On The Hypotheses Which Lie At The Bases Of Geometry
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On the Hypotheses Which Lie at the Bases of Geometry
This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
Bernhard Riemann — On the Hypotheses Which Lie at the Bases of Geometry
This book presents William Clifford’s English translation of Bernhard Riemann’s seminal text, accompanied by detailed mathematical, historical, and philosophical commentary. It explores Riemann’s revolutionary ideas on space, placing them within the broader framework developed by later thinkers such as Helmholtz, Ricci, Weyl, and Einstein. A historical introduction situates Riemann’s work in its 19th-century context, while subsequent chapters trace the evolution of the concept of space across philosophy, physics, and mathematics, and examine its enduring influence up to modern research. The second edition includes expanded mathematical commentary, a new section on metric geometry and machine learning, a systematic bibliography, and numerous updates throughout. Appealing to mathematicians, historians, and readers with an interest in physics or philosophy, this book provides a comprehensive perspective on Riemann’s groundbreaking contributions and their lasting impact.
The Development of Peirce's Philosophy
Author: Murray G. Murphey
language: en
Publisher: Hackett Publishing
Release Date: 1993-01-01
A reprint of the Harvard University Press edition of 1961. Includes a new preface and a new appendix with footnotes keyed to the manuscript classifications by Max Fisch.