Émile Borel: A Life in Mathematics and Politics Across Two Centuries PDF
Preview Émile Borel: A Life in Mathematics and Politics Across Two Centuries
P ierre Guiraldenq É mile Borel A Life in Mathematics and Politics A cross Two Centuries P ierre Guiraldenq É mile Borel A Life in Mathematics and Politics A cross Two Centuries Translated and edited by Arturo Sangalli About the author and the translator Pierre Guiraldenq is professor emeritus at the École Centrale de Lyon, France. In addition to his scientific career as a metallurgist, his interest in the history of science has resulted in the publication of several biographical articles and books. Arturo Sangalli is the author of numerous scientific articles, books, and transla- tions. He has a PhD in mathematics from the Université de Montréal. This book is a translated and adapted version of Pierre Guiraldenq, Émile Borel, 1871–1956 : l’espace et le temps d’une vie sur deux siècles. Librairie Albert Blanchard, Paris, 1999. The translated quotes by Camille Marbo are taken from the book Camille Marbo, À travers deux siècles : souvenirs et rencontres (1883–1967) © 1968 Éditions Grasset & Fasquelle and are used with permission. The cover drawing by André Aaron Bilis (1893–1971) comes from the Biblio- thèque nationale de France, Réf. N2 – D 094 300. ISBN 978-3-98547-013-6, eISBN 978-3-98547-513-1, DOI 10.4171/ST/17 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche National- bibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. Published by EMS Press, an imprint of the European Mathematical Society – EMS – Publishing House GmbH Institut für Mathematik Technische Universität Berlin Straße des 17. Juni 136 10623 Berlin, Germany https://ems.press 2022 European Mathematical Society © Typesetting: Nicole Bloye, Cardiff, UK; Apostolos Damialis, Berlin, Germany Printed in Germany Printed on acid free paper ♾ Foreword ÉmileBorelisoneofthoseforemostscientistswhosenameringsso manybellstotheearsofmathematicianswhilebeingalmostunknown tothegeneralpublic,saveforthosepeoplewholiveintheFrenchtown ofSaint-Affrique. Therethehospital,inparticular,isnamedafterhim. Notthathewasamedicaldoctornorwasheinvolvedinmedicine. He wasinfactthemayorofthetownwhenthehospitalwasbuilt,anditis farfrombeingtheonlyconstructionhecanbecreditedwith. Borelwasindeedabuilder,amongmanyotherfacetsofhisperson- ality. Healsoconstructed,andranasdirectoruntilhisdeath,theInstitut HenriPoincaréinParis. WhenItookoverthedirectionofthisfamous andinternationallyrenownedhouseofmathematics,thefactthatithad beenfoundedbyBorelwasquiteimpressive. So,Iamhonouredanddelightedtohavecontributedalittlebittothe publicationofthisvolume,thankstothelinkswehavebeendeveloping withEuropeanMathematicalSocietyPress,whichnowpublishestwo ofthefourjournalsstemmingfromtheoriginalAnnalesdel’Institut HenriPoincaré. AsfarasIknow,thisisthefirstbookeverwritteninEnglishabout Borel,eventhoughonecanhaveaglimpseofhislife,forinstance,in thebookMathematiciansatwar: VolterraandhisFrenchcolleaguesin WorldWarI byLaurentMazliakandRossanaTazzioli. Infact,thefewhistoriansofmathematicsinterestedinBorelhave longrefrainedfromwritingdownhisbiography. HélèneGisperteven wroteapaper(inFrench)in2012toexplaintheirreasons. Abiography ofBorelwouldbetoodifficultastorytelling,withtoomanychoicesto bemadewithinhisnumerousintellectual,mathematical,andpolitical commitments,letalonetheclassicaldangerofinstrumentalisationof hischaracter. Nevertheless,Gispertacceptedtocurateanexhibitionabouthim at the Institut Henri Poincaré library in 2021. Entitled Émile Borel, unmathématicienaupluriel,itwasdesignedtoavoidthepitfallsshe had pointed out in her paper, and reflects her suggestion to focus on specific topics, and actually also on specific years in the life of the Borels,withinformationabouthiswifeandwriterCamilleMarbobeing showcasedalongwiththoseabouthim. Thankstoourlibrariansand thisgroupofhistorians,inparticularMarthaCeciliaBustamante,the exhibition’s material was soon translated into Spanish and shown in CaliinColombia,whereBorelisahero. Inaddition,wealsopublished a booklet (in French) about the exhibition together with the Société MathématiquedeFrance. Backin1999,thebiographywritteninFrenchbythephysicistand BorelenthusiastPierreGuiraldencqfilledagapinawaythatwasnot competedwithuntilMichelPinault’smonumentalworkentitledÉmile Borel: unecarrièreintellectuellesouslaIIIeRépublique. Todayweare luckyenoughtohaveawidelyrenewedversionofPierreGuiraldencq’s bookinEnglish,thankstothejointworkoftheauthorandthetranslator ArturoSangalli. Iwishthisbookbeenjoyedbyawideaudience,rangingfromprofes- sionalmathematiciansorhistorianstostudentsandthegeneralpublic. WewillsurelybeproudtodisplayitontheshelvesoftheInstitutHenri Poincarélibrary. Paris SylvieBenzoni vi Foreword to the French edition PierreGuiraldenq’sÉmileBorelofferstheportraitofamathematician who had a considerable influence on the development of twentieth- century mathematics, and, in addition, the discovery of his lifelong contributiontotheawarenessofthisscience’sculturalsignificance. Borel’s1894doctoralthesiscontainedthebasisofanewtheoryof measurethathewouldexpandinhisLeçonssurlathéoriedesfonctions –anessentialtoolforthedevelopmentofanalysis–publishedin1898; atheorythatwouldcompletelyrevitalisethefieldandpavethewayto theLebesgueintegral. Thisworkalsocontainedthefirststatementof theBorel–Lebesguetheorem, whichwouldleadtooneofthefunda- mentalconceptsofgeneraltopology,thatofcompactness. Itisworth mentioningthatinhisproofofthetheoremBorelusedthenotionof transfiniteformulatedbyCantor, demonstratingforthefirsttimethe practicalapplicationofCantor’shierarchyofinfinities,whichwould laterallowBairetoelaboratehisfamousclassificationofdiscontinuous functions. OneofBorel’sdefiningtraitswashisdesire,veryearlyinhiscareer, todevotehisscientificknowledge,hisprodigiousintelligence,andhis forceofcharactertotheserviceofhiscountry. Tenyearsafterhisthesis, whenhewasatthesummitofhisscientificcareerandfame,heembarked inanewdirection,favouringwhatseemedtohimtopossessa“practical value”, foremost the calculus of probability, until then considered a minordiscipline,andforwhichhewoulddevelopthetheory. Hewas theauthorof“thearticle”thatin1909gaveanewdimensiontothefield; butalso,andespecially,toallitsapplications,fromstatisticalphysics– whichhadbeenrebornwiththeflourishingofmoleculartheories–to everyhumanactivitythatinvolvesstatistics,includinggamesofpolitical andmilitarystrategies,ofwhichhewasapioneer. Itisimpossibletounderstandthisradicalchangeofdirectionwithout consideringBorelthemaninhisentiretyandhisdeepattachmenttohis origins. Inthissense,PierreGuiraldenq’sbookisunique. Onecannot envisionBorelwithoutaland,aroot,ananchoringpointwhosesolidity restsoncenturiesofwisdomandhumanvalues. TheauthortellsusagreatdealaboutBorel,theman,theteacher, thescientist,theadministrator,thepolitician. Wediscover,amongother things,hisforetellingvisionofthenecessitytobuildEurope,andhis pledgeforagreaterrepresentationofthe“feminineelement”inpublic administration. His involvement in the creation of the Institut Henri PoincaréinParis,whichheheadeduntilhisdeath,wasdecisive. Pierre Guiraldenq’sbookwillbeofparticularvaluetoallthoseinterestedin thehistoryofscienceandculture;thescienceandculturethatÉmile Borelsoeminentlyrepresented. Paris BernardBruandPierreDugac† viii
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