Mathematical approaches to modeling science from an algorithmic- historiography perspective

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 an analysis of the diffusion of "past" models (from past to present) with an analysis of the historical roots (in terms of bibliographic antecedents) of current or "present" mathematical models of the sciences (from present to past). Starting from a collection of articles from core journals in the field of scientometrics, we explore the present use of mathematical models in this community and their traces back through the past. By combining both perspectives, we hope to understand better why some of the modeling streams have reached a certain consolidation while others remain singular encounters, and why the overall cohesion between different modeling approaches is still insufficient to talk about a subfield inside of scientometrics.