跨越千年的计算人物志：从菲尔兹奖得主追溯数学导向的谱系
Computational Prosopography across a Millennium: Mathematically Oriented Lineages Traced from the Fields Medalists
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中文总结 AI 辅助
该研究重建了跨越9世纪的数学领域师生网络，以菲尔兹奖得主为示踪集发现莱布尼茨谱系的沙漏结构等特征，通过工具批判和可逆遍历引擎验证宏观结构的稳健性。
中文摘要 AI 辅助
我们重建了跨越约九个世纪的有记录学术训练的师生网络，并对该网络及重建方法进行了来源批判。从聚合了数学谱系项目（Mathematics Genealogy Project）和麦克塔特档案（MacTutor Archive）的维基数据（Wikidata）中，我们提取了约470000条师生断言，得到了包含372853人的有向无环图。以全部64位历史菲尔兹奖得主作为固定的先验示踪集，反向遍历枚举了约2550万条不同路径，覆盖57代。得出三个结构观察：1. 莱布尼茨的谱系流呈沙漏状：上游较细，平均每个节点有5.3条路径，下游较粗，平均每个节点有53.4条路径，比例接近10:1；牛顿仅出现在64条谱系中的4条，无对应特征。2. 在以莱布尼茨为中心的窗口内，7个独立提取的谓词维度共同重组，记录的学会成员占比从6.5%上升至82.1%。3. 上游64条谱系中的54条汇聚于相同的5位12至13世纪伊斯兰及拜占庭学者，最终终止于我们命名为“修道院墙”的11世纪边界。我们认为，若不进行工具批判，便无法评估这些观察结果。遍历引擎在代数上可逆，因此其做出的每一个排序决策都可事后重建。我们以闭式形式表征其测量偏差，证明宏观结构在关闭该偏差后仍存在，并报告遍历在不同分辨率下返回的谱系族，而非单一排序列表。
英文摘要
We reconstruct the mentor--student network through which documented scholarly training passed across roughly nine centuries, and subject both the network and the means of reconstructing it to source criticism. From Wikidata, which aggregates the Mathematics Genealogy Project and the MacTutor Archive, we extract approximately 470,000 mentor--student assertions, yielding a directed acyclic graph of 372,853 persons. Using all 64 historical Fields Medalists as a fixed, ex ante tracer set, backward traversal enumerates some 25.5 million distinct paths reaching 57 generations. Three structural observations follow. Genealogical traffic through Leibniz forms an hourglass: thin upstream, 5.3 paths per node on average, and thick downstream, 53.4, a ratio near 10:1, with no counterpart at Newton, who lies on only four of the 64 lineages. Across a window centered on Leibniz, seven independently extracted predicate dimensions reorganize together, and recorded learned-society membership rises from 6.5 to 82.1 percent of the cohort. Upstream, 54 of the 64 lineages converge on the same five twelfth- and thirteenth-century Islamic and Byzantine scholars before terminating at an eleventh-century boundary we name the Monastery Wall. We argue that such observations cannot be assessed without tool criticism. The traversal engine is algebraically reversible, so every ranking decision it makes can be reconstructed afterward. We characterize its measurement bias in closed form, show that the macro-structures survive switching that bias off, and report the family of lineages the traversal returns at different resolutions rather than a single ranked list.
