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Using data on the ‘career’ paths of one thousand ‘leading scientists’ from 1450 to 1900, what is conventionally called the ‘rise of modern science’ is mapped as a changing geography of scientific practice in urban networks. Four distinctive networks of scientific practice are identified. A primate network centred on Padua and central and northern Italy in the sixteenth century expands across the Alps to become a polycentric network in the seventeenth century, which in turn dissipates into a weak polycentric network in the eighteenth century. The nineteenth century marks a huge change of scale as a primate network centred on Berlin and dominated by German-speaking universities. These geographies are interpreted as core-producing processes in Wallerstein’s modern world-system; the rise of modern scientific practice is central to the development of structures of knowledge that relate to, but do not mirror, material changes in the system. [ABSTRACT FROM AUTHOR]