Our narratives of liberal modernity have made mathematical reasoning a focal point of both freedom and coercion. Classic accounts since at least Cassirer take Nicholas of Cusa and other thinkers as examples of how mathematics enables humans to surpass finite bounds in a bid for infinite perspectives; meanwhile, influential critics point out the pernicious consequences of mapping the world, of constraining it within a numbered grid to enable the extractive, surveilling state. This talk attempts to trace an emerging sense—and dismissal—of this tension in the wake of Cusanus. It will use Renaissance assumptions of how to do mathematics to find a way into the tensions between coercion and freedom, and from there examine the place of mathematical regimes in Renaissance political thought. Brief biographyAfter a degree in biology at Redeemer University College, I was seduced by optional courses in history, and completed a PhD in the history and philosophy of science at the University of Notre Dame, IN (2013). For some years I was a member of the ERC project Genius before Romanticism: Genius in Early Modern Art and Science, based at CRASSH, University of Cambridge. At Cambridge I was also a JRF and then Fellow and Tutor at St Edmund’s College. Among the fellowships I’ve been fortunate enough to hold, some are from the Warburg Institute (University of London), the Notre Dame Institute for Advanced Study, the Huntington Library, and the Houghton Library (Harvard University). At Edinburgh, I have served as the Director of Undergraduate Teaching for History (Pre-Honours); I’ve also been an elected member of the Senatus Academicus (2020–22).