Bernhard Riemann, Uber die Hypothesen, welche der Geometrie zu Grunde liegen, Hrsg. von Juergen Jost, Klassische Texte der Wissenschaft. Springer 2013

摘要

These two famous texts surely deserve to appear in a series devoted to classics of science, and thanks to the efforts of their editors both are now available in a format that provides much else besides. In their respective commentaries, Jiirgen Jost and Klaus Volkert offer readers several new insights and reflections, in part by drawing on and calling attention to the rich scholarly literature concerned with these works and their specific intellectual contexts. For general background, I would also especially recommend Max Dehn's essay, Die Grundlegung der Geometrie in historischer Entwick-lung [6], which places the work of Riemann and Hilbert in an interesting historical perspective. As one of Hilbert's many gifted students, Dehn did groundbreaking work on the foundations of geometry, but he was also a leading authority on the historical developments that preceded. His views on Riemann's as well as Hilbert's contributions are therefore very well worth reading. Dehn's express purpose, in fact, was to stimulate interest among mathematicians to read the classical literature [6, viii]. This new Springer series would surely have met with his approval.