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This chapter examines the history of mathematical modeling of science. We mainly rely on the method of algorithmic historiography to reconstruct the emergence and diffusion of different model approaches to the science system. This chapter provides a historiographical context of the models that will be explained in detail in some of the subsequent chapters. Algorithmic historiography is based on bibliometrics, and more particularly follows the citation flows between papers. We take a closer look at three popular models: the stochastic distribution of productivity among scientists as described by Lotka in 1926; the population-dynamic approach to the epidemic spreading of ideas as proposed by Goffman and Nevil in 1964; and the network model of scientific papers introduced by Derek de Solla Price in 1965. We aim to provide a coherent reconstruction of their reception by tracing citation patterns. We combine …