The Years 1838–1855 1981 W. K. Bühler.pdf

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TheYears1838-1855
OurpictureofGauss,asithascomedowntousfromtheyearsbetween
1838and1855,
severaleyewitnessreportsfromstudentsandvistiors,buteventheydonot
contributemuch.!MostofthelettersfromthisperiodweretoSchumacher,
nowbyfarhismostfrequentcorrespondent,buttheystayonthesurface,
projectingthepictureofaperpetuallybusymanwithmanydiverseinterests,

hisastronomicalandmagneticobservatories,butthereweremanyother
,amongthem
combinatorialonesposedbySchumacher,2experimentalandtheoretical
physics,andoncemoreforeignlanguages.
TherearequiteafewsurprisesevenintheSchumachercorrespondence

1824(#),hepleadswithSchumachernottodismisshisyoung
assistantKlauseneventhoughhewasclumsyandhaddroppedaprecious

...
incidentwiththebarometermaynothavebeenthefirstofitskindandletsme

teaching,however,arecurrentlytheonlywayswhichallowamathematician
•
thingexceptionallygoodcouldhehopetofindapositionatanacademy,the
waytheyareorganizedtoday,andeventhenyoucouldbet99to1thathewould
;youarethe

perhapsdobesttogointoadifferentprofession,hecouldjointhearmyordo

toworkforone'slivingitdoesnotmatterwhetheroneteachesbeginnersor

offreetime...3
ühler,Gauss
©Springer-
THEYEARS1838-1855147
ThispassageistypicalforGauss'sattitudeduringthelast30or40yearsof

alwaysmaintainit,thisseemedtobeagenuineexpressionofthewayhesaw
thingsduringthisperiod.
Intheearly1840s,GausstookupRussianafterashortflirtwithSanskrit,

literature;atriumph,immediatelyreportedtoSchumacher,wastheidenti•
ficationandcorrectionofthesentence"Themoonrisesbroadlyinthenorth•
west"'sconcern


relatedtraitinhismathematicalinvestigations:theywerealwaysinductive,
proceedingfromparticularfactstogeneralstatementsandavoidingunnec•

.,thoughhedevelopedtheminthecourseofthe
,we
havestressedinthisbiographythemathematicalcharacterofGauss'swork
inthenaturalsciences,butoneshouldnotoverlookthe"scientific",often
'sthinkingwas
inductivetoanextraordinarydegree,hencehishungerforfacts,hisloveof
details,beitinmathematics,inthenaturalsciences,orinanyothersectorof

discussionsofastronomicalorgeodeticmeasurementsandhisexperiments
onbehalfoftheHanoveriancommissiononweightsandmeasures,aswell
ashisendlesscomputations,hisinterestintablesofprimefactors,orhis
computationaldeterminationofoneoftheperiodsofthelemniscate.
In1842,thoughGausshadnotspentasinglenightoutofhishousefor
overtenyears,heenteredintonegotiationswithVienna,whereaposition
attheuniversityhadbeenoffered;ifhisBerlinnegotiations,20yearsearlier,
hadnotbeenverypurposeful,theshortnegotiationswithViennawereeven

TheyearsfollowingWeber'
sparedtheextremehumiliationwhichoftenaccompaniesoldage,butit
wouldbedeceptivetotrytoprojectthepictureofasereneeveningina
,whoinsomany
respectshadbeenlikeasontoGauss,followedtheemigrationofWilhelm;
shortlybeforeWeber,MinnaEwaldandherhusbandhadleftG6ttingen.
In1839,Gauss'soldmother,nowblind,died;hergranddaughterMinna
followedin1840,-she
andJosephhadbeenthesurvivingchildren,the"pledges",ofthefirstmar•
,herfather'sfavoriteamongthechildren,wassaidtohave
,thereveredOlbersdiedin1840,
148CHAPTER14
,
,Gaussmentionedhisphysical
ailments:therewasatemporary,unexplaineddeafnessin1838,increasing
lossofmemoryandvision,,despiteallthis,the
mechanicaldutiesoftheobservingastronomerandhisdiverseotherinterests
gaveGaussthedistractionheneeded.
ItisnotpossibletodiscernaradicaldifferenceinGauss'sbehaviorbetween
,heremainedunaffectedbythepainful
experienceshehadtoundergo;whatweobserveisasteadydecline,pre•

beexpected-
scientificcollaborationwerereplacedbypersonalhonors,medals,andother
,Dirichlet,andEisenstein,perhapsthemostgifted
GermanmathematiciansofthetwogenerationsafterGauss,paidtheirre•
spects,buttheydidnotestablishlastingorpersonalcontacts.*6In1838,
GaussreceivedtheCopleymedalfromtheRoyalSocietyinLondon;later,
hewasmadeamemberoftheorderpourIemeriteinPrussia.
Oftheimmediatefamily,onlyhisdaughterTheresestayedinGot•
;in1838shetookoverthemanagementofher
father'
fatheranddaughterhadmuchincommon,exceptastrongbondofmutual
appreciation,thankfulnessfromthefather'ssideandadmirationfromthe
daughter'
Reportsfromseveralofhisstudentswhoattendedhislectureswhenhe
wasanoldmanshowthatGaussnowenjoyedteachingandlecturingmuch
.
Oneofthereasonsforhischangeofattitudemayhavebeenthatstudents
'slast
,whoisknownastheauthorofavoluminoushistory
ofmathematics,,famousforhisworkinnumbertheory
(trans•
latedin[DunningtonJ):8
...usuallyhesatinacomfortableattitude,lookingdown,slightlystooped,
,veryclearly,simplyand
plainly;butwhenhewantedtoemphasizeanewviewpoint,inwhichheused
anespeciallycharacteristicword,thenhesuddenlyliftedhishead,turnedto
oneofthosesittingnexttohim,andgazedathimwithhisbeautiful,penetrating
*,hewroteavery
complimentaryprefacetoacollectionofhisnumber-theoreticalpapers.
tThereisanironicpostscripttoTherese''sdeathshefirstwasincoQ.•
,onlyayearafterherfatherdied,shemarriedatheatricalproducerandactor

frowneduponbyothermembersofthefamily,certainlybyJoseph,presumablybecauseitwas
consideredamesalliancewhichdesecratedthefamilynameandthememoryofthegreatman.
THEYEARS1838-1855149
blueeyesduringtheemphaticspeech....Ifheproceededfromanexplanation
ofprinciplestothedevelopmentofmathematicalformulas,thenhegotup,and
instately,veryuprightposturehewroteonablackboardbesidehiminhis
peculiarlybeautifulhandwriting;healwayssucceededthrougheconomyand
•
icalexamples,onwhosecarefulcompletionheplacedspecialvalue,hebrought
alongtherequisitedataonlittleslipsofpaper.
IfonegoesthroughthelistofcoursestaughtbyGaussoneseesthatmost
ofthemwereinastronomyandonlyveryfewinnumbertheoryandother


numbertheorywasin1807/08,
Gauss'sinvolvementinconcreteexperimentalquestionsdates,aswesaw,

astronomers;mostofthefriendshipsofhisadultlifehavetheirrootsinjoint
-that
thisinvolvementprecludedadeeperinvolvementinpuremathematics,his
always-rememberedfirstlove.
In1838,theyearWeberhadtoleaveG6ttingen,Gausscompletedthe61st

hadeverbeenabletoestablishagenuineandmutuallyfruitfulworkingrela•
,and
yetGausswasabletogoonwithhisobservationswithoutinterruption,to
contributetothecollectionofgeomagneticdatawhichwasbeingcompiled,
tocorrespondwithSchumacher,Gerling,Olbers,andBesselaboutastro•

workhad:Gausswentontomakeusefulscientificcontributionsatanage
whenhisoriginalmathematicalproductivitywouldperhapsnolongerhave
heldup,andinthefaceofthevariouspersonaldisasterswhichhehadtoface
•
tialscientificcontributions,buthisworkactuallyhelpedhimretainhisequa•
,wesaw
theothersidetothis-Gauss'sunresponsiveandinflexibleattitudeinthe
conflictswithhissons,andtheendofconcentratedmathematicalresearch
soonafter1810,butthesesacrificesmayhavebeennecessaryifacontinuation
,theautomatic
componentoftheexperimentalworkcontainedanenormouslypositive,sal•
vagingfactorandshouldnotmerelybeseenasanunwelcomedistraction
frommorecreativeand"valuable"activities.
WhatwassaidaboveshouldnotindicatethatGausscompletelygave

life,twentyorthirtyyearsafterhislastoriginalresearch,therearestill
manyinterestedandinterestingremarksandobservationsinthecorre•


150CHAPTER14
thefirstmathematiciansinwesternEuropetounderstandandappreciate
Lobachevski'sresearchonnon-
presentedhisresultsisquitedifficult,evenobscure;hisearlierpapers,includ•
ingthosewhichappearedinGerman,
In1846(),Gausshadoccasiontomakethefollowingremarksina
lettertoSchumacher:
RecentlyIhadreasontolookagainthroughLobachevski'sbooklet(Geome•
,
Sheets).Itcontainstheelementsofageometrywhichwouldhold,andwhich
couldrigorouslyhold,
certainSchweikartcalledsuchageometryastralgeometry,Lobachevskicalls

years(since1792),withacertainlaterextensionwhichIdonotwanttogo
'spaper,
butheexplainshistheoryinawaywhichisdifferentfrommine,anddoesthis
inamasterfulway,
attentiontothebook,
Thispassage,interestingforseveralreasons,containstheapparentlyerro•
neousstatementthatthepossibilityoftheexistenceofnon-Euclideangeo•
metrieshadbeencleartoGausswhenhewas15yearsold.
ItwasinconnectionwithLobachevski'sworkthatGaussstartedhis
,andcom•
plainedinalettertoSchumacherthattheselectionofRussianliteraturein


In1849,theUniversityofG6ttingencelebratedthe50thanniversaryof
Gauss'sdoctorate,hisgoldenjubilee*.Themaineventwasaceremonyin
whichGausssubmittedanimprovedversionofhisdoctoraldissertation,