1830-1930: A Century of Geometry: Epistemology, History and Mathematics (Lecture Notes in Physics)

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. The birth of non-Euclidean geometry.- Riemann’s vision of a new approach to geometry.- Poincar and Klein – groups and geometries.- Klein, Lie, and the “Erlanger programm”.- Apparent contours from Monge to Todd.- L’Espace : Concept abstrait et/ou physique ; la gomtrie entre formalisation mathmatique et etude de la nature.- Geometrie und Erfahrung.- The geometric challenge of Riemann and Clifford.- Poincar et Enriques : deux points de vue diffrents sur les relations entre gomtrie, mcanique et physique.- Physical geometry and special relativity. Einstein et Poincar.- Transport parallle et connexions en Gomtrie et en Physique.- De la Gomtrie Formelle l’Algbre Abstraite.- Le Principe de Dualit : sa Signification Historique et Epistmologique.- The formal and the transcendental in mathematics.- Un Panorama des Mathmatiques.- Mathematical progress as synthesis of intuition and calculus.- What is space?.- La “lineale ausdehnungslehre” (1844) de Hermann Gnther Grassmann.- La capture de l’extension comme dialectique gomtrique : Dimension et puissance selon l’ausdehnung de Grassmann (1844).- Helmholtz and Poincar’s considerations on the genesis of geometry.- Le continu contre l’espace.- Geometrical concepts in quantum physics.- Physics and differential geometry.- Actuality of transcendental sthetics for modern physics.