Hermann Grabmann

by Petsche, Hans-joachim; Minnes, Mark

• ISBN13: 9783764388591
• ISBN10: 3764388595
• Format: Hardcover
• Copyright: 2009-10-01
• Publisher: Birkhauser

Summary

Hermann Grassmann whose career was spent as a high-school teacher in Stettin is known as the founder of n-dimensional vector algebra as well as for his lasting contributions to physics and linguistics. In his opus magnum, the "Ausdehnungslehre" he developed, mainly inspired by Schleiermacher's philosophical method, an entirely new mathematical discipline. Ignored by his contemporaries, his remarkable work is now recognized to have been that of a pioneer. The biography goes into detail of the complex network of internal and external factors that shaped Grassmann's development.

Table of Contents

Translator's note	p. VII
Foreword	p. IX
Introduction	p. XIII
Notes	p. XIX
Graßimann's life	p. 1
Hie historical context	p. 1
The family: traditions and relatives	p. 9
Graßmann's youth and university years	p. 15
The path to independent mathematical achievements (1830-1840)	p. 26
Mathematical productivity and the struggle for recognition (1840-1848)	p. 33
The Revolution comes to Germany (1848)	p. 45
Renewed struggles for recognition as a mathematician	p. 58
Farewell to mathematics, success as a philologist and late acclaim in mathematics	p. 77
Notes	p. 89
Graßimann's sources of inspiration	p. 101
Justus Graßmann: Father and precursor of his son's mathematical and philosophical views	p. 101
Robert Graßmann (1815 - 1901): Brother and collaborator	p. 117
Friedrich Schleiermacher's impact on Graßmann and fundamental thoughts from his lectures on dialectics	p. 130
Notes	p. 155
Hermann Günther Graßmann's contributions to the development of mathematics and their place in the history of mathematics	p. 165
Some basic aspects concerning the development of geometry from the 17th to the 19th century	p. 166
Graßmann's examination thesis on the theory of tides	p. 171
The 1844 Extension Theory and Graßmann's theory of algebraic curves	p. 175
The prize-winning treatise on geometric analysis (1847)	p. 193
The Extension Theory of 1862	p. 196
Work on the foundations of arithmetic (1861)	p. 198
The impact of Graßmann's ideas on the development of mathematics	p. 205
Notes	p. 212
The genesis and essence of Hermann Günther Graßmann's philosophical views in the Extension Theory of 1844	p. 221
The genesis of Extension Theory's basic principles	p. 222
Hermann Graßmann's basic philosophical principles concerning his determination of the essence of mathematics	p. 227
Hermann Graßmann's views on restructuring mathematics and on locating Extension Theory	p. 235
Hermann Graßmann's views on the essence of the mathematical method and its relation to the method of philosophy	p. 241
Gra^szlig;mann's Extension Theory and Schleiermacher's Dialectic	p. 244
Closing remarks	p. 248
Notes	p. 249
Chronology of Graßmann's life	p. 257
Abbreviations	p. 263
Bibliography	p. 265
List of illustrations	p. 293
List of persons mentioned	p. 295
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