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