Ludwig Schläfli -- an ingenious Swiss mathematician (Q613906)

The author gives a nicely written overview on the main mathematical activities of the famous Swiss mathematician Ludwig Schläfli (1814--1895). The reader, being not familiar with Schläfli's life and contributions to different mathematical fields, such as Algebraic Geometry, \(n\)-dimensional geometry (here also the classification of the \(n\)-dimensional regular polytopes), Differential Geometry, Number Theory, Analysis, Mechanics etc., is surprised regarding the versatility of this ingenious mathematician! And also examples of his very wide correspondence with famous colleagues (J. Steiner, A. Cayley etc.) are discussed. Also singular observations and results are surprising, such as the remark that Schläfli was most likely the first who discovered the fact that the projective plane cannot be oriented, what he also wrote to F. Klein. Basic notions and methods related to Schläfli's approach to the class of regular polytopes (like Schläfli's differential form, his reduction formula and the rational simplex conjecture) are presented in a more detailed way.