**Wilhelm Fiedler** was a German mathematician, known for his textbooks of geometry and for his contributions to descriptive geometry.

- He realised that Wilhelm took a keen interest in the pictures and showed considerable drawing abilities.
- Fiedler quickly showed his talents and progressed to the top of the class.
- Caspary himself began to teach Fiedler but discovered that despite his drawing abilities, he was passionate about mathematics.
- Fiedler was always very grateful for the help and inspiration he received from Caspary.
- Fiedler now made an ink drawing of Leonardo da Vinci's 'Last Supper' and the money he made by selling it, and other works, helped him continue with his education.
- In 1846 Fiedler won a state scholarship which enable him to attend the School of Arts and Crafts in Chemnitz.
- He took Fiedler deeper into his field and suggested that he should continue his studies under Weisbach.
- Weisbach was professor of applied mathematics and mechanics at the Bergakademie in Freiberg and, in 1849, Fiedler began his studies in Freiberg as an external student.
- At first Fiedler lived with a shoemaker in Freiberg, studying mathematics sitting in one of the windows of the workshop while there was hammering and sewing of shoes in the other window.
- Fiedler's studies at the Bergakademie in Freiberg lasted for three years.
- Fiedler studied both practical mechanics and applied mathematics during his three years at the Bergakademie.
- This was not exactly what Fiedler wanted since his ambition had been to study at the University of Freiberg.
- It was through this private study that Fiedler intended to teach himself university level mathematics and, more than this, he wanted to become expert enough to be able to undertake research of sufficient standard that he could earn a doctorate.
- Fiedler was not content to study just mathematics but he wanted to give himself an all-round university level education which he felt he totally lacked.
- Not only did Fiedler do a great deal of self-study but with his friends, the geologist Adolf Knop and the chemist Alexander Müller, he led an organised series of scientific and literary lecture evenings in Chemnitz.
- Fiedler himself lectured on a wide variety of topics in addition to mathematics, physics and astronomy.
- Fiedler's introduction to mathematics had come through practical applications and applied mathematics.
- However, he learnt of Alfred Clebsch's work, in particular he discovered that he was writing a major work on elasticity so Fiedler decided to change areas.
- Fiedler turned to geometry and studied the ideas of Jakob Steiner, Julius Plücker, August Möbius, Karl von Staudt and the French mathematicians Jean-Victor Poncelet, Michel Chasles and Gabriel Lamé.
- In 1858 Fiedler submitted his thesis Die Zentralprojektion als geometrische Wissenschaft Ⓣ(The central projection as geometric science) to August Möbius at the University of Leipzig who recommended that Fiedler be awarded a doctorate.
- It is interesting to note that Fiedler's thesis was much influenced by his knowledge of art and he gives a purely geometric description of perspective in his doctoral dissertation.
- At this time, Fiedler continued to teach at the Gewerbeschule in Chemnitz.
- Another of their sons, Alfred Fiedler (1863-1894), lectured on zoology at the University of Zürich.
- Fiedler read George Salmon's 1855 A Treatise on Conic Sections containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods.
- The first edition of Fiedler's translation, with title Analytische Geometrie der Kegelschnitte mit besonderer Berücksichtigung der neueren Methoden Ⓣ(Analytical geometry of conic sections with special emphasis on newer methods), was published in 1860 but Fiedler went on to bring out a total of seven editions each of contains material which he added to bring the work up to date.
- For example the second edition, published in 1866, is described by Fiedler as "second revised and modernised edition".
- In 1862 Fiedler published Die Elemente der neueren Geometrie und die Algebra der binären Formen: Ein Beitrag zur Einführung in die Algebra der linearen Transformationen Ⓣ(The elements of modern geometry and the algebra of binary forms: A Contribution to the introduction to the algebra of linear transformations).
- Salmon's A Treatise on the Analytic Geometry of Three Dimensions (1862) was translated by Fiedler and was published in two volumes, the first under the title Analytische Geometrie des Raumes.
- Fiedler supported Otto von Bismarck who led the Prussian side but these were difficult times with the population of Prague split as to who they supported.
- Fiedler spent only three years in Prague before he was appointed in 1867 to fill the chair of descriptive geometry at the Polytechnic in Zürich, which had become vacant following the death of Josef Wolfgang von Deschwanden (1819-1866).
- The President of the Swiss School Board had visited Fiedler in Prague in the winter of 1866-67 to complete the final negotiations for his move to Zürich but these proved quite difficult and lengthy as Fiedler was unhappy with the time allocated to the teaching of descriptive geometry in the Polytechnic.
- It was a book of descriptive geometry by Wilhelm Fiedler (1832-1912).
- It was certainly appropriate to have Fiedler's book alongside Cremona's 'Projective Geometry' in the parallel course of descriptive geometry at the Technical Institutes.
- According to Fiedler, the main scope of the teaching of descriptive geometry is the scientific construction and development of "Raumanschauung".
- Fiedler reinforced this point of view in a paper translated and published in the 'Giornale di Matematiche'.
- Fiedler sees a complete symbiosis between descriptive and projective geometry and holds that starting from central projection, which corresponds to the process of viewing, we can develop the fundamental part of projective geometry in a natural and complete way (Fiedler, 1878).
- Fiedler sees these strategies as the best method for the reform of geometry teaching at all levels.
- The position of Fiedler was very close to Cremona's.
- Fiedler never mentions Cremona in his paper, but in a letter to Cremona, at the beginning of 1873, he praises his book and the simple way in which Cremona introduces the topics.
- Of course, Fiedler was very sad at his son's illness and his reaction to grief was always to throw himself even more into his work.
- It was in 1870 the Fiedler made his most important research contribution when he recognised homogeneous coordinates as cross-ratios which were invariant under linear transformations.
- However, Möbius's discovery went unnoticed while Fiedler's rediscovery was widely read and incorporated into mathematical knowledge.
- Of course, Fiedler's love of descriptive geometry fitted in to a certain extent with his love of drawing.
- Perhaps this love of drawing was a factor in Fiedler's approach to geometry where he always gave great emphasis to constructions.
- Among the honours given to Fiedler, we mention his election to the German Academy of Scientists Leopoldina in 1889 and to the Bavarian Academy of Sciences and Humanities in 1906.
- Fiedler's colleagues knew nothing about his suffering because, although he increasingly withdrew from almost everything, he made an exception with his university duties which he continued to undertake with much vigour.
- Fiedler retired from his professorship at the Polytechnic in Zürich in 1907.

Born 3 April 1832, Chemnitz, Saxony, Germany. Died 19 November 1912, Zürich, Switzerland.

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Astronomy, Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive