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.
This book caters for the general public. Solving Riemann hypothesis proposed by famous German mathematician Bernhard Riemann in 1859 has resulted in important Fundamental Laws for Living and Nonliving Things. Open problems in Number theory of Riemann hypothesis, Polignac's and Twin prime conjectures have been unsolved for over 150 years. They are finally solved when sine qua non treated as Incompletely Predictable problems in 2019. Riemann hypothesis belongs to one of seven Millennium Prize Problems in mathematics stated by Clay Mathematics Institute on May 24, 2000. The author serendipitously cross path with the Institute's website Riemann Hypothesis on Thursday March 10, 2016 in permanently altering its information content from previous incorrect [sic] "...the first 10,000,000,000 solutions" to current correct [sic] "...the first 10,000,000,000,000 solutions". Configured as containing useful materials on Medicine, Physiology and Religion, Chapters 1 to 10 as beginning part concentrate on materials related to Alphabet and Language of Science emphasizing its important role in the two innovative 'Spherical Model of Science' and 'Spherical Model of Numbers'. Chapters 11 to 15 contain introductory materials for our three open problems with Chapter 11 explaining the important Fundamental Laws. Chapters 16 to 21 concentrate on describing in layman's terms how rigorous proofs for our three open problems are derived as two complete research papers first published in viXra (reproduced in Appendix 1 and 2). Chapters 22 to 25 as end part contain materials that speculate on important role of Umbral ("Shadow"), Mathieu and Monstrous Moonshine in String theory potentially uniting Einstein General Relativity and Quantum gravity, and refute a common misconception that solving Riemann hypothesis will lead to E-Commerce apocalypse. The exotic A228186 Hybrid integer is also outlined in this book.
Bernhard Riemanns Werk hat bis heute wesentlichen Einfluß auf die Entwicklung der Mathematik genommen. Seine Ideen sind überraschend modern und prägen die heutige mathematische Forschung. Die Gesammelten Abhandlungen (1892) samt Supplement von 1902 waren seit langer Zeit vergriffen. R. Narasimhan hat die mühevolle Edition dieser Neuausgabe übernommen. Es können nur einige Höhepunkte genannt werden: - H. Weils Kommentare über Riemanns Habilitationsschrift - C.L. Siegel über Riemanns Nachlass zur analytischen Zahlentheorie - W. Wirtingers berühmter Vortrag beim internationalen Mathematikerkongress Heidelberg 1904 über Riemanns Vorlesungen über die hypergeometrische Reihe. Neben diesen historischen Würdigungen von Riemanns Werk gibt es aktuelle Beiträge, insbesondere zur Mechanik und über "shock waves" von S. Chandrasekhar, N. Lebovitz und P. Lax. Raghavan Narasimhan gibt in einer ausführlichen Einleitung eine Würdigung, insbesondere des funktionentheoretischen Werks von Bernhard Riemann. Ferner sind Fotos und zahlreiche Nachträge zum Lebenslauf aufgenommen worden. Eine Bibliographie mit mehr als 800 Literaturstellen erarbeitet von E. Neuenschwander und W. Purkert rundet diese Werkausgabe ab.
Printed in the original German, this highly prized, unabridged text of the complete works of the legendary mathematician includes 31 monographs, three complete lecture courses, and 15 miscellaneous papers.
The collected works, in German, of the groundbreaking mathematician Bernhard Riemann (1826-66) first appeared in 1876. Included here is his famous 1854 lecture 'On the hypotheses which underlie geometry', which set in motion studies which culminated in Einstein's general theory of relativity.
In diesem Werk wird einer der klassischen Texte der Mathematik umfassend historisch, mathematisch, physikalisch und philosophisch von Jürgen Jost ausführlich kommentiert und die gesamte Entwicklung dieser Disziplinen eingeordnet. Neben dem Urtext wird auch der historisch wichtige Kommentarteil von Hermann Weyl wiedergegeben.
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