[What is Practical in Mathematical Knowledge? : The Positions of Mining Master J. A. Scheidhauer and Building Master C. F. Steiner Around 1800].

This article investigates the notion of 'practical mathematics' and its evolution over the last third of the eighteenth and first third of the nineteenth century. Two detailed case studies, taken together, give a sense of both the richness and the difficulties of what practical knowledge could mean at the turn of the nineteenth century. After some preliminary remarks about the institutional context and the social status of practical mathematicians (actually mathematical practitioners) in the German regions the first case study is dedicated to the mining master Johann Andreas Scheidhauer (1718-1784). The biography of this previously unknown mathematical practitioner leads to an analysis of his writings and their reception, after which we analyze the diffusion of his work, most prominently through J. F. Lempe, professor of mathematics at the Freiberg mining academy. The second case study deals with a practitioner from the following generation: the architect Carl Friedrich Steiner (1774-1840), who lived in Weimar as a contemporary of Goethe. In a certain sense his textbook on Geometry descriptive reflects the consequences of the ongoing mathematisation, the status of mathematical knowledge for the training of young artisans and artists. Both case studies provide information about the historical understanding of practical mathematics.