Constantin Carathéodory: Mathematics and Politics in Turbulent Times PDF
Preview Constantin Carathéodory: Mathematics and Politics in Turbulent Times
maria georgiadou ConstantinCarathéodory MathematicsandPolitics inTurbulentTimes Springer-Verlag BerUn Heidelberg GmbH maria georgiadou Constantin Carathéodory Mathematics and Politics in Turbulent Times Springer A hardcover edition of this book is available with the same title with the ISBN 978-3-540-20352-0 Cataloging-in-Publieation Data applied for Bibliographie information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publieation in the Deutsche Nationalbibliografie; detai1ed bibliographie data is avai1able in the Internet at http://dnb.ddb.de Mathernatics Subject Classification (2000): 01A70, 0lA60, 01A73, 0lA74 ISBN 978-3-540-20352-0 ISBN 978-3-642-18562-5 (eBook) DOI 10.1007/978-3-642-18562-5 With 87 illustrations This work is subject to copyright. All rights are reserved, whether the whole or part of the material is eoneerned, specifieally the rights of translation, reprinting, reuse of illustrations, recitation, broadeasting, reproduetion on microfilm or in any other way and storage in data banks. Duplieation of this publieation or parts thereof is permitted only under the provision of the German Copyright Law of September 9, 1965, in its eurrent version, and permission for use must a1ways be obtained from Springer-Verlag. Violations are liable for proseeution under the German Copyright Law. springeronline.eom © Springer-Verlag Berlin Heidelberg 2004 Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Typeset in Word by the author and edited by PublieationService Gisela Koch, Wiesenbach using a modified Springer LATEX maero-paekage. Cover design: design & production GmbH, Heidelberg Printed on acid-free paper 4113142Ko-54 321 0 Foreword The life and times of Constantin Carathéodory (1873–1950), a brilliant German mathematician of Greek descent, should surely interest mathematicians, German and Greek academics, historians of science as well as many others. The author of thisdocumentarybiographyhasresearchedwithgreatcarealargepartofCarathéo- dory’scorrespondence,papersandotherrelevantdocumentsandarchives,andhas constructed a narrative that is driven by Carathéodory’s own words and thoughts. She has provided excellent personal, historical and mathematical background in- formation, as well as lean and precise comments and interpretation. The result is stunninglyeffective.Carathéodoryandhistimespringtolife:hismathematicsand science,hisloveofhistory,hispolitics,hisunshakeablebeliefinthepowerofthe Germanintellectualtradition,hisemotionalattachmenttoGreece,hissetbacks,his lostcauses,andhisdisappointments.Weseetheworldchangingaroundhim,some- timestoofast.Butwealsoseehisowneffortstomakechanges,forhewasenormously influential both in the academic world and more broadly in science and education politics. The dramatic events of the first half of the twentieth century changed the worldandseeingtheminthisgrippingnarrativethroughtheactionsandthoughtsofa leadingintellectual,mathematicianandacademicprovidesauniqueandfascinating perspective. Carathéodorydidnotdecidetogointomathematicsuntilhewastwenty-seven, afterhehadstudiedengineeringattheMilitarySchoolofBelgiumandworkedfor a few years as an engineer. He was born in 1873 in Berlin, where his family was residingwhilehisfatherwasthediplomaticrepresentativeoftheOttomanEmpire in Germany. He studied mathematics at first in Berlin, attracted to the lectures of H.A.Schwarzonfunctiontheory.HethenwenttoGöttingen,receivingadoctoral degree in 1904 with a dissertation entitled “On the discontinuous solutions in the calculus of variations”. He was close to Klein and Hilbert in Göttingen but his dissertationwassignedbyMinkowski.HisfirstteachingpositionwasinGöttingen, wherehestayeduntil1908.HesubsequentlymovedtoBonn,HanoverandBreslau beforereturningtoGöttingenin1913asfullprofessor.In1918hewenttoBerlinand stayedtilltheendof1919.HismeteoricriseintheGermanacademicworldwas,of course,adirectrecognitionofhismanyseminalcontributionsinfunctiontheory,the theoryofmeasure,first-orderpartialdifferentialequations,thecalculusofvariations andthefoundationsofthermodynamics. Hismathematicalinterestsweredeeplyrootedingeometryandmechanics,but Carathéodory was above all a powerful analyst who understood and appreciated VI Foreword theimportanceofsimplicity,naturalnessandeleganceinmathematics.Heactively sought these qualities in his work. He was also very interested in the origin and historicalevolutionofimportantmathematicalideasandmethods,whichareoften lostinmoreefficientandabstractformulations.Hisworkinfunctiontheoryisclosely tiedtothegeometryofconformalmapping,elegantandunexpectedusesofSchwarz’s lemma, the various variational forms of the Riemann mapping theorem and many results that are part of harmonic analysis today. He published his beautiful lecture notesonconformalmappingin1932and,verylateinhislife,hewroteanelegant treatiseoncomplexfunctiontheorythatappearedin1950. Functiontheorymusthavebeenhisfirstandenduringlove.Itsuitedhismathemat- icalstyleverywellandhemusthavelikedlecturingonit.Thecalculusofvariations must not have been very far behind, however, as his favorite area in mathematics. He had a very specific point of view here: that the elaboration of the equivalence betweentheHuygensprincipleandFermat’sprincipleinOpticsisinfactcentralto themathematicalfoundationsofthecalculusofvariations.InCarathéodory’swork thisidealeadstoafar-reachinggeneralizationandextensionoftheHamilton–Jacobi theory, in which the level surfaces of the action, or travel time, that are solutions of the Hamilton–Jacobi equation, are also generated by families of extremals of theassociatedLagrangefunctional.Hisworkispresentedinhisfamous1935book VariationsrechnungundpartielleDifferentialgleichungenersterOrdnung(Calculus of Variations and Partial Differential Equations of the First Order), translated into Englishin1965.Thisisstilloneofthebestbooksintheareaeventhoughthemodern theory of control and dynamical systems is often oriented toward the inclusion of stochasticeffects,whichenteredmuchmorerecently. ThewaythattheHamilton–Jacobitheoryemergesinhigh-frequencyasymptotics inwavepropagationwassurelyknowntoCarathéodorybutitisnotdiscussedinhis book. It played a very important role in the development of quantum mechanics, whichCarathéodoryfollowedclosely,andbeforethatinoptics.Themathematical foundationsofhigh-frequencyasymptoticsthatconnectHamilton–Jacobitheoryto wavepropagationdidnotemergeuntilmanyyearsafterCarathéodory’swork,inthe sixtiesandseventies,sohecouldnotdealwithitmathematicallyevenifheunderstood itphysically.Itisinteresting,however,thathisintenselygeometricalpointofview isbecomingincreasinglyimportanttoday,inconnectionwithlevel-setmethodsfor theefficientnumericalcomputationoftraveltimesforimagereconstruction. Carathéodorybeganhisworkonmeasuretheoryaround1913andinthefollow- ingfiveyears,untilthepublicationofhisbookVorlesungenüberreelleFunktionen (LecturesonRealFunctions)in1918,madeseveralfundamentalcontributionsthat solidified his standing as a leading mathematician of his generation in Germany andaroundtheworld.Histheoryofoutermeasure,andtheCarathéodoryextension theorem, are now part of the standard material taught in every graduate-level real variables course. For forty years, until the sixties, his real variables book was one ofthebestsourcesforlearningmeasureandintegrationtheory.Whatmakesitlook abitstrangetodayistheabsenceofbasicHilbertspacetheoryandfunctionalanal- ysis,whichdidnotemergeuntilthethirties.Anotherfieldthatdidnotexistbefore thethirtiesisthemeasure-theoreticfoundationofprobabilitytheory,establishedby Foreword VII Kolmogorov in 1933, which provided a major thrust for the further development of general measure theory. For a mathematician with Carathéodory’s command of classicalanalysis(functiontheory,calculusofvariations)itissomewhatsurprising thatatagefortyhisresearchintereststurnedintoamoreabstractdirection,measure andintegrationtheory. Hiselegantmathematicalformulationofthermodynamicsattractedtheattention ofseveralphysicistsbutremainedsomehowoutsidethemainstream.Thephysicist MaxBorn,alifelongfriendofCarathéodory,appreciatedandpromoteditbutmathe- maticalfoundationsofestablishedphysicalfieldsseemtopenetrateslowlyandwith difficultyintotheworldofphysics.Itisinterestingtoseehowhisinvolvementwith applicationsofmathematics,thermodynamicsinparticular,aswellashisbackground inengineeringinfluencedhisappointmentsandpromotions.Itappearsthattheydid playarolebutnotabigone.ItisalsointerestingtoseehowtheGermanmathematics communityviewedappliedmathematicsjustbeforetheFirstWorldWar.Itisonlya partialview,ofcourse,butitseemstobemainlyasawaytomaketheteachingof mathematicsmoreeffective.Carathéodorywaslessinterestedinapplicationsthanin thewaymathematicsinteractsintimatelywithphysicsatabasiclevel,asinthegen- eraltheoryofrelativityandinquantummechanics.Anexceptionishisverydetailed studyofaberrationsinopticalinstrumentsinthelatethirties. Carathéodory’slifechangeddramaticallyinthefallof1919whenheaccepteda mandatefromE.Venizelos,theprimeministerofGreece,toorganizeanewuniver- sityinSmyrna.HeleftBerlinattheendofthatyearandspentthenextfouryears in Athens and Smyrna before returning to Germany as professor of mathematics in Munich. He remained there for the rest of his life, resuming his brilliant career almostasifnothinghadhappened.Butagreatdealhadhappened,andithadtouched Carathéodoryinaverypersonalway,evenifitdidnotdiminishhisself-confidence andhiscreativedrive.AcceptingVenizelos’callinghadclearlybeenanemotional decision,notarationalone,forCarathéodorybelongedtoanextendedfamilyofdis- tinguisheddiplomatsandknewatfirsthandthecomplexandunstablepoliticalscene inGreeceatthetimeoftheVersaillesPeaceConference.Bythefallof1920,when Venizeloswasvotedoutofoffice,Carathéodorywasunabletorecruitevenclosefor- mercolleaguestothenewuniversityandwasatoddswiththeroyalistgovernmentin AthensasaVenizelist(aliberal).Heclungtothenoblecauseofbuildingauniversity, a civilizing mission if ever there was one. In the words of Arnold Toynbee, a war correspondentfortheManchesterGuardianinAsiaMinorduringthisperiod,Cara- théodory the scientist-humanist looked like fish out of water. The background and eventsofthisperiodarepresentedwithsuchclarityandprecisioninthisbiography that even readers familiar with the complicated and little-known historical details will find the narrative fascinating. Focusing on Carathéodory’s doomed efforts to buildauniversityinSmyrnaisspecial,personalandeventragic.Butitisalsoarare glimpseattheendofanerainEurope. Remarkably, Carathéodory was able to continue his research in mathematics throughtheturbulentperiodinSmyrnaandAthens,andnodoubtkeephismental balancebydoingso.AfterreturningtoGermanyasprofessorinMunichhereceived manyhonorsandmuchinternationalrecognition.In1928hebecamethefirstVisiting VIII Foreword LectureroftheAmericanMathematicalSocietyandvisitedandlecturedatseveral Americanuniversities,includingHarvard,theUniversityofTexasatAustin,Stanford andBerkeley.HewasconsideredforapermanentappointmentatHarvardbuthedid notreceiveanoffer.Hedid,however,receiveanofferofaprofessorshipatStanford,in early1929,whichhedidnotaccept.TheAmericanWestwasbeautifulandattractive butattheotherendoftheworldforacosmopolitanEuropeanlikeCarathéodory.His academiclifeinMunichwasfulfillingandproductiveandtherewas,ofcourse,no hintthatastormwasabouttogripGermanyandEurope. Carathéodory’srelationswithGreecetookanotherinterestingturnwhenVenize- losreturnedtopowerandappointedhim,inearly1930,advisertotheGovernment forthereorganizationofGreekuniversities.HetookaleaveofabsencefromMunich forabouttwoyearstoconductanin-depthstudyofuniversitiesinGreece.Hispres- tigewasenormous,butevenanapoliticalacademicofhisstature,whosurelyacted inthebestinterestsofGreekuniversities,couldnotovercomethepoliticaldivisions thatplaguedtheGreekuniversitysystem.Heeventuallyterminatedhisformalrela- tionswithGreecein1932,andfromthenonhisacademicpositionremainedfixed inMunichuntilhisretirementin1938attheageofsixty-five. ThearrivalofnationalsocialisminMarch1933tookmanyacademicsinGermany bysurprise,especiallythespeedwithwhichracialandpoliticaldiscriminationsetin, aswellasthelossofpersonalfreedomandtheobligationtodemonstratecompatibil- itywithandadherencetothenewregime.CarathéodoryhadbeenborninGermany, studiedmathematicsinGermany,becameadistinguishedprofessorinseveralGer- manuniversities,buthewasnotaGerman.HewasanethnicGreek,aChristian,and wasabletofunctioninNaziGermanyaslongashedidnotopenlyopposetheregime evenifhedidsoprivately.HisbehaviorandactionsduringtheNaziperiod,meticu- louslyresearchedandaccuratelyreportedinthisbiography,wereexactlylikethose ofmanyGermanacademicsofhisgeneration.Heactivelyandenergeticallyhelped hisJewishfriendsandcolleagueswhobecamepersecutedundesirablesintheirown countryalmostovernight,andsometimes,inlateryears,intervenedontheirbehalf throughmorepowerfulcolleagueswhowereclosertotheregime.Persecutionwas notunknowntoCarathéodorywhocamefromafamilyofethnicGreeksthathadrisen toprominentpositionsintheOttomanEmpire.Atanymoment,eventsoutoftheir control could, and did many times, turn the state against them with unpredictable intensity. He no doubt understood very well that his academic status and prestige could hardly protect him should his loyalty to the state be questioned, especially since he was not German. Where he crossed the line, however – and the author is verycarefulhere–isinallowinghimselftobeusedbytheNazisintheirinternational propaganda.Whenhe,asadistinguishedacademic,representedGermanmathemat- icsatinternationalmeetingsthatthestateallowedhimtoattend,hewasbeingused. DuringthewarhecontinuedtohelpcolleaguesoutsideGermanywhonowwerenot only losing their positions and their property but also were increasingly in danger oftheirlives.However,neitherhenorotherengagedacademicscoulddomuch,and thereisnoindicationatwhattimeCarathéodorybecameawareoftheHolocaust,or whathisreactionwastotheinvasionandoccupationofGreecebytheGermansin April1941. Foreword IX Carathéodorytriedtore-establishhiscontactsoutsideGermanyafterthewarbut hequicklyfoundthattheworldhadchangedcompletely.HiscolleaguesinAmerica helpedhimgenerouslybutnotenthusiastically.Whenhetriedtodifferentiatehimself from other Germans as an ethnic Greek living in Germany he discovered that the Americanoccupyingforcesdidnotunderstandthedifference.Whenhetriedtomove to Greece with his family he was rebuffed by the Greeks. The only escape he had wasinmathematics,andthatiswhenhewrotehisbookonfunctiontheory.Hewas diagnosedwithanenlargedprostateinthespringof1947anddiedinFebruary1950. Carathéodory is a towering figure in the world of mathematics. His work on first order partial differential equations and the calculus of variations is still cited andstudiedtoday,asarehiscontributionsinrealandcomplexanalysis.Helivedin complicatedandturbulenttimes,andhadrootsinmanyculturesandtraditions,most ofwhicharefadingmemoriestoday.Hewasacultivatedandengagedintellectual, andthisbiographyisafittingtributetohislifeandwork. GeorgePapanicolaou
The list of books you might like
