Émile Borel: A Life in Mathematics and Politics Across Two Centuries

126 Pages·2022·10.81 MB·English

by  Pierre Guiraldenq

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