Titlebook: On the Hypotheses Which Lie at the Bases of Geometry; Bernhard Riemann,Jürgen Jost Book 2016 Springer International Publishing Switzerland

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On the Hypotheses Which Lie at the Bases of Geometry

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2365-9963 aders from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.978-3-319-79880-6978-3-319-26042-6Series ISSN 2365-9963 Series E-ISSN 2365-9971

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Introduction, Alexander Grothendieck on the systematic unification of algebraic geometry and arithmetic. We are talking here of Bernhard Riemann’s “.” (“.”), and this short script, written in 1854, but only published in 1868 after Riemann’s death, whose wide ranging effects even take it beyond these works. This

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Historical Introduction,it is like any other, and isotropic, that is, in all directions it looks the same. No point and no direction is in any way distinguished. Aristotle (384–322 .) in contrast thought of the world as a collection of places. According to him, the location of an object is determined by its bounding surfac

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Presentation of the Text, certain natural constraints). This structure can then be restricted on the one hand by conditions of simplicity and on the other hand by empirical testing if it is supposed to describe the actual physical space. Riemann then describes the quantitative structure by a so-called metric tensor, which f

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