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Bernhard Riemann -- on the hypotheses which lie at the bases of geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Bernhard Riemann -- on the hypotheses which lie at the bases of geometryby Jürgen Jost.
Author:	Jost, Jürgen.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xii, 188 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry.
Online resource:	https://doi.org/10.1007/978-3-031-91489-8
ISBN:	9783031914898$q(electronic bk.)

Bernhard Riemann -- on the hypotheses which lie at the bases of geometry
Jost, Jürgen.

Bernhard Riemann -- on the hypotheses which lie at the bases of geometry[electronic resource] /by Jürgen Jost. - Second edition. - Cham :Springer Nature Switzerland :2025. - xii, 188 p. :ill. (some col.), digital ;24 cm. - Classic texts in the sciences,2365-9971. - Classic texts in the sciences..

Introduction -- Historical background -- Riemann's habilitation -- Presentation of the texts -- Reception and impact on history -- Modern research -- Bibliography.

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.

ISBN: 9783031914898$q(electronic bk.)

Standard No.: 10.1007/978-3-031-91489-8doiSubjects--Personal Names:

745039
Riemann, Bernhard,
1826-1866.Subjects--Topical Terms:

183883
Geometry.

LC Class. No.: QA445

Dewey Class. No.: 516

Bernhard Riemann -- on the hypotheses which lie at the bases of geometry
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505 0 $a Introduction -- Historical background -- Riemann's habilitation -- Presentation of the texts -- Reception and impact on history -- Modern research -- Bibliography.
520 $a 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.
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