1830--1930: a century of geometry. Epistemology, history and mathematics. Selection of articles based on lectures presented at the international conference
type: Item
instance of: scholarly article
title: 1830--1930: a century of geometry. Epistemology, history and mathematics. Selection of articles based on lectures presented at the international conference
zbMATH Open document ID: 0757.01001
published in: Lecture Notes in Physics
publication date: 1993-01-23T00:00:00Z
review text: From the Foreword, ``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.'' Contents. Part 1. Pluralization of geometry: New foundations and continuity of problems: \textit{Christian Houzel}, The birth of non-Euclidean geometry (3--21); \textit{Erhard Scholz}, Riemann's vision of a new approach to geometry (22--34); \textit{J. J. Gray}, Poincaré and Klein -- groups and geometries (35--44); \textit{David E. Rowe}, Klein, Lie, and the ``Erlanger Programm'' (45--54); \textit{Bernard Teissier}, Apparent contours from Monge to Todd (55--62). Part 2. Historical and epistemological aspects of the connexion between physics and geometry: \textit{Luciano Boi}, L'espace: concept abstrait et/ou physique; la géométrie entre formalisation mathématique et étude de la nature [Space: abstract and/or physical concept; geometry in mathematical formalization and in the study of nature] (65--90); \textit{F. Balibar}, Geometrie und Erfahrung (English) [Geometry and experience] (91--97); \textit{Ruth Farwell} and \textit{Christopher Knee}, The geometric challenge of Riemann and Clifford (98--106); \textit{Giorgio Israel}, Poincaré et Enriques: deux points de vue différents sur l…
Mathematics Subject Classification ID: 01-06
Mathematics Subject Classification ID: 00B25
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 81-03
Mathematics Subject Classification ID: 83-03
Mathematics Subject Classification ID: 52-03
Mathematics Subject Classification ID: 53-03
Mathematics Subject Classification ID: 57-03
Mathematics Subject Classification ID: 14-03
Mathematics Subject Classification ID: 51-03
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 03-03
zbMATH DE Number: 108065
zbMATH Keywords: Paris (France)
zbMATH Keywords: Century
zbMATH Keywords: Geometry
zbMATH Keywords: Epistemology
zbMATH Keywords: History
zbMATH Keywords: Mathematics
zbMATH Keywords: Conference
zbMATH Keywords: Lectures
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 108065