Journey through genius - Math Sciences Computing Facility

315 Pages·2009·6.55 MB·English

Journey
Through Genius
THE REA THEOREMS
G T
OFMA THEMATICS
THE SCIEENDCIET IONS
• WILEY
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byR iacrhPd.B rennan
1990s,
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Zonderman
Journey
Genius
Through
THE GREATTHE OREMS
OFM ATHEMATICS
WILLIAM DUNHAM
WILEY
SCIEENDCIET IONS
WILEY
JOHN SONISN,C .
WILEY &
NEWYORK• CHICHES·T BERRISB·A NTEORONT,OS INGAPORE
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Prfeace
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got hearleo nteow atch stuhnesa entdc ontempsluaitce.i dIe ndo,ith do w­
everc,o mmistu ic,ib deecauIsw ei shteodk nowm oreo fm athematics.
Admidtltfyee,w pefionspdul ceah b soslaultveia nmt aitohnte im,ca s
bumta nayp pcraietiet s paon,wd emrco rrielt yii,tcb sae la_uT thyiboso k
idse sigfnotreh do wsheow oludlk iet op roabb ei mto rdee eply into
thleo nagng dl orhiiosyuto sofm r athaetmics_
Fodri sicenisap sdl ivearsls eiertu ar,tme usiacn,ad r, tt heiraset ra­
ditoifeo xnma inimnags tieercpes"-rgtehnaeote v sl,t"h" erg esaytm ­
phon,i"teh s"erg epata inst"i-natgshfi et taensdt miolslitaun tming
objeocfst tsu Bdoyo.ak rswe r itatnecdno urasrteeas u ognhp tr ecisely
thetspoei cosr ditenoar c quuaswi intth osfto hmceer eamtieilsvteo nes
oft hdei sciapnlwdii tnthehm ee na nwdo mewnh op orductehde m.
Thep resbeonotok ff earnsa naloagpopursot aomc ahte hmtai,c s
wherec rtehaeut niiivnsteo t thoer s ynmopvhebolun ttyh ,te h eeomr.
Consequetnhitinslso y at,t y pimcatabhlo oiknt h iadtto ensop tr ovide
as teyp--sbdteeevpol pmeonfst o mber anocfth hs eu btjN-eocdro es it
strtehsaespp laiblciyio tfm athemaitndi ectmsein rinpgl aanreoybtr i,t s
v
JOUNREYT HROUGGHE NIUS
vi•
inu nderasntdgit nhweor lodfc opmutseo,rr f,ot rh maatt tienbr a,l ­anc
ign ycohuerb cokoMka.t hateimocfcs o,u ,rh sabese esnp ectascuucl­arly
cefsusilns ucahpp liuendde rntga.sBk uiitwt a ns otw oilrtdsul tlyii ty
thatE ulceoldriA drhc imeodreG seo rCgan totrod evostome uc ho f
theeinrreg ayn gde ntioum sa theimc.Tas hteisdnei vailddsui ndo ftee l
comlpleteodj ustthiefywi orrw ki tuhti itlaarpipalni caantmyio ornes
thaSnah kespheaatdro ae p olofgowirriz tei lnogvs eo nniesnttseo afd
cobookookrVs a Gn oghha tdoa polofgoirz ep acianntviiannsgse tse ad
ofb illboa.r ds
Int hbioso sk haIe lpxollr aeh andofftu hle immpoosrtt parnoto fs­
antdh meo sitn genliooguiasrc mgaeuln trso-mtf hhesi toorfmy at h­e
matiwcitsh,e mphiaossn w hy tthhoeer ewmesr sei ganniatfin chdo w
thmea theimcairtaense odlo,vn ce foaarnl tdlh p,er eslsoigniigscu sael.
Eacchh apotJfe ornrue yTrh ouGgehn hiatushs r pereir myca ompon:e nts
The fiirsthtsi siatsleo m rpishciaTsh.e" rgeatth eo"ro enmt she
pagaehse sapda mno rteh a2n03 0y eaorfhs u mahni storyd.i sB­efore
cussapi antrgi crru ellsatIus ,ah lslet ths ec ebnyde e scrtihbseit naogtf e
mathteim,aca nspder hatphsse t attehw eoor flg de nerparlitlootyr h, e
theoLrieeekm v.e trhyienlgsm eat,h eimciascst r eawtihetidtn h ceo ntext
ofhs itoarnyid,it os f it nerteos tp Claarcde'a ssno oluotfti hocenu bic
twyoe aarfstt ehpreu baltiiocofCn o peursnh'iescol cientthreyiao cnr d
two ybeeafrtoshrd eee aotfEh n gnldaH'esny V rIIIo,rt oe mphiaztseh e
impactth Reoe fs ttoirouanp oCnam briUdngiev ewrhseianty yo ung
schonlaamreI adsa Nce wton einittn1 e r6.e6d 1
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ucotfr aelfl,e sh-anhdu-mbablneo giosnwd h oslveie msa yr efltehcet
insatpiior,tn hatelrg aiocr,t hbezi ar.Tr hee otrheecmosn tahienreed
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apepcrtiiaooftn h iewro r.k
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ativiidteyin ntte h ve"smaet heimcamatals ptieer.cJ"eu sassto nceo lud
nohto pteou ndersatg arneda tw itnhoovrueetla diitonr,g a tpoep icrate
ag repaati nwtiitnhgso euetii ntsg,oo ncea nnraoeltcl oym teog rips
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conncteiroaantn edff oarnttd,h ceah ptteofr losol wa rmee atnots r eve
asag uiidnte h uandte trankgi.
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thmeo sets teewmrietsdei rnE ngliltsieahrt u;tr oed,ha eyi sr egarded
PREAFCE.
vii
consaibdlleyer esnst hsuctsaiilIalny .tt wehnet iceetnhts uurpsyet,ra rs
comaen d wgiotb hr eathstpaekaeindnid,ged atsh saete dme sttion ed
chantghweeo r lodf teennud p o nt hien ltlceetusaclrh aepa. p
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orecmo,r rpercotvlweyid t thhisene vceoren storfla oigniitascst , h eo­
refmo rreE.vu ecdl'pisr oooftf h Pyteh agortehaenof rreomm has
30B0.C .
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be:s t
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whaotn eh ase stlaibshaendo thuenrd o.eI snm atheatmiaclso neea cghe n­
erataidodnas n ews totroyt hoel sdt ruec.t ur
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An umboeffra cthoarvgseo nien tthose e lteiocofnt hefseetw h eo­
remtsor epretshbeeen sottf m athteim.Aca ssn oetdm,y c hiceosfni d­
eratiotnofi nwadar msge utnts hwaetr peat riacruillnyS tifgouhrli n­ge
niuosT.hi so,fc ou,ri stneruocdeasne leenmotfp esrontaal,s a tneId
recogtnhiadztffie e ar aeunttrwh ooludc earitngleyna etared iffelriesntt
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satihdta ta liedsno iten sagi wlhyao tt hsfie nrddi fficbuulttth g,a te nius
isdo ienags wihlaoytt hsfie nridm opsslieAb.sw ilble e ivdetnhtee,i r s
muchg endiiulssap yoentd h pea gaehse .Ha edrea rgee nucilnaes sics­
thMeo nLsaia osrH almeotfms a thecm.sa ti
Buott hceorn sideirnafltuietonhncceseh doo iftc hee eomrsF.oo rn ,e
I watnoti endce ls uadmpflreohsmi stslo erayd'miahntemga tni.scI ita
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hisytw oirthmoeuntt iothnweio nrogkfR emabnrdotrC enzna.e
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mathtecim.sTa hep roposiintt hibeoo nosck o mfer otmh ree alomfs
plagneeoe mtragyle,b ,nr uambtehre oarnyas,li,a ys ntdh teh eyoo fsr est.
The vaorfi ettthypoe isceas n,d otchsceia olnianlak nsdi t nerypsl a
amonteghm m,a ayd adn otoeff rsehnteost shw iosr k.
Ia lwsaon tteopd r esiepmnotar ntmta themtahteieocm,rasr la ther
thamne recllvyeel ri tttcrslkio erp uzz.Il dneesemdo,so tft hrese usli tn
thbeo oekti herrel svoeldo nsgtd-ainnpgr lobemisnm athecm,soa rt i
JOURNEY THROUGHG ENIUS
viii•
genaetreedv emno rper ofoquuneds tfiotorhn festu u,ro erb o.tA htt he
issrauiesb eyd
endo fe acchh aptiesar nE piloguuseu,a aldldyr esasni ng
the tghreeeoamart n fdlo lwionigat si e tc ohedso wtnh rotuhghehi story
ofm athteimcas.
Thetnh eirtseh qeu esotfilv oeelno fd ifficyu.Ol bitvousmaltyh,e ­
maitchssa m angyr elaatn dmwahroksse adnecdpo tpmhl eyxr ietnder
theimcn omphreenstioab lblluee t x pte.sIr wto lubde f oloitsoih n cel ud
sucrhel sstui nabo oka imaettdh gee nae,lsr citeinfilclyta iealrtree eard.
Thteh eeomrtsh falotol wr eiqeruo nytl hteo oolfas l geabngrdea o m,e try
oft he soarctq uoiinnref e eashw i gshc hocooslue rTsh.te w eocx ep­
tioanraseb riuesofef t hsei ncuer fvreot mr igoniondm iestcruys sing
thweo rokfE ulienCr ha pt9ea rna dna plpaitcioofen l eenmtianrtye gral
callcuiusnt hweo rokfN ewtionCn ha pt7em;ra nrye admearays le rady
be acquwaitithnh tetesodep , ai ncfdso trh owsheoa rneo t, itasbh ietr e
ofe xplantaost mioooontv het rhd ei ffilctuy.
Is housltdrt ehstasht ii nsso ats chotloamr.Tel hye arrece e ritnya l
questoifgo rnesma att heimcaoatrlh istosruibectttaylhl ac ta nnboet
adedsrsienadw orokf thiWshi lkIhei a nvtdeer. di t oa voiindc luding
falosrhe i stoirniacrcaaclmtulaeeyt r ,it ahlwiasss i mnpolty ttihmneeo r
platcoie n vesatliflga acotefaet ls il su seTsh.ib so oakf,ta elirlms ,e ant
fotrh peo pluanro,t stchifieec np,tr ie.s s
Alotnhge lsien Ie sm,au dsadtw oradb outa utthheie tnytt ihocef
pro.oI fnps repatrhbieno goI kh ,a vfeo uinitdm psoisbtloae v otihde
needs ofmocero mpromiset habeue tth'woo erreisngn ionttaialot ne,r ­
minooglya,nl do gistcraalat netdgh ryee iqerumetnhtta htme a theim­at
camla treibaeul n dsetrabnldteaot hmeo derrena dAce orm:lp eatdeh er­
encteot hoer igwionluadml ask seo moeft herseelss tvu erdyi ffictuol t
comphreenydea;tS ifigcnaidneitva tfirootnmh o er ilgwsio nluadco niflct
witmhyh istoorbijvceeacsIlt.ng i enae,lr hIa vter iteord e tVaiiurnat lly
alolft hsep iarniadtg ,o obdio tft hdeea tiolft, h oer igtihonerael.m s
Thmeo dificIa thiiaonvntesrc oesddeu etmom et ob en om orsee uriso,
thasna,pye ,r foMrmozianorgntm odeirsnnt rusm.e nt
Ansd ow,ea raeb otuobt e goiunjr uo nretyh rotuwgmohi elnlnoifa
matheimclaaatln dm.Ta hrekrsseels tuosla,dst haery,re etaaf eirsnh ness
anddi syp slapa airgnkv lirtueovseainft tsyeom r a ncye unrtiIeh so.p e
thtahtre e awdileblre a bltoeu ndsetratnhdep sreo aonftdsor eciozgen
what tmhaedgmer e.Fa ottrh ose whoi nts huviencstc ue,re eedIx pect
theew rilble n ootn lasy e nsaew teoh fca otm ferso amp pcraietitnhge
greatonfoe tshseb ruastl ,as s oe nosfpe e rssoantailis otfnha oacnttce a n,
inedecdo,m ephretnhdwe o rokfasm as.t er
W.D unham
ComlbuusO,hi o
Acknowledgments
Ia m indteoabn tuemdbo efar g enacniiden sd ivfiodtruh aelisr efforts
onm yb ehianl fpt rheep aroaftt hbiiooson Fk i.rI ms uts,at c knowledge
grafnrtosbm o tthhp er ivatthepe ub alnsidcec t otrhswa etr ievn laubale:
a1 893S ummSetri pfernotdmh L eiy El nldomwenItcn,.a n,d ftnuhdei ng
ofa1 898S ummSeerm airtn it"lTheeGd re aTth eoroefMm ast hematics
inH sitorCionctaelbx ytt "hN ea tiEonnodawlm efnottr h Heum ani.t ies
Thseu ptpo ofLr iylE lndowmeanntNd E Ha lwleodm yp reovuisulnyf o·
cusiendt eirnte hhseti syto ofmr athemtaott aiskches a ipnteh feo romf
courastHe asn oCvoellre ganeOd h iSot a. te
ToT heO hiSot aUtnei vearnspdia ttriylc,au rtloiy tD se aprtmoefn t
MathteimgCaoSm ,ys inctehraefn oktrsh ewiarrh mo spiitwtyhia llaesa,
vsiitfiancgum letmyb ientr h emiird Isw ta,ws r ititnhbgio so Iks .h all
alawyasp pcriteaet hkei ndonfeD sespr atmeCnhtaJ iors eFpehra rnadr
oft hLee itJzoealansn J-di mw-how eruena fiinlghleylu plaf nsdu p­
portdiuvrei ng myv it.sw iot-year
Maniyn divaildscuooan ltsr itbotu htwieosrd kT .h angkots oR uth
Eavn,ms yf arvioltbierr ai,aw nhoi tnrocdeumde t ot hceo ltlieoocnfs
per1-090m athemdaotciucnmatdelsu rimyn1 g89 0s abtbaiaclt;oS teven
ix