Henri Poincaré

List of Figures ix

Preface xi

Introduction 1

- Views of Poincaré 3

- Poincaré's Way of Thinking 6

1 The Essayist 27

- Poincaré and the Three Body Problem 27

- Poincaré's Popular Essays 34

- Paris Celebrates the New Century 59

- Science, Hypothesis, Value 67

- Poincaré and Projective Geometry 76

- Poincaré's Popular Writings on Physics 100

- The Future of Mathematics 112

- Poincaré among the Logicians 123

- Poincaré's Defenses of Science 144

2 Poincaré's Career 153

- Childhood, Schooling 153

- The École Polytechnique 157

- The École des Mines 158

- Academic Life 160

- The Dreyfus Affair 165

- National Spokesman 169

- Contemporary Technology 177

- International Representative 187

- The Nobel Prize 192

- "1911", "1912" 200

- Remembering Poincaré 202

3 The Prize Competition of 1880 207

- The Competition 207

- Fuchs, Schwarz, Klein, and Automorphic Functions 224

- Uniformization, 1882 to 1907 247

4 The Three Body Problem 253

- Flows on Surfaces 253

- Stability Questions 265

- Poincaré's Essay and Its Supplements 266

- Les Méthodes Nouvelles de la Mécanique Céleste 281

- Poincaré Returns 291

5 Cosmogony 300

- Rotating Fluid Masses 300

6 Physics 318

- Theories of Electricity before Poincaré: Maxwell 318

- Poincaré's Électricité et Optique, 1890 329

- Larmor and Lorentz: The Electron and the Ether 338

- Poincaré on Hertz and Lorentz 346

- St. Louis, 1904 356

- The Dynamics of the Electron 361

- Poincaré and Einstein 367

- Early Quantum Theory 378

7 Theory of Functions and Mathematical Physics 382

- Function Theory of a Single Variable 382

- Function Theory of Several Variables 391

- Poincaré's Approach to Potential Theory 402

- The Six Lectures in Göttingen, 1909 416

8 Topology 427

- Topology before Poincaré 427

- Poincare's Work, 1895 to 1905 432

9 Interventions in Pure Mathematics 467

- Number Theory 467

- Lie Theory 489

- Algebraic Geometry 498

10 Poincaré as a Professional Physicist 509

- Thermodynamics 513

- Probability 518

11 Poincaré and the Philosophy of Science 525

- Poincaré: Idealist, Skeptic, or Structural Realist? 525

12 Appendixes 543

- Elliptic and Abelian Functions 543

- Maxwell's Equations 545

- Glossary 548

References 553

- Articles and Books by Poincaré 554

- Other Authors 564

Name Index 585

Subject Index 589