Wilhelm Fiedler: His Life, his Opus and his Activities. The Fights of a Geometer

• Applicant: Professor Dr. Klaus Volkert
• Subject Area: History of Science
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 515951245

The aim of the project is to prepare the publication of a book entitled "Wilhelm Fiedler: His Life, his Opus, his Activities. The Fights of a Geometer". This book will be composed of two volumes, the first being dedicated to a detailed study of Fiedler’s life, his carrier, his work, placed in the context of his time (1832 – 1912) and of the institutions where he was engaged (Höhere Gewerbeschule Chemnitz (1851 – 1864), Polytechnics at Prague (1864 – 1867) and Zürich (1867 – 1907)). This will be the first comprehensive study on Fiedler who served at Zürich as professor of descriptive geometry and geometry of position. Fiedler’s field of research was geometry, in particular descriptive and projective geometry: besides own research papers (more then 40) he published three books. Fiedler became highly influential by publishing the German editions of books written by George Salmon. These German editions were widespread, often re-edited and used by generations of mathematicians in order to learn „new geometry“ – often called „analytic geometry“ at that time - closely linked to „new algebra“ and invariant theory. The name „Salmon-Fiedler“ was known to everybody working in mathematics at that time, it was a highly prominent trademark. Fiedler’s own book on descriptive geometry (1871; four editions, translated into Italian) had a certain influence (also on the international level); its central idea was a synthesis of descriptive and projective, of synthetic and analytic geometry - getting a brandmark of Fiedler's. Fiedler played a role in the process of defining the nature of projective geometry, ongoing at that period. Fiedler left a huge correspondence and a great number of interesting materials; he was an active member of a network, mainly based at Polytechnics, engaged in defending geometry against the decline of its importance due to prominent tendancies („Arithmetisierung“) in the last third of the 19the century. The network also fought for the preservation and the installation of professorships for geometry. Fiedlers case provides additional information from a new viewpoint on this important period of the development of mathematics; it completes our knowledge by a new perspective – that of a professor of geometry completely trained in institutions of the polytechnical system and employed as a descriptive geometer. Descriptive geometry was the brandmark of polytechnical mathematics and Fiedler was deeply rooted in this tradition, a tradition more or less neglected in the historiography. Interesting enough descriptive geometry was even exported to some universities whereas most mathematics was imported by the Polytechnics from universities. In Fiedler's papers there are many other interesting documents like drafts for courses, lectures notes taken by his students, papers written by the students as homework, drawings, and so on. They provide an authentic picture of Fiedler's teaching in particular and of the teaching in general at Polytechnics.

• DFG Programme: Research Grants