Model and Mathematics

The open access book »Model and Mathematics: From the 19th to the 21st Century«, published in August 2022, collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics. Contributions and expert interviews range from, for example, the physical mathematical models of the 19th century to the simulation and digital modeling of the 21st century. The aim of this anthology, edited by MoA members Michael Friedman and Karin Krauthausen, is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models.

What is a model? Today, this question may be answered either with a high degree of abstraction and generality, or with a more specific and precise contextualization, since the concept of ‘model’ and the practice of modeling are ubiquitous — in all the sciences and arts, in engineering and design. But what is meant when one speaks of mathematical models in the 19th, 20th, and 21st centuries? That is the subject of the present volume, and this question is answered by the contributors in detailed historical studies of mathematical model practices in the long 19th century in France and Germany, and in a series of interviews on model practices in the sciences between the 19th and the 21st century. Moreover, there can and will be no single answer that encompasses all the interweavings between mathematics and models: mathematical models have been and continue to be so productive because their definition, function, and appearance was and is capable of change. When the talk is of mathematical models, then, from a historical perspective, these include both the haptic-concrete model constructions of the 19th century and the abstract, formal model concepts of the 20th century. The central concern of the present volume is to show the historical diversity and the capacity for change as well as the pedagogical and epistemic importance of mathematical models.

With contributions from Arianna Borrelli, Frédéric Brechenmacher, Moritz Epple, Myfanwy E. Evans, José Ferreirós, Axel Gelfert, Gabriele Gramelsberger, Ulf Hashagen, Andreas Daniel Matt, David Rowe, Anja Sattelmacher, Tilman Sauer, Klaus Volkert, Fernando Zalamea, and an introduction by Michael Friedman and Karin Krauthausen.

The publication is part of the series »Trends in the History of Science« at Birkhäuser and can be downloaded or ordered on the Springer website.