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The goal of this conference is to investigate the role of mathematics as a heuristic device for analogical reasoning in science and philosophy. Empirical science relies heavily on mathematics. Mathematical models enable physicists to simulate dynamical ‘dumb hole’ analogues to gravitational black holes (Curiel 2019; Dardashti, Thébault, and Winsberg 2017; Gryb, Palacios, and Thébault 2019), chemists to study the behaviour of molecules, medical researchers to examine the spreading rate of diseases, and biologists to understand changes in animal populations. There is no doubt that mathematics is an indispensable scientific tool.