The author starts by discussing different ways that can be used to explore the trends in German mathematics in the first decades of the seventeenth century – looking through the catalogues of contemporary annual Frankfurt fairs, reading the works of mathematically interested authors whom Edouard Mehl indicated as potentially influential for the development of Descartes as a philosopher, or reading Descartes’own papers. However, all different approaches lead to the same list of names which includes those of Bramer, Bürgi, Kepler, Roth and Faulhaber, and the author goes on analyzing their contributions to mathematics during the period in question. (ZDM/Mathdi)