Bernhard Riemann On The Hypotheses Which Lie At The Bases Of Geometry
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On The Hypotheses Which Lie At The Bases Of Geometry
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Author : Bernhard Riemann
language : en
Publisher: Birkhäuser
Release Date : 2016-04-19
On The Hypotheses Which Lie At The Bases Of Geometry written by Bernhard Riemann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
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
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Author : Jürgen Jost
language : en
Publisher: Birkhäuser
Release Date : 2025-07-09
Bernhard Riemann On The Hypotheses Which Lie At The Bases Of Geometry written by Jürgen Jost and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-09 with Mathematics categories.
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 Emergence Of The Fourth Dimension
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Author : Mark Blacklock
language : en
Publisher: Oxford University Press
Release Date : 2018
The Emergence Of The Fourth Dimension written by Mark Blacklock and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Literary Criticism categories.
This volume examines the emergence of the idea of the fourth dimension in fiction of the fin de siecle and how these new theories of the possibilities of time and space influenced writers such as Joseph Conrad, Ford Madox Ford, H.G. Wells, Henry James, H. P. Lovecraft, and others.
The Poetry Of Victorian Scientists
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Author : Daniel Brown
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-31
The Poetry Of Victorian Scientists written by Daniel Brown and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-31 with Literary Criticism categories.
A surprising number of Victorian scientists wrote poetry. Many came to science as children through such games as the spinning-top, soap-bubbles and mathematical puzzles, and this playfulness carried through to both their professional work and writing of lyrical and satirical verse. This is the first study of an oddly neglected body of work that offers a unique record of the nature and cultures of Victorian science. Such figures as the physicist James Clerk Maxwell toy with ideas of nonsense, as through their poetry they strive to delineate the boundaries of the new professional science and discover the nature of scientific creativity. Also considering Edward Lear, Daniel Brown finds the Victorian renaissances in research science and nonsense literature to be curiously interrelated. Whereas science and literature studies have mostly focused upon canonical literary figures, this original and important book conversely explores the uses literature was put to by eminent Victorian scientists.
From Past To Future Gra Mann S Work In Context
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Author : Hans-Joachim Petsche
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-16
From Past To Future Gra Mann S Work In Context written by Hans-Joachim Petsche and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-16 with Mathematics categories.
On the occasion of the 200th anniversary of the birth of Hermann Graßmann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Graßmann's hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Graßmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. This book contains 37 papers presented at the conference. They investigate the significance of Graßmann's work for philosophical as well as for scientific and methodological questions, for comparative philology in general and for Indology in particular, for psychology, physiology, religious studies, musicology, didactics, and, last but not least, mathematics. In addition, the book contains numerous illustrations and English translations of original sources, which are published here for the first time. These include life histories of Graßmann (written by his son Justus) and of his brother Robert (written by Robert himself), as well as the paper "On the concept and extent of pure theory of number'' by Justus Graßmann (the father).
Differential Geometry
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Author : Elisabetta Barletta
language : en
Publisher: Springer Nature
Release Date : 2025-04-22
Differential Geometry written by Elisabetta Barletta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-22 with Mathematics categories.
This book, Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B), is the first in a captivating series of four books presenting a choice of topics, among fundamental and more advanced in differential geometry (DG). Starting with the basics of semi-Riemannian geometry, the book aims to develop the understanding of smooth 1-parameter variations of geodesics of, and correspondingly of, Jacobi fields. A few algebraic aspects required by the treatment of the Riemann–Christoffel four-tensor and sectional curvature are successively presented. Ricci curvature and Einstein manifolds are briefly discussed. The Sasaki metric on the total space of the tangent bundle over a Riemannian manifold is built, and its main properties are investigated. An important integration technique on a Riemannian manifold, related to the geometry of geodesics, is presented for further applications. The other three books of the series are Differential Geometry 1: Manifolds, Bundle and Characteristic Classes (Book I-A)Differential Geometry 3: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C)Differential Geometry 4: Advanced Topics in Cauchy–Riemann and Pseudohermitian Geometry (Book I-D) The four books belong to a larger book project (Differential Geometry, Partial Differential Equations, and Mathematical Physics) by the same authors, aiming to demonstrate how certain portions of DG and the theory of partial differential equations apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG machinery yet do not constitute a comprehensive treatise on DG, but rather authors’ choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions—isometric, holomorphic, Cauchy–Riemann (CR)—and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.
Deleuze And The History Of Mathematics
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Author : Simon Duffy
language : en
Publisher: A&C Black
Release Date : 2013-07-04
Deleuze And The History Of Mathematics written by Simon Duffy and has been published by A&C Black this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-04 with Philosophy categories.
Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges are an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. In the wake of Alain Badiou's recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze's work, Simon Duffy offers a robust defence of the structure of Deleuze's philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze's seeming incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze's philosophy, rebuffing the recent challenges against it.
Multiplicity And Ontology In Deleuze And Badiou
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Author : Becky Vartabedian
language : en
Publisher: Springer
Release Date : 2018-03-21
Multiplicity And Ontology In Deleuze And Badiou written by Becky Vartabedian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Philosophy categories.
This book approaches work by Gilles Deleuze and Alain Badiou through their shared commitment to multiplicity, a novel approach to addressing one of the oldest philosophical questions: is being one or many? Becky Vartabedian examines major statements of multiplicity by Deleuze and Badiou to assess the structure of multiplicity as ontological ground or foundation, and the procedures these accounts prescribe for understanding one in relation to multiplicity. Written in a clear, engaging style, Vartabedian introduces readers to Deleuze and Badiou’s key ontological commitments to the mathematical resources underpinning their accounts of multiplicity and one, and situates these as a conversation unfolding amid political and intellectual transformations.
Evolution Of Black Holes In Anti De Sitter Spacetime And The Firewall Controversy
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Author : Yen Chin Ong
language : en
Publisher: Springer
Release Date : 2015-11-27
Evolution Of Black Holes In Anti De Sitter Spacetime And The Firewall Controversy written by Yen Chin Ong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-27 with Science categories.
This thesis focuses on the recent firewall controversy surrounding evaporating black holes, and shows that in the best understood example concerning electrically charged black holes with a flat event horizon in anti-de Sitter (AdS) spacetime, the firewall does not arise. The firewall, which surrounds a sufficiently old black hole, threatens to develop into a huge crisis since it could occur even when spacetime curvature is small, which contradicts general relativity. However, the end state for asymptotically flat black holes is ill-understood since their curvature becomes unbounded. This issue is avoided by working with flat charged black holes in AdS. The presence of electrical charge is crucial since black holes inevitably pick up charges throughout their long lifetime. These black holes always evolve toward extremal limit, and are then destroyed by quantum gravitational effects. This happens sooner than the time required to decode Hawking radiation so that the firewall never sets in, as conjectured by Harlow and Hayden. Motivated by the information loss paradox, the author also investigates the possibility that “monster” configurations might exist, with an arbitrarily large interior bounded by a finite surface area. Investigating such an object in AdS shows that in the best understood case, such an object -- much like a firewall -- cannot exist.