Hermann Graßmann (eBook)

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