Dirichlet (eBook)

A Mathematical Biography

Uta C. Merzbach (Autor)

eBook Download: PDF

2018 | 1st ed. 2018
XIX, 311 Seiten
Springer International Publishing (Verlag)
978-3-030-01073-7 (ISBN)

Infos

This is the ?rst extensive biography of the in?uential German mathematician, Peter Gustav Lejeune Dirichlet (1805 - 1859). Dirichlet made major contributions to number theory in addition to clarifying concepts such as the representation of functions as series, the theory of convergence, and potential theory. His mathematical methodology was explicitly based on a thorough knowledge of the work of his predecessors and his belief in the underlying unity of the branches of mathematics. This uni?ed approach is exempli?ed in a paper that effectively launched the ?eld of analytic number theory. The same orientation pervaded his teaching, which had a profound in?uence on the work of many mathematicians of subsequent generations.

Chapters dealing with his mathematical work alternate with biographical chapters that place Dirichlet's life and those of some of his notable associates in the context of the political, social, and artistic culture of the period. This book will appeal not only to mathematicians but also to historians of mathematics and sciences, and readers interested in the cultural and intellectual history of the nineteenth century.

Inhalt

Preface 6
Acknowledgements 8
Publisher’s Acknowledgements 9
Contents 10
Abbreviations and Conventions 15
Institutions 15
Publications 15
Place Names 15
1 Rhineland 16
1.1 Düren 16
1.2 Bonn 19
1.3 Cologne 19
2 Paris 23
2.1 Early Reports Home 23
2.2 Madame Lorge and the Deutgens 24
2.3 Professors 24
2.4 Smallpox 26
2.5 Water Flow 26
2.6 First Employment 27
2.7 Obligations at Home Draft Call
2.8 The Mysterious Research Project 29
3 First Success 30
3.1 Fermat's Claim 30
3.2 Lacroix and Legendre 30
3.3 The Draft Board and the Institut of the Académie 31
3.4 The Review Committee's Report 32
3.5 Legendre's Proof Dirichlet's ``Addition''
4 Return to Prussia 36
4.1 Political Background 36
4.2 The Death of Foy 37
4.3 Fourier and Humboldt 37
4.4 Approaches to Prussia 40
4.5 Gauss 40
4.6 The Cultural Ministry 41
4.7 The Breslau Appointment 42
4.8 Bonn and the Doctorate 43
4.9 Political Suspect 44
4.10 The Visit with Gauss 45
4.11 Breslau 45
4.12 Confirmation and Recognition 49
4.13 Radowitz and the Kriegsschule 50
4.14 Departure from Breslau 50
5 Early Publications 52
5.1 Some Indeterminate Equations of Degree 5 52
5.2 Biquadratic Residues 55
5.3 The Habilitationsschrift 59
5.4 Wilson's and Related Theorems 60
5.5 A Challenge 61
6 Berlin 62
6.1 The 1828 Convention 62
6.2 Meeting Scientists 64
6.3 Geomagnetism 65
6.4 Leipzigerstraße 3 67
6.5 Fanny and Wilhelm Hensel 68
6.6 Kriegsschule 70
6.7 Steps to a University Appointment 71
6.8 The University 73
6.9 Rebecca Mendelssohn Bartholdy 74
6.10 Family Concerns 75
6.11 New Security 76
7 Publications: 1829–1830 78
7.1 Definite Integrals 78
7.2 Convergence of Fourier Series 79
7.3 A Problem from Heat Theory 83
7.4 Summary 83
8 Maturation 84
8.1 Educational Commissions 84
8.2 The Kriegsschule 86
8.3 The University 87
8.4 The Akademie and the Académie 90
8.5 The Repertorium 90
8.6 Gaussian Interactions 91
8.7 Family: 1833–1835 93
8.8 Family: 1836–1838 95
8.9 The Death of Gans 96
9 Publications: Autumn 1832–Spring 1839 98
9.1 Quadratic Residues in the Complex Field 99
9.2 Fermat's Last Theorem for n=14 104
9.3 Quadratic Forms and Divisors 104
9.4 Existence and Uniqueness Issues 108
9.5 Gauss Sums 111
9.6 Eulerian Integrals 115
9.7 Efficacy of Least Squares 116
9.8 Primes in Arithmetic Progressions 118
9.9 The Repertorium Report on Arbitrary Functions 121
9.10 Series Expansions and Spherical Functions 125
9.11 Pell's Equation and Circular Functions 126
9.12 Asymptotic Laws in Number Theory 127
9.13 Infinite Series and Number Theory 129
9.14 The New Method: Using a Discontinuity Factor 137
9.15 Observations 140
10 Expanding Interactions 143
10.1 Professor Designate 143
10.2 Paris 143
10.3 Return to Berlin 146
10.4 Jacobi 148
10.5 Preparations for a Vacation 149
10.6 Switzerland and Italy North of Rome 151
10.7 Rome 152
10.8 Illnesses 154
10.9 The Birth of Flora 154
10.10 Return to Berlin 155
11 Publications: 1839–1845 156
11.1 Analytic Number Theory 157
11.2 Primes in Quadratic Forms 159
11.3 Extract of a Letter to Liouville: The Unit Theorem for Degree 3 160
11.4 The Theory of Complex Numbers 162
11.5 Certain Functions of Degree Three and Above 163
11.6 A Generalization re Continued Fractions and Number Theory 165
11.7 Complex Quadratic Forms and Class Numbers 167
11.8 Comments 167
12 A Darkling Decade 168
12.1 The University 169
12.2 The Heidelberg Offer 169
12.3 Growing Tensions at the Akademie 170
12.4 Family Tragedies 171
12.5 Political Turmoil 172
12.6 Return to Surface Normalcy 177
12.7 Göttingen 1849 and 1852 183
12.8 The Death of Jacobi 185
12.9 Family Deaths: 1848–1853 187
12.10 The Death of Gauss 188
12.11 The Call to Göttingen 188
13 Publications: 1846–1855 191
13.1 Stability of Equilibrium 192
13.2 The Unit Theorem 194
13.3 Potential Theory 196
13.4 Reduction of Ternary Quadratic Forms 200
13.5 Mean Values in Number Theory 202
13.6 Three-Squares Decomposition 204
13.7 Composition of Binary Quadratic Forms 205
13.8 The Division Problem: 1851c, 1854c, 1856f 206
13.9 A Resting Solid in a Moving Fluid 206
13.10 Derivation of Two Arithmetical Statements 207
13.11 Gauss's First Proof of Quadratic Reciprocity 207
13.12 Continued Fractions Quadratic Forms with Positive Determinant
13.13 Quadratic Forms with Positive Determinant 210
13.14 Summarizing Comments 213
14 Göttingen 214
14.1 The Societät der Wissenschaften 214
14.2 The University 214
14.3 Music 220
14.4 Adaptation and Social Life 221
14.5 Continuing Mathematical Contacts 223
14.6 Publications 224
14.7 Aging 227
14.8 Travel 228
14.9 Illness and Deaths 229
15 Aftermath 231
15.1 Family 231
15.2 Associates 234
15.3 Institutions 240
16 Lectures 248
16.1 Summary of Lectures 249
16.2 The Editors 250
16.3 The Topics 252
17 Centennial Legacy and Commentary 259
17.1 The Centennial. I: Minkowski's Address 260
17.2 The Centennial. II: The Memorial Volume 265
17.3 Vorono? 276
17.4 1909: Thue and Landau 277
17.5 Commentary 278
17.6 Minkowski: What is a Mathematical School? 281
Bibliography 283
Name Index 309

Produkt-Details

• Erscheint lt. Verlag: 29.12.2018
• Zusatzinfo: XIX, 311 p. 19 illus., 2 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Schlagworte: Analysis • Humboldt • Mendelssohn • Number Theory • prussia
• ISBN-10: 3-030-01073-2 / 3030010732
• ISBN-13: 978-3-030-01073-7 / 9783030010737