Henri Poincaré : a biography through the daily papers PDF
Preview Henri Poincaré : a biography through the daily papers
HENRI POINCARÉ A Biography Through the Daily Papers May2,2013 14:6 BC:8831-ProbabilityandStatisticalTheory PST˙ws TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk 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. 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ISBN 978-981-4556-61-3 Printed in Singapore August20,2013 13:33 WorldScientificBook-9inx6in ws-book9x6 “Thought is only a flash between two long nights, but this flash is everything.” — H.Poincar´e1 1The Value of Science. v May2,2013 14:6 BC:8831-ProbabilityandStatisticalTheory PST˙ws TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk August20,2013 13:33 WorldScientificBook-9inx6in ws-book9x6 Foreword Henri Poincar´eis known all over the worldas a famous astronomer, math- ematician, physicist and philosopher. He has been dubbed by Eric Temple Bellasthe“LastUniversalist”. Asamathematicianandphysicist,hemade manyoriginalfundamentalcontributionstopureandappliedmathematics, 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´e won the Prize 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¨ostaMittag-LefflerinformedPoincar´eofthis probleminJuly 1889 and here is what he answered in December 1889: “Ithoughtthatalltheseasymptoticcurves(homoclinicorbits) 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 August20,2013 13:33 WorldScientificBook-9inx6in ws-book9x6 viii Henri Poincar´e: a biography through the daily papers Ithassincebeennoticed(seetheworksofJ.-C.Yoccoz)thatthis“fruit- fulmistake”ledPoincar´etothe discoveryofdeterministic chaos. Hisletter 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). Inthethirdvolume,Poincar´e(1899)wroteabout 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- oryandCellularAutomata, Poincar´e’smethodswerethefoundationsupon whichsomeofmydemonstrationsarebasedon. Asanexample,inanarticle 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 ofPoincar´e’sworksis universallyrecognizedin Pure andApplied Mathematics, in Physics, in Astronomy and in Philosophy, and in spite of the factthat many workshavebeen devotedto them, veryfew 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 ofPoincar´e’s lateryears),when adistinguished mathematician had come all the way from Finland to Paris to confer with Poincar´eonscientificmatters,Poincar´edidnotleavehisstudy 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 intheadjoining room, barred from themasteronly by flimsy porti`eres. At last the drapes parted and Poincar´e’s buffaloheadwasthrustforaninstantintotheroom. “Vousme August20,2013 13:33 WorldScientificBook-9inx6in ws-book9x6 Foreword ix derangezbeaucoup”(Youaredisturbingmegreatly), thehead exploded,anddisappeared. Thecallerdepartedwithoutanin- terview,whichwasexactlywhatthe“absent-minded”professor wanted.” (Bell, 1937, p. 588) Regardinghisworkingmethod,Bellsaid,quotingGastonDarbouxwho was the President of the jury of the thesis: “Poincar´ewasanintuitionist. Havingoncearrivedatthesum- mitheneverretracedhissteps. Hewassatisfiedtohavecrashed throughthedifficulties andleft toothersthepainsof mapping theroyalroadsdestined tolead moreeasily totheend.” (Bell, 1937, p. 592) TheaboveanecdotesprovidesomeinsightonPoincar´e’spersonalityand 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 Universita¨t, Mu¨nchen
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