Victor Schlegel

Victor Schlegel (1843–1905) was a German mathematician. He is remembered for promoting the geometric algebra of Hermann Grassmann and for a method of visualizing polytopes called Schlegel diagrams.

In the nineteenth century there were various expansions of the traditional field of geometry through the innovations of hyperbolic geometry, non-Euclidean geometry and algebraic geometry. Hermann Grassmann was one of the more advanced innovators with his anticipation of linear algebra and multilinear algebra that he called "Extension theory" (Ausdehnungslehre). As recounted by David E. Rowe in 2010:

In 1872 Schlegel published the first part of his System der Raumlehre which used Grassmann’s methods to develop plane geometry. Schlegel used his book to put forth Grassmann’s case, arguing that "Grassmann’s ideas had been neglected because he had not held a university chair." Continuing his criticism of academics, Schlegel expressed the reactionary view that

Schlegel’s attitude was that no basis for scientific method was shown in mathematics, and "neglect of foundations had led to the widely acknowledged lack of interest in mathematics in the schools."

The mathematician Felix Klein addressed Schlegel’s book in a review criticizing him for neglect of cross ratio and failure to contextualize Grassmann in the flow of mathematical developments. Rowe indicates that Klein was most interested in developing his Erlangen program. In 1875 Schlegel countered with the second part of his System der Raumlehre, answering Klein in the preface. This part developed conic sections, harmonic ranges, projective geometry, and determinants.

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