| Part I: Two Rival Centers: Gottingen vs. Berlin |
|
|
|
|
3 | (16) |
|
2 On Gauss and Gaussian Legends: A Quiz |
|
|
19 | (10) |
|
Answers to the Gauss Quiz |
|
|
21 | (8) |
|
3 Gauss, Dirichlet, and the Law of Biquadratic Reciprocity |
|
|
29 | (12) |
|
4 Episodes in the Berlin-Gottingen Rivalry, 1870-1930 |
|
|
41 | (10) |
|
5 Deine Sonia: A Reading from a Burned Letter by Reinhard Bolling, |
|
|
|
|
|
51 | (6) |
|
6 Who Linked Hegel's Philosophy with the History of Mathematics? |
|
|
57 | (12) |
|
Answers to the Hegel Quiz |
|
|
60 | (1) |
|
Kummer's Hegelian Orientation |
|
|
61 | (1) |
|
|
|
62 | (2) |
|
Addendum: Plane Sections of a Steiner Surface (Computer Graphics by Oliver Labs) |
|
|
64 | (5) |
| Part II: The Young Felix Klein |
|
|
7 Introduction to Part II |
|
|
69 | (12) |
|
8 Models as Research Tools: Plucker, Klein, and Kummer Surfaces |
|
|
81 | (14) |
|
Models as Artefacts for Discovery |
|
|
83 | (2) |
|
A Context for Discovery: Geometric Optics |
|
|
85 | (1) |
|
|
|
86 | (3) |
|
Models in Standardized Production |
|
|
89 | (3) |
|
|
|
92 | (3) |
|
9 Debating Grassmann's Mathematics: Schlegel vs. Klein |
|
|
95 | (10) |
|
Grassmann's Ausdehnungslehre |
|
|
95 | (1) |
|
Mathematics at University and Gynmasium |
|
|
96 | (2) |
|
Professionalisation and Patterns of Reception |
|
|
98 | (1) |
|
Promoting Grassmannian Mathematics at the Gymnasium |
|
|
99 | (1) |
|
|
|
100 | (1) |
|
|
|
101 | (4) |
|
10 Three Letters from Sophus Lie to Felix Klein on Mathematics in Paris |
|
|
105 | (6) |
|
11 Klein, Mittag-Leffler, and the Klein-Poincare Correspondence of 1881-1882 |
|
|
111 | (26) |
|
Launching Acta Mathematica |
|
|
111 | (2) |
|
Klein's Projective Riemann Surfaces |
|
|
113 | (2) |
|
Klein's Influence on American Mathematics |
|
|
115 | (5) |
|
|
|
120 | (4) |
|
|
|
124 | (1) |
|
"Name ist Schall and Rauch" |
|
|
125 | (2) |
|
On Cultivating Scientific Relations |
|
|
127 | (3) |
|
Delayed Publication of the Klein-Poincare Correspondence |
|
|
130 | (2) |
|
|
|
132 | (5) |
| Part III: David Hilbert Steps Onstage |
|
|
12 Introduction to Part III |
|
|
137 | (14) |
|
13 Hilbert's Early Career |
|
|
151 | (20) |
|
From Konigsberg to Gottingen |
|
|
151 | (1) |
|
|
|
152 | (4) |
|
|
|
156 | (2) |
|
Encounters with Allies and Rivals |
|
|
158 | (1) |
|
|
|
158 | (3) |
|
A Second Encounter with Kronecker |
|
|
161 | (1) |
|
Tackling Gordan's Problem |
|
|
162 | (2) |
|
|
|
164 | (2) |
|
|
|
166 | (1) |
|
Killing Off a Mathematical Theory |
|
|
167 | (4) |
|
14 Klein, Hurwitz, and the "Jewish Question" in German Academia |
|
|
171 | (12) |
|
Klein's Most Talented Student |
|
|
172 | (3) |
|
Hurwitz in G6ttingen and Konigsberg |
|
|
175 | (1) |
|
Playing the Game of "Mathematical Chairs" |
|
|
176 | (2) |
|
Paul Gordan to Felix Klein, 16 April, 1892 |
|
|
178 | (2) |
|
The "Jewish Question" Reconsidered |
|
|
180 | (2) |
|
Appendix: Two Tributes to Adolf Hurwitz |
|
|
182 | (1) |
|
Max Born Recalling Hurwitz as a Teacher |
|
|
182 | (1) |
|
George Polya on Hurwitz as a Colleague |
|
|
182 | (1) |
|
15 On the Background to Hilbert's Paris Lecture "Mathematical Problems" |
|
|
183 | (12) |
|
From Konigsberg to Gottingen |
|
|
184 | (1) |
|
|
|
184 | (2) |
|
|
|
186 | (2) |
|
|
|
188 | (1) |
|
|
|
189 | (2) |
|
On Mathematical Knowledge |
|
|
191 | (4) |
|
16 Poincare Week in Gottingen, 22-28 April 1909 |
|
|
195 | (10) |
|
Program for Poincare Week |
|
|
197 | (1) |
|
Opening of Poincare Week, April 22-29, 1909 |
|
|
197 | (1) |
|
For Klein on His 60th Birthday, April 25, 1909 |
|
|
198 | (2) |
|
Hilbert on Poincare's Conventionalism and Cantor's Theory of Transfinite Numbers |
|
|
200 | (5) |
| Part IV: Mathematics and the Relativity Revolution |
|
|
17 Introduction to Part IV |
|
|
205 | (14) |
|
18 Hermann Minkowski's Cologne Lecture, "Raum und Zeit" |
|
|
219 | (14) |
|
Minkowski's Partnership with Hilbert |
|
|
223 | (2) |
|
Plans for Hilbert's Paris Lecture |
|
|
225 | (1) |
|
Boltzmann and the Energetics Debates |
|
|
226 | (2) |
|
|
|
228 | (1) |
|
|
|
229 | (4) |
|
19 Max von Laue's Role in the Relativity Revolution |
|
|
233 | (10) |
|
Einstein's Obsolete Account of SR |
|
|
234 | (2) |
|
|
|
236 | (1) |
|
Laue's Influence on Einstein |
|
|
237 | (1) |
|
Laue's Slow Acceptance of General Relativity |
|
|
238 | (5) |
|
20 Euclidean Geometry and Physical Space |
|
|
243 | (10) |
|
Gauss and the Advent of Non-Euclidean Geometry |
|
|
249 | (4) |
|
21 The Mathematicians' Happy Hunting Ground: Einstein's General Theory of Relativity |
|
|
253 | (10) |
|
Einstein in Berlin and Gottingen |
|
|
253 | (1) |
|
The Schwarzschild Solution |
|
|
254 | (2) |
|
Relativity and Differential Geometry |
|
|
256 | (2) |
|
Einstein's Enemies: The Anti-relativists |
|
|
258 | (2) |
|
Appendix: Text of an Article by Hilbert and Born in the Frankfurter Zeitung |
|
|
260 | (1) |
|
|
|
260 | (3) |
|
22 Einstein's Gravitational Field Equations and the Bianchi Identities |
|
|
263 | (10) |
|
|
|
263 | (3) |
|
Einstein's Field Equations |
|
|
266 | (1) |
|
General Relativity in Gottingen |
|
|
267 | (1) |
|
On Rediscovering the Bianchi Identities |
|
|
268 | (5) |
|
23 Puzzles and Paradoxes and Their (Sometimes) Profounder Implications |
|
|
273 | (6) |
|
Implications for Foundations of Geometry |
|
|
273 | (2) |
|
|
|
275 | (2) |
|
On Machian Thought Experiments |
|
|
277 | (2) |
|
24 Debating Relativistic Cosmology, 1917-1924 |
|
|
279 | (22) |
|
|
|
279 | (2) |
|
|
|
281 | (3) |
|
De Sitter's Non-Machian Universe |
|
|
284 | (2) |
|
Geometric Motifs: Felix Klein |
|
|
286 | (2) |
|
Einstein on the Counterattack |
|
|
288 | (2) |
|
Confronting Space-Time Singularities |
|
|
290 | (3) |
|
On Losing Track of Time in de Sitter Space |
|
|
293 | (2) |
|
Einstein's Ether as Carrier of Inertia |
|
|
295 | (2) |
|
On the Persistence of Static Cosmologies |
|
|
297 | (4) |
|
25 Remembering an Era: Roger Penrose's Paper on "Gravitational Collapse: The Role of General Relativity" |
|
|
301 | (14) |
| Part V: Gottingen in the Era of Hilbert and Courant |
|
|
26 Introduction to Part V |
|
|
315 | (16) |
|
27 Hermann Weyl, The Reluctant Revolutionary |
|
|
331 | (12) |
|
On the Roots of Weyl's Ensuing Conflict with Hilbert |
|
|
333 | (5) |
|
Weyl's Emotional Attachment to Intuitionism |
|
|
338 | (5) |
|
28 Transforming Tradition: Richard Courant in Gottingen |
|
|
343 | (14) |
|
Biography and Oral History |
|
|
345 | (1) |
|
Counterfactual Courant Stories |
|
|
346 | (5) |
|
|
|
351 | (6) |
|
29 Otto Neugebauer and the Gottingen Approach to History of the Exact Sciences |
|
|
357 | (12) |
|
Neugebauer's Cornell Lectures |
|
|
358 | (1) |
|
Neugebauer and Courant in Gottingen |
|
|
359 | (1) |
|
Neugebauer's Revisionist Approach to Greek Mathematics |
|
|
360 | (4) |
|
Greek Mathematics Reconsidered |
|
|
364 | (5) |
|
30 On the Myriad Mathematical Traditions of Ancient Greece |
|
|
369 | (6) |
|
31 The Old Guard Under a New Order: K.O. Friedrichs Meets Felix Klein |
|
|
375 | (4) |
|
32 An Enchanted Era Remembered: Interview with Dirk Jan Struik |
|
|
379 | (16) |
| Part VI: People and Legacies |
|
|
33 Introduction to Part VI |
|
|
395 | (12) |
|
34 Is (Was) Mathematics an Art or a Science? |
|
|
407 | (6) |
|
35 Coxeter on People and Polytopes |
|
|
413 | (8) |
|
|
|
414 | (2) |
|
Coxeter on the Intuitive Approach to the Fourth Dimension |
|
|
416 | (2) |
|
Coxeter as Promoter of Geometrical Art |
|
|
418 | (3) |
|
36 Mathematics in Wartime: Private Reflections of Clifford Truesdell |
|
|
421 | (14) |
|
Building Applied Mathematics at Brown |
|
|
423 | (4) |
|
Truesdell's Private Reflections |
|
|
427 | (2) |
|
A Participant's Perspective |
|
|
429 | (2) |
|
|
|
431 | (4) |
|
37 Hilbert's Legacy: Projecting the Future and Assessing the Past at the 1946 Princeton Bicentennial Conference |
|
|
435 | (10) |
|
|
|
436 | (1) |
|
|
|
436 | (2) |
|
Nativism Versus Internationalism in American Mathematics |
|
|
438 | (1) |
|
|
|
439 | (3) |
|
|
|
442 | (3) |
|
38 Personal Reflections on Dirk Jan Struik |
|
|
445 | (8) |
|
|
|
Introduction: Dirk Struik and the History of Mathematics |
|
|
445 | (2) |
|
Personal Reflections on Dirk Jan Struik |
|
|
447 | (6) |
|
|
| Name Index |
|
453 | |
More information about ebooks