Institutions and the transmission of upper-tail human capital: scientific lineages across a millennium

2026-05-29

AI Summary

This study investigates the key institutional mechanisms underlying the intergenerational transmission of elite human capital and their evolution over a millennium. Leveraging 470,000 advisor–advisee records from Wikidata, the authors construct an academic genealogy network encompassing all 64 Fields Medalists, apply a deterministic graph traversal algorithm to analyze 25.5 million lineage paths, and integrate multidimensional attributes—including society membership, discipline, and language—for structural analysis. The research achieves the first comprehensive measurement of academic lineages across a thousand-year timescale, revealing Leibniz in the 17th century as a pivotal hub through whom 47 of the 64 lineages pass, and identifying that 84% of these lineages converge on just five Islamic and Byzantine scholars from the 12th–13th centuries. It further pinpoints the 11th century as the origin boundary of documented European mentorship and advances a novel perspective that scientific growth is driven more by knowledge transmission than by discovery alone.

Abstract

What made useful knowledge cumulative was not discovery alone but the institutions that transmitted it. We provide the first exhaustive structural measurement of the network through which upper-tail human capital passed from master to student across a millennium. Using 470,000 mentor-student records from Wikidata (which integrates the Mathematics Genealogy Project and MacTutor Archive), and all 64 historical Fields Medalists as a fixed, ex ante tracer set, backward traversal yields a directed acyclic graph of 25.5 million paths reaching 57 generations. We document two institutional transitions. First, a 17th-century watershed concentrates lineage traffic on Leibniz: 47 of 64 lineages pass through him with a 10:1 downstream-to-upstream ratio, and seven independent attributes -- learned-society membership (a 46-fold rise per scholar), field, language, employer, institutional diversification, student production, and diffusion entropy -- re-organize coherently across the same window. This is the network signature of Mokyr's Republic of Letters, and it reframes the Newton-Leibniz priority dispute as a distinction between the possession and the transmission of upper-tail human capital: it is transmission that generates the spillovers on which growth depends. Second, 84% of lineages converge upstream on five 12th-13th-century Islamic and Byzantine scholars before terminating at an 11th-century boundary -- the ``Monastery Wall'' -- at which personal academic mentorship first becomes record-generating in Europe. Our claims are descriptive-structural, not causal. Because exhaustive traversal at this scale defeats standard tools, we also contribute a deterministic, algebraic graph-traversal instrument whose measurement bias we characterize in closed form, and report one emergent property of independent methodological interest.

Problem

• upper-tail human capital
• knowledge transmission
• scientific lineages
• institutional transitions
• mentor-student networks

Innovation

• algebraic graph traversal
• directed acyclic graph
• structural measurement
• mentor-student network
• upper-tail human capital