料支持AI参与哪些动作；未知比例保持null。","speed":"速度的含义：证据节点之间的日历间隔、流程交接变化；指标/样本/预算不一致时，不计算能力增长率或外推一年三年。","sourcePolicy":"综述用于发现任务和原始文献；每条公开主张引用原始论文/官方记录。转载及同一文献家族不累计成独立验证。","selection":"目的性选择三个领域的代表任务，不是穷尽检索或无偏职业采样；基础时间轴于2026-10-14核对，本次精选补充与证据截止2026-10-15，固定论文优先，不把动态榜排名倒填历史。"}}