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

威廉·费德勒：他的生活、他的作品和他的活动。

• 批准号: 515951245
• 负责人: Professor Dr. Klaus Volkert
• 金额: --
• 依托单位: Arbeitsgruppe Didaktik und Geschichte der Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/515951245?language=en
• 关键词: Wilhelm; Fiedler; His; Life; his

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.

该项目的目的是准备出版一本题为“威廉·费德勒：他的生活，他的作品，他的活动。几何学家的战斗”的书。本书由两卷组成，第一卷致力于详细研究费德勒的生活、他的载体、他的作品，并置于他所处的时代（1832 - 1912）和他所就职的机构（开姆尼茨高等理工学院（1851 - 1864）、布拉格理工学院（1864 - 1867）和苏黎世理工学院（1867 - 1912）的背景下。 1907））。这将是对曾在苏黎世担任画法几何和位置几何教授的费德勒的首次全面研究。费德勒的研究领域是几何，特别是画法几何和射影几何：除了自己的研究论文（超过 40 篇）外，他还出版了三本书。费德勒因出版乔治·萨尔蒙所著书籍的德文版而变得极具影响力。这些德文版本广泛传播，经常被一代又一代的数学家重新编辑和使用，以学习“新几何”——当时通常被称为“解析几何”——与“新代数”和不变理论密切相关。 “Salmon-Fiedler”这个名字当时所有从事数学工作的人都知道，它是一个非常突出的商标。费德勒自己的画法几何著作（1871年；四版，翻译成意大利语）有一定影响（也在国际层面）；它的中心思想是描述几何和射影几何、合成几何和解析几何的综合——带有费德勒的烙印。费德勒在定义射影几何性质的过程中发挥了重要作用，这一过程正在进行中。费德勒留下了大量信件和大量有趣的材料；他是一个主要以理工学院为基地的网络的活跃成员，该网络致力于捍卫几何学，以防止其重要性由于 19 世纪后三分之一的突出趋势（“Arithmetisierung”）而下降。该网络还为保留和设立几何教授职位而奋斗。费德勒的案例从新的角度为数学发展的这一重要时期提供了更多信息；它以一种新的视角完善了我们的知识——一位在理工系统机构中接受过全面培训的几何学教授，并被聘为画法几何学家。画法几何是理工数学的标志，而费德勒深深植根于这一传统，而这一传统在史学中或多或少被忽视了。足够有趣的画法几何学甚至被出口到一些大学，而大多数数学是由理工学院从大学引进的。费德勒的论文中还有许多其他有趣的文件，例如课程草稿、学生的讲课笔记、学生作为作业写的论文、图画等等。它们提供了费德勒教学的真实情况，特别是理工学院教学的真实情况。