Petsche Hermann Graßmann

Biography
1. Auflage 2009
ISBN: 978-3-7643-8860-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 306 Seiten, eBook

Hermann Günther Graßmann was one of the most remarkable personalities in 19th-century science. A 'small-town genius', he developed a groundbreaking n-dimensional algebra of space and contributed to a revolution in the understanding of mathematics. His work fascinated great mathematicians such as W. R. Hamilton, J. W. Gibbs and A. N. Whitehead. This intellectual biography traces Graßmann's steps towards scientific brilliance by untangling a complicated web of influences: the force of unsolved problems in mathematics, Friedrich Schleiermacher's Dialectic, German Romanticism and life in 19th-century Prussia. The book also introduces the reader to the details of Graßmann's mathematical work without neglecting his achievements in Sanskrit philology and physics. And, for the first time, it makes many original sources accessible to the English-language reader.

Zielgruppe

Research

Autoren/Hrsg.

Petsche, Hans-Joachim

Inhaltsverzeichnis

1;Contents;4
2;Translator’s note;6
3;Foreword;7
4;Introduction;10
4.1;Notes;16
5;1 Graßmann’s life;18
5.1;1.1 The historical context;18
5.2;1.2 The family: traditions and relatives;26
5.3;1.3 Graßmann’s youth and university years;32
5.4;1.4 The path to independent mathematical achievements (1830 – 1840);43
5.5;1.5 Mathematical productivity and the struggle for recognition ( 1840 – 1848);50
5.6;1.6 The Revolution comes to Germany (1848);62
5.7;1.7 Renewed struggles for recognition as a mathematician;75
5.8;1.8 Farewell to mathematics, success as a philologist and late acclaim in mathematics;94
5.9;Notes;106
6;2 Graßmann’s sources of inspiration;118
6.1;2.1 Justus Graßmann: Father and precursor of his son’s mathematical and philosophical views;118
6.2;2.2 Robert Graßmann (1815 – 1901): Brother and collaborator;134
6.3;2.3 Friedrich Schleiermacher’s impact on Graßmann and fundamental thoughts from his lectures on dialectics;147
6.4;Notes;172
7;3 Hermann Günther Graßmann’s contributions to the development of mathematics and their place in the history of mathematics;182
7.1;3.1 Some basic aspects concerning the development of geometry from the 17th to the 19th century;183
7.2;3.2 Graßmann’s examination thesis on the theory of tides;188
7.3;3.3 The 1844 Extension Theory and Graßmann’s theory of algebraic curves;192
7.4;3.4 The prize-winning treatise on geometric analysis (1847);210
7.5;3.5 The Extension Theory of 1862;213
7.6;3.6 Work on the foundations of arithmetic (1861);215
7.7;3.7 The impact of Graßmann’s ideas on the development of mathematics;222
7.8;Notes;229
8;4 The genesis and essence of Hermann Günther Graßmann’s philosophical views in the Extension Theory of 1844;238
8.1;4.1 The genesis of Extension Theory’s basic principles;239
8.2;4.2 Hermann Graßmann’s basic philosophical principles concerning his determination of the essence of mathematics;244
8.3;4.3 Hermann Graßmann’s views on restructuring mathematics and on locating Extension Theory;252
8.4;4.4 Hermann Graßmann’s views on the essence of the mathematical method and its relation to the method of philosophy;258
8.5;4.5 Graßmann’s Extension Theory and Schleiermacher’s Dialectic;261
8.6;Closing remarks;265
8.7;Notes;266
9;Chronology of Graßmann’s life;273
10;Abbreviations;278
11;Bibliography;280
12;List of illustrations;307
13;List of persons mentioned;309

Graßmann’s life.- Graßmann’s sources of inspiration.- Hermann Günther Graßmann’s contributions to the development of mathematics and their place in the history of mathematics.- The genesis and essence of Hermann Günther Graßmann’s philosophical views in the Extension Theory of 1844.