Mathematical models as artefacts for research: Felix Klein and the case of Kummer surfaces

Already as a student in Bonn, Felix Klein was exposed to model-making through his teacher, Julius Plücker, who used models to visualize the properties of special surfaces that arise in line geometry. Afterward, Klein attended Kummer’s seminar in Berlin, where he began to explore the connections between general Kummer surfaces and so-called complex surfaces, first studied by Plücker. In the late 1870s, Klein and Alexander Brill supervised the work of several students at the Munich Technische Hochschule who designed a large collection of models there. There followed a new era in model production, based in Munich but marketed through the Darmstadt firm owned by Brill’s brother. By 1900 the plaster models of L. Brill could be found at leading universities around the world. Our story here centres on Kummer’s famous models, which began as research artefacts in Berlin, before passing to Munich and then proliferating to points beyond.