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Henri Poincare: A Scientific Biography

by Edward G Gray Princeton University Press
Pub Date:
Hbk 608 pages
AU$97.00 NZ$101.74
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Henri Poincaré (1854-1912) was not just one of the most inventive, versatile, and productive mathematicians of all time - he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today.

Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarised France.

Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionised math, science, and the greater world.

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


''Poincaré was much more than a mathematician: he was a public intellectual, and a rare scientist who enthusiastically rose to the challenge of explaining and interpreting science for the public. With amazingly lucid explanations of Poincaré's ideas, this book is one that any reader who wants to understand the context and content of Poincaré's work will want to have on hand.''--Dana Mackenzie, author of The Universe in Zero Words

''This engaging book recounts the achievements of Henri Poincaré, covering his mathematics, physics, and philosophy, and his activities as a public intellectual. He is an eminently worthy subject for an intellectual biography of this kind.''--Benjamin Wardhaugh, University of Oxford

''This comprehensive scientific biography of Poincaré situates the scientist's life and work in the sociopolitical context of his era. Covering his varied and wide-spanning work--from the most philosophical to the most technical--this book gives the general reader a clear historical sense of the man's voluminous accomplishments.''--Jimena Canales, Harvard University
Jeremy Gray is professor of the history of mathematics at the Open University, and an honorary professor at the University of Warwick. His most recent book is 'Plato's Ghost: The Modernist Transformation of Mathematics' (Princeton).