Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1999
|
| Schriftenreihe: | Modern Birkhäuser Classics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle — for mathematics and physics alike — to be a matter of "understanding the world through its behavior in the infinitely small." This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics. "There is excellent referencing throughout… Quotes are given almost always both in English and in the original German. Many readers will feel the original German brings them a bit closer to Riemann and his contemporaries… Laugwitz’s expertise on historical matters is most impressive… Thanks are due to both author and translator for making it much easier to enter into the literature on Riemann." —MAA Online "...the author has succeeded admirably...stating the technical details clearly and correctly while writing an engaging and readable account of Riemann’s life and work... Any reader of this book with even a passing interest in the history or philosophy of mathematics is certain to become engaged in a mental conversation with the author... The format of the book is excellent, especially the plentiful supply of photographs of people and places... The book will serve as an interesting read and also a useful reference... It is highly recommended." —Bulletin of the AMS |
| Beschreibung: | 1 Online-Ressource (XVII, 357 p) |
| ISBN: | 9780817647773 9780817647766 |
| ISSN: | 2197-1803 |
| DOI: | 10.1007/978-0-8176-4777-3 |
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| 500 | |a The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. | ||
| 500 | |a Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle — for mathematics and physics alike — to be a matter of "understanding the world through its behavior in the infinitely small." This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. | ||
| 500 | |a This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics. "There is excellent referencing throughout… Quotes are given almost always both in English and in the original German. Many readers will feel the original German brings them a bit closer to Riemann and his contemporaries… Laugwitz’s expertise on historical matters is most impressive… Thanks are due to both author and translator for making it much easier to enter into the literature on Riemann." —MAA Online "...the author has succeeded admirably...stating the technical details clearly and correctly while writing an engaging and readable account of Riemann’s life and work... Any reader of this book with even a passing interest in the history or philosophy of mathematics is certain to become engaged in a mental conversation with the author... | ||
| 500 | |a The format of the book is excellent, especially the plentiful supply of photographs of people and places... The book will serve as an interesting read and also a useful reference... It is highly recommended." —Bulletin of the AMS | ||
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| author | Laugwitz, Detlef |
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| building | Verbundindex |
| bvnumber | BV042419161 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)905441896 (DE-599)BVBBV042419161 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-8176-4777-3 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-10-22T12:01:09Z |
| institution | BVB |
| isbn | 9780817647773 9780817647766 |
| issn | 2197-1803 |
| language | English |
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| spelling | Laugwitz, Detlef Verfasser aut Bernhard Riemann 1826–1866 Turning Points in the Conception of Mathematics by Detlef Laugwitz Boston, MA Birkhäuser Boston 1999 1 Online-Ressource (XVII, 357 p) txt rdacontent c rdamedia cr rdacarrier Modern Birkhäuser Classics 2197-1803 The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle — for mathematics and physics alike — to be a matter of "understanding the world through its behavior in the infinitely small." This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics. "There is excellent referencing throughout… Quotes are given almost always both in English and in the original German. Many readers will feel the original German brings them a bit closer to Riemann and his contemporaries… Laugwitz’s expertise on historical matters is most impressive… Thanks are due to both author and translator for making it much easier to enter into the literature on Riemann." —MAA Online "...the author has succeeded admirably...stating the technical details clearly and correctly while writing an engaging and readable account of Riemann’s life and work... Any reader of this book with even a passing interest in the history or philosophy of mathematics is certain to become engaged in a mental conversation with the author... The format of the book is excellent, especially the plentiful supply of photographs of people and places... The book will serve as an interesting read and also a useful reference... It is highly recommended." —Bulletin of the AMS Riemann, Bernhard 1826-1866 (DE-588)118600869 gnd rswk-swf Mathematics Physics Mathematics, general History of Mathematical Sciences Physics, general Philosophy Mathematik Philosophie Riemann, Bernhard 1826-1866 (DE-588)118600869 p 1\p DE-604 https://doi.org/10.1007/978-0-8176-4777-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Laugwitz, Detlef Bernhard Riemann 1826–1866 Turning Points in the Conception of Mathematics Riemann, Bernhard 1826-1866 (DE-588)118600869 gnd Mathematics Physics Mathematics, general History of Mathematical Sciences Physics, general Philosophy Mathematik Philosophie |
| subject_GND | (DE-588)118600869 |
| title | Bernhard Riemann 1826–1866 Turning Points in the Conception of Mathematics |
| title_auth | Bernhard Riemann 1826–1866 Turning Points in the Conception of Mathematics |
| title_exact_search | Bernhard Riemann 1826–1866 Turning Points in the Conception of Mathematics |
| title_full | Bernhard Riemann 1826–1866 Turning Points in the Conception of Mathematics by Detlef Laugwitz |
| title_fullStr | Bernhard Riemann 1826–1866 Turning Points in the Conception of Mathematics by Detlef Laugwitz |
| title_full_unstemmed | Bernhard Riemann 1826–1866 Turning Points in the Conception of Mathematics by Detlef Laugwitz |
| title_short | Bernhard Riemann 1826–1866 |
| title_sort | bernhard riemann 1826 1866 turning points in the conception of mathematics |
| title_sub | Turning Points in the Conception of Mathematics |
| topic | Riemann, Bernhard 1826-1866 (DE-588)118600869 gnd Mathematics Physics Mathematics, general History of Mathematical Sciences Physics, general Philosophy Mathematik Philosophie |
| topic_facet | Riemann, Bernhard 1826-1866 Mathematics Physics Mathematics, general History of Mathematical Sciences Physics, general Philosophy Mathematik Philosophie |
| url | https://doi.org/10.1007/978-0-8176-4777-3 |
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