Poincaré’s Geometric Worldview and Philosophy

DOI10.1007/978-3-030-13609-3_10zbMath1455.01016OpenAlexW2981152938MaRDI QIDQ5129774

Ken'ichi Ohshika

Publication date: 23 October 2020

Published in: Geometry in History (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-13609-3_10

zbMATH Keywords

topologynon-Euclidean geometryconventionalismspontaneous philosophy of scientists

Mathematics Subject Classification ID

Philosophy of mathematics (00A30) History of mathematics in the 20th century (01A60) History of mathematics in the 19th century (01A55) History of manifolds and cell complexes (57-03) History of geometry (51-03) History of functions of a complex variable (30-03) History of general topology (54-03)

Cites Work

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• Pangeometry. Edited and translated by Athanase Papadopoulos
• Generalized Poincaré's conjecture in dimensions greater than four
• The topology of four-dimensional manifolds
• Poincaré conjecture and related statements
• On the works of Euler and his followers on spherical geometry
• Kant, Herbart and Riemann
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• The Origin of the Notion of Manifold: From Riemann’s Habilitationsvortrag Onward
• Flat Affine, Projective and Conformal Structures on Manifolds: A Historical Perspective
• A Glimpse into the Problems of the Fourth Dimension

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