A century of geometry 1830 - 1930 ; epistemology, history and mathematics

In the first half of the 19th century geometry changed radically, and withina century it helped to revolutionize both mathematics and physics. It also put the epistemology and the philosophy of science on a new footing. In this volume a sound overview of this development is given by leading mathematicians, physicists, philosophers, and historians of science. This interdisciplinary approach gives this collection a unique character. It can be used by scientists and students, but it also addresses a general readership. front-matter......Page 1 1The birth of non-Euclidean geometry......Page 8 2Riemann's vision of a new approach to geometry......Page 29 3Poincaré and Klein — groups and geometries......Page 42 4Klein, Lie, and the “Erlanger programm”......Page 52 5Apparent contours from Monge to Todd......Page 62 6L'Espace Concept abstrait et-ou physique la géométrie entre formalisation mathématique et etude de la nature......Page 70 7Geometrie und Erfahrung......Page 98 8The geometric challenge of Riemann and Clifford......Page 105 9Poincaré et Enriques deux points de vue différents sur les relations entre géométrie, mécanique et physique......Page 114 10Physical geometry and special relativity. Einstein et Poincaré......Page 134 11Transport parallèle et connexions en Géométrie et en Physique......Page 157 12De la Géométrie Formelle à l'Algèbre Abstraite......Page 172 13Le Principe de Dualité sa Signification Historique et Epistémologique......Page 182 14The formal and the transcendental in mathematics......Page 185 15Un Panorama des Mathématiques......Page 191 16Mathematical progress as synthesis of intuition and calculus......Page 199 17What is space......Page 206 18La “lineale ausdehnungslehre” (1844) de Hermann Günther Grassmann......Page 212 19La capture de l'extension comme dialectique géométrique Dimension et puissance selon l'ausdehnung de Grassmann (1844)......Page 229 20Helmholtz and Poincaré's considerations on the genesis of geometry......Page 252 21Le continu contre l'espace......Page 257 22Geometrical concepts in quantum physics......Page 272 23Physics and differential geometry......Page 277 24Actuality of transcendental æsthetics for modern physics......Page 280 In the first half of the 19th century geometry changed radically, and within a century it helped to revolutionize both mathematics and physics. In this volume, an overview of this development is given by leading mathematicians, physicists, philosophers, and historians of science. L. Boi, D. Flament, J.-m. Salanskis (eds.). Proceedings Of An International Conference Held Sept. 18-23, 1989 At The Institut Henri Poincaré In Paris. Includes Bibliographical References.