Weaving and Mathematics: An Impossible Interlacing?

Mathematics is usually considered as a formal and abstract discipline; however, this conception is more an invention of the late 19th century. In the history of science, geometry and algebra have always been understood in a tense relation with or even as a consequence of craft and artisanal practices, and this applies in particular to the practice of weaving. Indeed, not only threads must be counted and patterns must be formed, but also the behavior of the textile (rigidity or flexibility, ›flat‹ or as spatially extended) must be decided in advance and calculated accordingly. The research in this sub-project aims to recall these forgotten ›interlacements‹ between materiality, calculation, and (mathematical) theory to overcome the current gap between practice and theory. In particular, we have asked about the designers' knowledge of the activity of the materials (the thread as material as well as the woven fabric) and the extent to which this knowledge has found its way into mathematics.

The results include the open-access anthology Model and Mathematics. From the 19th to the 21st Century (ed. Michael Friedman and Karin Krauthausen, Birkhäuser/Springer 2022), in which historians of mathematics, mathematicians, and cultural scientists use historical and contemporary examples of models and modeling to show how closely intertwined material production, creative illustration and mathematical abstraction were in the 19th century, what kind of transformations these symbolic-material models, which also combine practice and theory, endured, and how they even gained popularity in the 20th and 21st centuries.

The further development of the research field focuses on the mathematical reconceptualization of the knowledge of textiles, mainly during the Early Modern Period, since the studies from the first phase of the project have shown that at that time the association of mathematics and weaving was common in Europe. Especially Joachim Jungius, Johann Joachim Becher, and Gottfried Wilhelm Leibniz considered the practices, looms, and machines associated with weaving and knitting as carrying and embodying mathematical and geometrical knowledge. The subproject examines the hitherto unexplored relationship between these artisanal practices and the evolving conceptions of mathematics in the 17th century. A first important result is the publication of Michael Friedman, On Joachim Jungius’ Texturæ Contemplatio. Texture, Weaving and Natural Philosophy in the 17th Century. Springer 2023. The book offers an analysis of Joachim Jungius’ hitherto-unpublished manuscript written between the 1620s and the 1640s, which dealt with textile practices and attempted to present these techniques in a scientific and even mathematical framework.