Institutions and the transmission of upper-tail human capital: scientific lineages across a millennium
This research provides a novel structural understanding of how scientific knowledge transmission evolved over a millennium, which is important for historians of science and economists studying human capital and growth.
This paper constructs the first exhaustive structural measurement of mentor-student networks for upper-tail human capital across a millennium, using 470,000 records and tracing lineages of 64 Fields Medalists. They found two institutional transitions: a 17th-century concentration of lineages through Leibniz, and an 11th-century "Monastery Wall" where academic mentorship records begin in Europe, with 84% of lineages converging on five 12th-13th-century Islamic and Byzantine scholars.
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.