1830-1930: A Century of Geometry, Epistemology History and Mathematics, Springer

Description: 1830-1930: A Century of Geometry Epistemology, History and Mathematics edited by L. Boi, D. Flament, J.-M.Salanskis Springer-Verlag, 1992, 0387554084, 3540554084, Hardcover without Dust Jacket, Good condition, no ex-library usual markings. 304 pages. Lecture Notes in Physics 402 Foreword This volume contains a selection of articles based on lectures presented at the international Conference "1830-1930: Un Siecle de Geometrie: de C.F. Gauss et B. Riemann a H. Poincare et E. Cartan; epistemologie, histoire et mathematiques", which was held in Paris, 18-23 September 1989, at the Institut Henri Poincare. The initiative was taken by two research groups: the Seminaire d'Epistemologie des Mathematiques of the Ecole des Hautes Etudes en Sciences Sociales and the group Recherches Epistemologiques et Historiques sur les Sciences Exactes et sur les Institutions Scientifiques of the Centre National de la Recherche Scientifique. Since the discovery of non-Euclidean geometries by Gauss, Lobatchevsky and Bolyai at the beginning of the last century, many new geometrical structures and theories have been developed: differential Riemannian geometry, projective geometry, algebraic geometry, symplectic geometry, differential topology, etc. These have deeply modified and extended the concept of space and under the influence of mathematicians like Gauss, Riemann, Grassmann, Poincare, Lie, Hilbert and Cartan, have supported a fertile process of geometrization which has affected in an essential way mathematics, physics, and our understanding of their relations. From the space-time of Minkowski, Einstein, and Weyl to non-Abelian gauge theories, this process of geometrization has continued at an ever-increasing pace in modern times. While geometry holds a leading position in modern mathematics and physics, epistemology and the philosophy and history of science still seem to concentrate upon the problem of foundations, formal logic and classical analysis, or the epistemological status of quantum mechanics. But this is obviously insufficient. We therefore urgently need to revisit the philosophical problems concerning the status of geometry and to renew our present epistemological trends with some of the rich reflexions developed at the beginning of this century. The conference took risks by gathering together historians, philosophers, mathematicians and physicists to re-examine the recent history of geometry in the light of the contemporary developments of mathematics and physics, but we think that the talks and discussions showed that this mixture generated more light than heat, as we had hoped. The book is divided into five sections, which roughly correspond to the thematic organisation of the five days of the meeting. In any case, these parts seem to us to reflect faithfully the various aspects of geometry as they were addressed by the contributors. The Editors CONTENTS Part 1 Pluralization of Geometry: New Foundations and Continuity of Problems The Birth of Non-Euclidean Geometry by Ch. Houzel Riemann's Vision of a New Approach to Geometry by E. Scholz Poincare and Klein — Groups and Geometries by J.J. Gray Klein, Lie, and the "Erlanger Programm" by D. E. Rowe Apparent Contours from Monge to Todd by B. Teissier Part 2 Historical and Epistemological Aspects of the Connexion Between Physics and Geometry L'Espace: Concept Abstrait et/ou Physique ; la Geometrie Entre Formalisation Mathematique et Etude de la Nature by L. Boi "Geometrie and Erfahrung" by F. Balibar The Geometric Challenge of Riemann and Clifford by R. Farwell and Ch. Knee Poincare et Enriques : Deux Points de Vue Differents sur les Relations entre Geometrie, Mecanique et Physique by G.Israel Physical Geometry and Special Relativity. Einstein and Poincare by M. Paty Transport parallele et Connexions en Geometrie et en Physique by J.-P. Bourguignon Part 3 Formalism and Intuition De la Geometrie Formelle a l'Algebre Abstraite by H. Sinaceur Le Principe de Dualite : sa Signification Historique et Epistemologique by L. Geymonat The Formal and the Transcendental in Mathematics by G.G. Granger Un Panorama des Mathematiques by R. Thom Mathematical Progress as Synthesis of Intuition and Calculus by K. Volkert Part 4 The Philosophical Problem of Space What is Space? by H. Freudenthal La "lineale Ausdehnungslehre" (1844) de Hermann Gunther Grassmann by D. Flament La Capture de l'Extension comme Dialectique Geometrique : Dimension et Puissance Selon l'Ausdehnung de Grassmann (1844) by G. Chatelet Helmholtz and Poincare's Considerations on the Genesis of Geometry by G. Heinemann Le Continu contre l'Espace by J.-M. Salanskis Part 5 Some Insights About Modern Physics Geometrical Concepts in Quantum Physics by G. Cohen-Tannoudji Physics and Differential Geometry by T. Regge Actuality of Transcendental Aesthetics for Modern Physics by J. Petitot Powered by SixBit's eCommerce Solution

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