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Henri Poincare: a Biography Through the Daily Papers HENRI POINCARÉ A Biography Through the Daily Papers May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory PST˙ws This page intentionally left blankThis blank HENRI POINCARÉ A Biography Through the Daily Papers Jean-Marc Ginoux LSIS, CNRS, Université de Toulon, France Archives Henri Poincaré, CNRS, Université de Nancy, France Christian Gerini Université du Sud Toulon Var, France & Université Paris-11 Orsay, France World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. HENRI POINCARÉ A Biography Through the Daily Papers Copyright © 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-4556-61-3 Printed in Singapore August 20, 2013 13:33 World Scientific Book - 9in x 6in ws-book9x6 “Thought is only a flash between two long nights, but this flash is everything.” — H. Poincar´e1 1The Value of Science. v May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory PST˙ws This page intentionally left blankThis blank August 20, 2013 13:33 World Scientific Book - 9in x 6in ws-book9x6 Foreword Henri Poincar´e is known all over the world as a famous astronomer, math- ematician, physicist and philosopher. He has been dubbed by Eric Temple Bell as the “Last Universalist”. As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. In his seminal works “On the curves defined by differential equa- tions” Poincar´e (1881-1886) was led to define what is nowadays called a “dynamical system” to model the evolution of phenomena by using ordi- nary differential equations (O.D.E.). Then, he developed many tools to analyze the behavior (stability) of the solutions of such systems including “characteristic exponents” and “first return maps” which has since been named in his honor as “Poincar´e maps”. In 1889, Poincar´ewonthePrize Competition sponsored by the king Oscar II of Sweden and Norway prov- ing thus the efficiency of his new mathematical concepts to establish the stability of the Solar system. Unfortunately, very few months later, the Swedish mathematician Lars Edvard Phragmen responsible for proofread- ing, discovered a mistake in the memoir (entitled: “On the three body problem and the problem of dynamics”) sent by Poincar´e. The Editor in Chief, G¨osta Mittag-Leffler informed Poincar´eof this problem in July 1889 and here is what he answered in December 1889: “I thought that all these asymptotic curves (homoclinic orbits) after moving away from a closed curve representing a periodic solution would then asymptotically approach the same closed curve. What is true is that there is an infinity of them that enjoy this property. I will not conceal from you the distress that this discovery has caused me.” vii August 20, 2013 13:33 World Scientific Book - 9in x 6in ws-book9x6 viii Henri Poincar´e: a biography through the daily papers It has since been noticed (see the works of J.-C. Yoccoz) that this “fruit- ful mistake” led Poincar´e to the discovery of deterministic chaos. His letter to Mittag-Leffler ends with this sentence: “I will write more when I see a little clearer in my works.” It will take ten years for Poincar´e to “see a little clearer” in his works. Ten years during which he wrote his famous “New Methods of Celestial Mechanics” (1892-1899). In the third volume, Poincar´e (1899) wrote about the homoclinic orbits which nowadays is considered as the signature of chaos: “The complexity of this figure will be striking, and I shall not even try to draw it.” Thus, as briefly recalled above, Poincar´e’s contribution to Dynamical Systems Theory and more particularly to Chaos Theory is obviously of great importance. In my own works concerning Nonlinear Circuit The- ory and Cellular Automata, Poincar´e’s methods were the foundations upon which some of my demonstrations are based on. As an example, in an article entitled: The Double Scroll family (Chua et al., IEEE, 11, pp. 1073-1118, 1986), I used the Poincar´e and half-return maps to establish a Rigorous Proof of Chaos in my electronic circuit (Chua’s circuit). Although the im- portance of Poincar´e’s works is universally recognized in Pure and Applied Mathematics, in Physics, in Astronomy and in Philosophy, and in spite of the fact that many works have been devoted to them, very few biographies have been written about his life. In the middle of the thirties Eric Temple Bell (1937) included in his book Men of Mathematics a chapter entitled “Henri Poincar´e: the last universalist” in which he told many anecdotes about him. Here is one: “One phase of Poincar´e’s absent-mindedness resembles some- thing quite different. Thus (Darboux does not tell the story, but it should be told, as it illustrates a certain brusqueness of Poincar´e’s later years), when a distinguished mathematician had come all the way from Finland to Paris to confer with Poincar´e on scientific matters, Poincar´e did not leave his study to greet his caller when the maid notified him, but continued to pace back and forth – as was his custom when mathemati- cizing – for three solid hours. All this time the diffident caller sat quietly in the adjoining room, barred from the master only by flimsy porti`eres. At last the drapes parted and Poincar´e’s buffalo head was thrust for an instant into the room. “Vous me August 20, 2013 13:33 World Scientific Book - 9in x 6in ws-book9x6 Foreword ix derangez beaucoup” (You are disturbing me greatly), the head exploded, and disappeared. The caller departed without an in- terview, which was exactly what the “absent-minded” professor wanted.” (Bell, 1937, p. 588) Regarding his working method, Bell said, quoting Gaston Darboux who was the President of the jury of the thesis: “Poincar´e was an intuitionist. Having once arrived at the sum- mit he never retraced his steps. He was satisfied to have crashed through the difficulties and left to others the pains of mapping the royal roads destined to lead more easily to the end.” (Bell, 1937, p. 592) The above anecdotes provide some insight on Poincar´e’s personality and allow us to better understand his work and his thought. Indeed, the work of a genius is an inexhaustible source of knowledge in which we should go over with a fine-toothed comb in order to draw the ideas that lead to new theories. Leon Chua University of California, Berkeley Technische Universit¨at, M¨unchen May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory PST˙ws This page intentionally left blank August 20, 2013 13:33 World Scientific Book - 9in x 6in ws-book9x6 Note from the translator Many different lives in one man’s life – this is the general feeling when going though a work like Henri Poincar´e : Une biographie au(x) quotidien(s),El- lipses, 2012. Henri Poincar´e was polyvalent, to say the least, considering his accomplished works in fields as various as mathematics, physics, astronomy, philosophy and literature. He was a man of science and a man of letter, and both these qualities made him part of controversies which the press of his time did not fail to write about throughout his life. The book being written on the basis of what the newspapers of the time had to say about him, its chapters are therefore as diversified as Poincar´e’s life itself. And this made the translation of this book as interesting as it made it challeng- ing. How to rightly translate a biography as multiple as Poincar´e’s? Surely by becoming a specialist in all the fields in which he distinguished himself. This is what I had to keep in mind while doing my research translation, but time was obviously missing to fully reach this purpose. And however faithful and clear I tried to remain, I would therefore like to apologize for the passages where the translation might not be perfectly accurate. My objective was to make the reading as convenient as possible, the original book, Henri Poincar´e : Une biographie au(x) quotidien(s), Ellipses, 2012, includes many references to books written by Henri Poincar´e himself, or by other French scientists and scholars of the time, as well as many titles of newspaper and journal articles. Most of Henri Poincar´e’s writings have been translated, and the English titles can therefore easily be found. However, as the English titles and the French titles often both appear in the various bibliographies, I usually leave the original title in French, followed by the translated English title into brackets. This was in my opinion the best way for a reader that would want to look further into the subjects mentioned in the book to have all the information he would need to do his research.
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