From Servant to Queen: A Journey through Victorian Mathematics

279 Pages·2019·13.441 MB·English

by  John Heard

From Servant to Queen
A Journey through Victorian Mathematics
Withafewexceptions,puremathematicsinBritainatthebeginningofthe
nineteenth century was a recreation for amateurs. Drawing on primary
sources, John Heard provides an engaging account of the process by
which it rose to become an academic discipline of repute which by the
FirstWorldWarwasledbyGHHardy,andsupportedbytheinternation-
ally respected London Mathematical Society. In chronicling that rise, this
book describes key contributions and the social environment in which
mathematicians operated, uses contemporary commentary where appro-
priate,andprovidesfullreferencestohelpanyresearcherswhowanttodig
deeper into the original sources. No mathematical knowledge is required,
andreaderswithawiderangeofinterestsandbackgroundswillfindmuch
toenjoyinthisuniqueinsightintotheworldofVictorianmathematicsand
science.
JohnHeardisanindependentresearcherwithadoctorateinthehistoryof
sciencefromImperialCollegeLondon.HeisalsoamemberoftheBritish
Society for the History of Science, the British Society for the History of
Mathematics, and a Fellow of the Institute of Chartered Accountants in
EnglandandWales.
ArthurCayley,paintedbyLowesCatoDickinsonin1872;asatiricalversebyJames
ClerkMaxwellconcludeswiththelines:
...byDickinsondepicted
Intwodimensions,wetheformmaytrace
Ofhimwhosemind,toolargeforvulgarspace,
Inndimensionsflourishedunrestricted.
From Servant to Queen
A Journey through Victorian
Mathematics
John Heard
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107124134
DOI:10.1017/9781316415726
©JohnHeard2019
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andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2019
PrintedintheUnitedKingdombyTJInternationalLtd.PadstowCornwall
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloging-in-PublicationData
NAMES:Heard,John(JohnMichael),author.
TITLE:FromServanttoQueen:AJourneythroughVictorianMathematics/JohnHeard.
DESCRIPTION:Cambridge;NewYork,NY:CambridgeUniversityPress,2019.|Includes
bibliographicalreferencesandindex.
IDENTIFIERS:LCCN2018042537|ISBN9781107124134
SUBJECTS:LCSH:Hardy,G.H.(GodfreyHarold),1877–1947.|Mathematicians–Great
Britain–Biography.|Mathematics–History–19thcentury.|Mathematics–History–
20thcentury.|Aesthetics.|Mathematicsinnature.
CLASSIFICATION:LCCQA29.H23H432019|DDC510.92/241–dc23
LCrecordavailableathttps://lccn.loc.gov/2018042537
ISBN978-1-107-12413-4Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof
URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication
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accurateorappropriate.
This book is dedicated to the memory of my dear parents,
Nancy and Percy.

CONTENTS
ListofFigures pageviii
Acknowledgements ix
NotesfortheReader x
1 SettingtheScene 1
2 TheLegacyofNewton 11
3 TheLondonMathematicalSociety 50
4 ThePureMathematicianasHero 111
5 MathematiciansinanAetherealWorld 145
6 ApologiasforPureMathematicians 190
7 EmbracingBeauty 214
Epilogue 243
SelectBibliography 247
Index 257
FIGURES
3.1 Invitationtothefirstmeetingofthe‘UniversityCollege
MathematicalSociety’ page58
3.2 OriginaldesignbyAugustusDeMorganofabadgeforthe
LondonMathematicalSociety 62
3.3 ConstructiondiagramfromthefirstpropositioninEuclid’s
Elements 63
3.4 TotalnumberofordinarymembersoftheLondon
MathematicalSocietyateachpositioninthetableof
wranglers 73
4.1 JamesWhitbreadLeeGlaisher 116
4.2 HenryJohnStephenSmith 129
5.1 Chartshowingreferencesto‘puremathematician(s)’ 146
5.2 Thecontroversial‘parallelpostulate’fromtheElementsof
Euclid 167
6.1 Sylvester’scharacterisationofmathematicaldiscovery 207
7.1 CartoonfromPunchbyGeorgeduMaurier 219
7.2 LoisCayley:clearlyamathematician 230
7.3 Theexistenceproof:Hardyontheleft,Littlewoodonthe
right 238
ACKNOWLEDGEMENTS
Thisbookcouldnothavebeenwrittenwithoutaccesstomanylibraries
and archives, and I extend my sincere thanks to the librarians and
archivistswho,overtheyears,haveallowedmetoconsultthematerials
intheircare.Someofthesematerialsarequotedorreproducedhere,and
in this respect I am pleased to make the following acknowledgements:
lettersfromHenryBaker,bypermissionoftheMasterandFellowsofSt
John’s College, Cambridge; the portrait of Arthur Cayley, the photo-
graphofGHHardyandJELittlewood,aletterfromHaraldCramér,
and an obituary speech by Alexander Ostrowski, by permission of the
MasterandFellowsofTrinityCollege,Cambridge;lettersfromAndrew
Russell Forsyth, by permission of the British Library; a letter from
G H Hardy, by permission of the Syndics of Cambridge University
Library;the journalofThomasArcher Hirst,bycourtesyof theRoyal
InstitutionofGreatBritain;minutebooksoftheLondonMathematical
Society, by courtesy of the Society; portrait of J W L Glaisher, by
permission of the Royal Astronomical Society; ‘My First Gorilla’, by
permissionoftheZoologicalSocietyofLondon;asketchofabadgefor
theLondonMathematicalSociety,alettertoThomasArcherHirst,and
letters from Sophia De Morgan, by permission of University College
(London)Library,SpecialCollections.
IamgratefultoJuneBarrow-Greenforaninitialsuggestionthat
led to the writing of this book, and to her and Tony Crilly for their
valuablecommentsonadraftofit;ofcourse,theresponsibilityforany
errorsoromissionsisminealone.Finally,mypartnerStellaPilavakihas
provided constant and loving support and encouragement throughout
theauthorialprocess.