Late nineteenth century background

pp. 11-81

in: Leo Corry, David Hilbert and the axiomatization of physics (1898–1918), Berlin, Springer, 2004

Abstract

Hilbert's first published, comprehensive presentation of an axiomatized mathematical discipline appeared in June of 1899, in the epoch-making Grundlagen der Geometrie (GdG).Based on a course taught in the winter semester of 1898–99, GdG was published as part of a Festschrift issued in Göttingen to celebrate the inauguration of a monument to honor two of its legendary scientists: Carl Friedrich Gauss (1777–1855) and Wilhelm Weber (1804–1891). Hilbert had been teaching courses on topics related to geometry and its foundations since 1891. Nevertheless, the conception and the results embodied in GdG signified a real innovation that was to make a deep impact on geometry and, indeed, on the whole of mathematics for decades to come. Like most of Hilbert's early important works, this one had deep roots in central developments of the classical theories that thrived in the nineteenth century. In order to understand those roots and the actual historical significance of GdG, the present chapter is devoted to describing in some detail the relevant background related to those developments. It comprises four main themes, all of them spanning the late nineteenth century: Hilbert's early career (§ 1.1), foundations of geometry (§ 1.2), foundations of physics (§ 1.3), and mathematics and physics in Göttingen at the time Hilbert arrived there (§ 1.4).