Henri Poincaré: A Scientific Biography

by Jeremy Gray

Overview

A comprehensive look at the mathematics, physics, and philosophy of Henri Poincaré

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 polarized France.

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

Product Details

ISBN-13:	9780691152714
Publisher:	Princeton University Press
Publication date:	11/25/2012
Pages:	608
Product dimensions:	6.50(w) x 9.30(h) x 1.90(d)

About the Author

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).

Table of Contents

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

What People are Saying About This

From the Publisher

"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

Editorial Reviews

The great French mathematician Poincaré's (1854–1912) rigorous research and quest for understanding influenced fields as diverse as algebra, geometry, astronomy, and physics. Drawing on Poincaré's voluminous notebooks, essays, and other writings, Gray, a math historian at Britain's Open University, chronicles Poincaré's remarkable achievements in language that is by turns sparkling and dense. The biography of a mind, Gray's narrative doesn't linger over the details of Poincaré's life but concentrates on mathematician's wide-ranging and penetrating insights into celestial mechanics, topology, number theory, and algebraic geometry. Gray reveals Poincaré's work pattern: when reflecting on a topic, he liked to walk about; he took few notes when preparing to work and often approached a problem without any idea of a solution. One of his most celebrated achievements was cracking the three-body problem, which asserted the impossibility of predicting the relationships among three bodies moving under mutual gravitational attraction. Chock full of the equations and formulas that Poincaré developed to support and prove his groundbreaking work, Gray's intellectual biography deftly illuminates the workings of a fertile mind but the volume will be most appreciated by the devoted math and science reader. 13 b&w photos. (Dec.)

Publishers Weekly

One of Choice's Outstanding Academic Titles for 2013

From the Publisher

"Comprehensive."

Science News

"Gray, a mathematics historian and scholar on the life and work of Henry Poincaré, has, with the support of a Leverhulme Research Fellowship, produced this comprehensive and definitive 'scientific biography.' Gray offers abundant rich information on Poincaré's ideas and scientific process, the evolution and maturity of his mathematics including missteps, the dexterity of his reasoning, and the influences that shaped his thought."

Choice

[A] comprehensive assessment of Poincare's work and its importance, essential for anyone interested in Poincare's scholarship or the history of mathematics.

Sacramento Book Review - Laura Tarwater Scharp

Full of the mathematical, physical and metaphysical ideas of a man who was not only a dispassionate observer of the world around us, but of our way of understanding it.

Standpoint Magazine - Mark Ronan

[A] comprehensive but uncluttered guide to Poincaré's extensive oeuvres.

Times Higher Education - Madeline Muntersbjorn

Gray shows us the full dazzling sweep of what Poincaré accomplished, including the work on dynamical systems and chaos that only came into its own in recent years. A tour de force, Gray's masterful treatment will long remain an invaluable resource for all who want to understand Poincaré, so embedded within his times and yet so far ahead of them.

Science - Peter Pesic

[M]asterly . . . Gray encapsulates Poincaré's multiple dimensions; his intellectual biography is both a tour de force and a triumph of readability.

Nature - George Szpiro

A fundamental study of the scientific work of one of the greatest mathematicians and mathematical physicists of the three decades straddling the 19th and 20th centuries. . . . Chapters are organized topically, not chronologically. Each illuminates in depth one or other of Poincaré's works but all are set in context both historical and temathic such that each can serve as an introduction into the many subjects to which Poincaré made a contribution.

CTK Insights - Alexander Bogomolny

In the first full-length English-language book to cover Henri Poincaré's (1854-1912) contributions to mathematics, physics, and philosophy, Gray (history of mathematics, Open Univ.; Plato's Ghost: The Modernist Transformation of Mathematics) illuminates how the French polymath tackled so many different problems with such success. Poincaré is best known for his work in mathematics, including Newton's n-body problem on the movement of celestial objects; his famous Millennium Prize-problem conjecture, which dealt with algebraic topology; and his general influence in that field. Gray uses Poincaré's manuscripts and supplementary archival sources to document his influence in divergent fields of interest, including celestial mechanics, Lorentz's transformations, and the philosophy of mathematics and science. Although he includes traditional biographical elements, Gray spends considerable time describing Poincaré's ways of thinking during a transitional period of French and scientific history. VERDICT This book is lengthy, written for a general audience, and devoid of mathematical proofs, though it also includes pictures, figures, and references. An interesting history that will be of special interest to students and scholars.—Ian D. Gordon, Brock Univ. Lib., St. Catharines, Ont.

Library Journal