CAP..L FJ.Ill)::1.:C:: GAU33: PRUCE CF LA"E:2:I·,A'7ICIAl.j 3Y HOLOTS Thesis, ID 49S Dr. LrCor,:licl: Jure ;.', 1<;71 (; ~f;l(:.. ~2.fc S ,cw b.r>-l tl,;~-I- }:r i::',,~) cf C2"Y>1 FT'~.~r~:rieL GCt13S ('12E: cf F:c Clc~t ""i::tt(2- ac(('-·~-Ji:",L:~.rLt~) ;:;,:.ould be r':!2t:.-d a:' 1. :::C::·Ui:T' A. G2.1_::':;~;' r:r~,L:1fi..l.+i:"· D. G,JlJ8~'" :{~ ~_-ber was ~ir:t,J.~o.r~ G-~1;0~;' Y:J(,tlJ"2' W' G u:-:rc:,r:€; Cit G:"ll;~'~' .j,:'.)~_~3:~. II. G~~~\)s.-" ctI2- A. ,"fa:::: C('o:J n <.iUI"LPY; ~~p·!·~e. t1=lf-trotl'lc~ waf~ Gec:l',c r • rli,='--J rJ2 0·J d.L ':"'o-i~~~: CJ.~. i -tj_ tJ~ 4.-·crr~.al r~c (c1.:! (" • G,:,,1.1~,3[:'. l)i.E: triC!l -"I'::;-hr(~ ;i:.I!-; j athc;,-.atic.:; at Lcr::c. n fer a 1. i fr a~· ~'\r'Gf(-)~;~-JGI' :.,at~ SJ::.~ti ciEtY • C~.1~3;C·' ,·,·hcaiic: vrc.~: fL::-.;:.c'· ~'er--:iLd::i'l of Jrl,11:~w5cl·~. ~ 1'1 ~ ( , Gal~S:-: :i;,; t- (.~ t· , 1 \ J'72-. -17'"'>[ b~ C~:rJ. Dl]].:C !tljl~v~m .L ... c. D. ')"c'"-tic: ('.- \ ..} ;1L'2'_ ~7='5-17,::r ) . t·· p .f' 1;' II:. d. 0!-: 1 c1_. -O.'i::l:" cf :.ur:_::I·~" J.' J' • 3. c. J. r ~, j.l. t r , ~' ~1" f••• Coy,' 1 .1' ..i.. • • , \'\T~ 1 i C'_ h. ~.G" .-_ ,1-. : t . , " ~, '. t .::0 ;: ,~ 1.... r,~ ; , D . ~(y'. c. ci' r, ~ : _"t: ... ;,' ...., F .. 2..". ,- "')- .... " ~ .. '" .J T J... v • v...L ~. 7' t., • ." u : J ..:_ ~~ Li.::..V. (au~33 2L..."\;;33 'j""~Tl:r' ~ C~ _~USS iL'.- C G~~l1.S;~ Wi)~ C;'J. ,~ LLC .1 L f ,_. , act ~~ ve ~. C~,·, Gtc~_10 (:"'-'~ wit>· c"~"ic~. 1 ,., :-:1~ " . , 1-;: ~ .. .".t.1. 1..- c (""r~ , . l"a-~:L.)·. ;-·ti +... iga1-(' J c:: :,::.. =:.~_. c .' .l. ....L.u if (? i " kt PT'ir[; 'vr~'s trul:' [;, "'riLc8 01' m;:L.ematiciars, 0.1 t",'Jvt;L If-nell of his Hork went uEnoticed. FRIrC:': CF LATUJ.A'l'ICIAL~ C 3':1'1 Frildrich G [.us~; Wc,2 ~-;orn on April ~:O, 1'/'17 to 8ebr,h1'(i ",1'; L. t nis home ire Brlln~;Hick, Germ&Y'Y D0r()t foe: :::8.1)88. CarJ. ' ., T -. c....::~(". .. t.J 1) r' t:,.I. ,_ l;"_~ ~'" "":drl ',r ~_ t. r ',1 ~ , "':- C r"t 1, • -.J_ ,~ E' ~:t: .~,:, 1 ,;(",-,-,.,.1 ... ,",,"' I'"U" '~i , . ' 'c' t:. ,-, -." ~1' , "TJ .{ 0. ,', ~ ,. (t 0-.; 1 ' ') ':' ~ ....:1 "'-'-! '-. ./ . '-, if r " , V{,l'''" .,. -1-' ( }' ,'-", -'-' .i ( .(). .-' ~ .. -L- ' c.. '1 _..... _ ..,. J (...' c.J ~,'. .- "I' ! a" (l, 1 r .-- +-" y "'-. w'- I . r cJ'. r -,/ ( - , C' .1 , 1 ' ,, ..... .!:. .;).- ) ~, j .,.... '~ , .; I,',:' u • + 1:i 1'. CJ C W(..t: I <-.'..' :~; "I ," VI r 1 '" , , ," .~. cr ; . ,. '- , 3 Carl 'Nas round to be til'" only stucient Wl. til the corre( t answer, once the other studerts had fil1.shed their laborious additions. Appar"ntly Carl reaLL zed that lanc1 100, 2 and 99, 3 and 98, 4 and 97, etc. each add to 101, and therefore the fifty pairs together must times 101 or 5050. Bartels was ~,-dd to ?O 4 attracte~ to this exceptional student and they became cl)se friends even though Carl was ei['~lt years youYl€::er than Bartels. By the timE Carl was eleven. Bartels had taur;ht him the jinorLial t!leorem ULd the theo:r'y of infinite series, two areas T,'/"hich later LteTested Carl verJ m1;.cL BartE-Is ::::1so hel~c:cl !'im b.~r t,?]linL perser s of iiif)l rc..p..k abcut hi:; -', a + :-, :--;~'~ ~ t j c i Ctr: 8 cr:wti cs. llr1 in which he b,:6e c:r'r'at :-:trir;('s. , ",' " 'J " -'- ~ -"Or V 1 , , " , r, , " c. .. v :.. - l"i U (; " " r , ., c. " 1 .LJ ;:......, It' " ~ 1/ 1 " h"I- ' ...., 11 V c. <.. , . " , ,II .r' ( , _1'" " , j .tt .~., :-, J... ".- ,- -.. - , J' 1'. ~ 0 r r' "- + yo' .. U, G " ,.., , " c, c.,f' .,.., " , ,~I ' ,1 \' l.' " i.~1' 1 , J , ,c. t ( , ,' ~- I .: I I." , a~r'FE,rer! SOLle + + II" L of r,umi,er tlleory, 1. ., , , ~,l1ie!l , a :::--:lC':l ,';' of tho,o( idea ... of 'Thieh anp:"areo in his Analysis Resirluorum, re"lrittr:::-: as :,urt of the Disquisi tiones Ari thmetic(lE'. m<':l, t \ ~ (' ,i -,"'"1 !'" .L i.:,: 1 - !. _j -log J( ~. l' : f' X ! , r- },-.,,- 'V' I l' t "._1 ~"7 " _.J ('( J)( log X , • -r .J..• - 1 -,-~ ... , .... Y' t! "I .'~ r" , 1 1 -I-I... I /09( .....i -'''' - + .J. ( . . - I.' '/ n --ro:, ··f +- "'~c:- ! ,--' '"I ; r -, 1-."""" I 0 .. +. '~---' i::t + c - _L' .~ , .. -'- J. ,- r, 1._ ---'-'-'-' '( (~.ei~ .... _( L i:~.:r(J 1.(')1"'1 .. , 1('l.-· ~, .1.' .. ), t 1 " \ .. "1 r ' c -, r '.'.'" (' 1 , :' ...... r , '/ v:lue ['Y'Q c;~sei'vaticr&l toe result~: is a cJ,rir.-;LAID for aIry sirl~l~? case and for t~~ ertire set of obcervbtions. (He used thlS netnoJ in his astronomlGal vTOrk much later in 11i8 lifu.) ,0, full ;'!r:vclor·D( Lt of this netrlor' of lc<:::.st scv<:::.rcs. ro :tCi.ticf .... y-, r '.'.I.L' l"!,'rr- . - ' ic'c nuct -, (, (' ';:'0 Gauss - ·1~. j i.,:'-"-,'i.. -'''f~: l-"Y",' + \~.; " ':l +.---. 1 ..t., 1 ,c .. f".:-, 1.... .:; ~. ;.·c. -f in I' .. ('irel, ·~L"cc:\"-~: _~(' f' . -y·1 Ca., tc :. rc:; t -f.:' l " n" 1 ': ••• Pr :3 ore. +~c 1c::- .. -i ctir:: !, y', J, c: DJso:,':i n f' \' -:-;:::::::G=:')(=:--- J VI S j +i ;~: ,('~' J'" 1-'oJ" , " -X r Art t1.- +' . . +,- ;, (':..._ r \' ,, ",......(" , 1"1 (1)~:1. ) _:;<' fe, 1'( r ~- -~ ,. ("f' also contained formul as concerning the elliptic theta constar~tst were rediscovererl ar,d brilliantly applied by J ::ccd, but Wh1Ctl Ge.uss published nothinL; about elli-ptic furlctioTS, ror did he claim to have miticiuated Abel or Jacoui, al though their discoveries c2I~e in the 1:'"20's. v.ra;:, I?XCfEdi:: ('1~' a1]Ea". of r:is +;i'--e i;:, +:->? fact that tllC ~. p] 1 " •.f H 1°,7.7" ...J_ --' .... i ), Gl_1: __ ~N ;..~l 10 .c, J. ~r- r,{' ,. \¥_,l-'o C,:.x-·'-·" 1 j ::otic ,..;..V" - ., " -, :.1 •. oj c;~!,,'~ , ... :. _ .' J J...' ; , , ;} (.I" .. '1" (-~. s ff ., I' 1'7 -+- (G:" (' ~,.: ( ..1.'_: .. r1 :, , :-', ~ "\"~: 1_1_~, .I. I. 1 '. '..J C~. \.." :1':"': ' Lc;J. r 1 8:.01'1 tLCt .. :::'f'\iOUS ?"Jr ., .. a1:3:-= __ 1"" ~~0" J' " - 1 D ,_'":~.; ~ d l}-;:: r l r,,....... r7 L:' . • _. - Zrj c Tr or, .,., Dr: '. ' , (" , or. ,~ , :-:rool's ',jCrf "uL,-,atisf&.ctory &r..cJ illusory" were morE like p-r:cir..cErs in tlleir Uiinkiq::. -- __ L __ ~ L, 10 Lost of tIle [,rent Iil!<.theruaticians of Gauss' time 1 "', . ; __-:, " to €:"ive a newly cor.stn..1cte'·' ri[,orous proof. -. " I" -. " (1) to ,0r:::,'-'" __ ,{ ,1 r: (f ar~d before Tne formulas tney , 1 ,"'" ]. I." 1'1 1 ~- ~, '''O-'',~,l~ .", ,..-' t" c -. + .; v- i - .r:';. ~ i r. - -, ,., t r 1 !I'L- \'1 c' . . . - i. :: +r -,-1- +' ., I., ,,1- .' , ,i J l. J_ ' t +- ar t -'r:, -.. , r+: ('::'1 = f- r."; c:. _, ~- ',--, rr: . .-i r "att" r'" 1 '7,_ - --" .dC' 11, ~~, ~' .;.;(. , c.. ~ .L n!\tt lie" '/ Di vi ,.J DivFo (2b +11, + r 1 t- ,,,. 0 2, l.....r. () t t (~('r ~ f ~- cf " ,~, " cc:d cal' J ~, 't"" C T "d" tl: ~, r. t j l-- , . 'j. s ! ,P lfj. ( '\1jcrl--::~, ~-, Gar::;;::, +, t ':it ,I, J-: ,- e r .. ' . . . . ... . t~... f' : r '+ .~ o ., t ~, " ~. ,,( , ~, . , '- ~ 1 .,1 i 1, -,lCl 1 " t () h P' .1 .,. .... JJl" ' :Jl &cti-;- •.L , t~ l~ f,'J i' + -'1"' . ,- (' , l 'C, - pc" .' J .. : '.e ,.,..,_._'r L' ;r ,~~ .t~ vol:. ~- +".,', ('; .i 'r' 1 J.' r' r -I.. ! _~ V.l.. + , 1. , , ;~('i c f' ,. r .... , .L _ i . . ...'-_ l' c,l " ,','r- , . , . , .L ~ , i -,:' .' t , 1 1 0..:.... ......... 1':', ;, f -~: ~ .• " l' L r ",] t' C'.. ',j ..I. w,: I' - (~ ~ oJ -, " (~J.:, ('~. _ ,'J r ,, _;CCT'Er~ {-' t.-._" , ( r. t, ~. 7'7 ~ ( . I. .; - C>"1 \j , ,'las nis "roof for t;.c law of (!uu:lratic (1 ":."'u f~_ct j1e f eve scveL proofs '.Ii tnin 17 yeCi~S. rc(":r:'~ocity, in Today tnis tlJeorem Ga1J ~ [-:: s·' ,"., . + v; ..... ~ L T ~. "Crtic, ", I '.• ~ J . I ~ _" i:..;..rj T i :1 , ~- + c'( 1" r, ~ . ~ 1 (' ;, c· •. ,-j .• j ,.["' J. ".1' f .j. ( 1 ~l + - +y l t Ci:;!·1'<' ,-f' ..r r, I~· ,)c: ,r- C"" J -'-.- lJ? J. Y 1, , J , ~, r, ; " ,,; r -'-" +-I t " S " )T-' -, f" ... 0":; (' ~ , .... ~ .. ~ .L,~ ~ ~. +, ., -, " J. , .~\ G. ., ,r r , '1 ~ ~ , ,-, i ,....· r V L -- , " , '. (' ,, , , f r " J' • t .~ ~-\'- \'! , 1- "J, ........ ---. . t', l-rT"_ -, 1-' - ... ,.-, l' '. c.....'-.J. ( l._ . 'l'i " ..; -j- ."ii. .;'i .; + .... -(""'r- t - .1.' ~ ". + . ...- ," .. ) J - ; '-~ '. 1 + (' r L, ./""'oI·. ·d0(. 1 1 1 1 , '0' I'v , " { -.~ ,, ,L ~ r, " . .' , I l' r '- (-~ , - , ""'! (' r : I' L ... ~' W'~. '. ," + r" ~ ,,! . ~ ..... -, .. ;--...: ., ~ + , " GL_ II . '- "" ,~ . 1"' '" 1 ,'" - ~ ,C' -' " u J" , .,' , I ......... .L , : ~. v "11. , '.. ,. l , ..1..,.... " " I'" ..,- Atl'" .; .,," -~ , ...........-.: (' .+ . , , .~. r., r ! - ....... ~, r· A" .. I':". J(~" 1'- ",' ( iYl ~.L_ she c.':~ll (.-','~·rr , 'Y1-,",-,- I('f'" u (" r, .. a. ::',,~ , " . -.- ;. .~ ,. +",""'1, • _A.-." -,.-.:i. eel 1" . ., ")1 .... .., ,,(\.,.- 1" '~ ..1.1. '. r .,L1 ,"." \'1. , -,' +I -- ~ ~ 1' 1 <...:d. (' • , p •• -,-. 1.,1 . ,... 0:;:"" .. - _ .C ii_ oJ ~ ,c+ irrierl on Au[ust 4, 1210 John's Cllurch in Gottjneen. to f;il; i~ St. he:::.th :'ly she suffereC! froL cOLsumrtior, wLicll ;~rew worSt da~' \~r day. B:::r Lin::a Gc:uss Lad t~lrcc -'OY(~ c'ii.L:lrrr ::Oy,' Jul: 2':', F'11; diErl;.) :r C " A.' j 1(':.... l' ., 1 'i r , r: 1 ._ '" ; .L ct."'+'!r al~· +,- ; r " '. ,- , )r-..,.., ct , • r ( Y .. , > ; + - .1-.., ,,-' +' '- + .-- J. .......~ i' , -:; r- r. ,~ :-.: . .. :- l '~, ~.~ _ r.' ~ L , 'iti. " 1- I r ;" "_1- +'-- 1. " " ,> - ..L ....... ..; -: ("t , + r '.'" l " " ,, ~. ,..., 'c -~ " ; :: \ r: , ~+ ) \" X \ ,,- ~ , ,; , = 1 ; + :~().. .-, . ,_1 + ,1 ,1 i" (' . ..t o +-i .'. "-,- +.:. ... +t"' -.. :'"Y'rr:'"' -,' r..,....r " ,-, ..(- 1C :. ct 1- ~':"':: ( +,~ 1 + ,,.,. c • , f.." , ,..." r, .- ~, , ~ J.."- i (' ......:.. t' - I, C, > -1--: '+ \., , +,- .(~ ( .1 0. (' t J. \.~, , ,-', ..'- I i . ,1 I _ 1 ·r ~ n 1 ' , (" cJ, ' " + (' I + .. c~ • I ._ t . ..; . ..,.. ....... -: .t. . . . . 1\_. .: (' _.. +;'""\' -;-. ,. 1,. ./ 1 '. - r .... (".,. ...... +[' 'p !"; I. ._( I J' -"I It l 1 r:-" " ~ ( t~~c -=- (" , ' ~. 1 '.J ell, ..' 1i ' ' , .. r l '>. , .L _ . \,1 , - -1 ~. ~(' _,..,. _ ""1 r' .J'_ .. 1i ~": I t: ,..Ji C0L1r&::,c + -- ~i :~ir; .... - 1 1--,,," '.' fron: C(" tinuin[:, his [('ocetic l' 1 S il Ir + tr,l . ., q .., , ~, , , f ----'y • ., " r c. , 'l.- . J' " " r .- r .) ! " rf r, '0 '!/Ii"" - ..... r r~ .L (-.1, i. +, ( +' ; :t ... ." ( -, , r 1 ~ \. . ( """r ... c , -~ -- ., .'.,- +., .&.-1 ( (:".:.. y .... .L ' l-vl rc +' ;, J (" -I, l"':'f ,r' +r--· ....: +- ~ . -, ' --t _,"' • :' r +-1 ''vI : ,' + .. L , .. ('- r'". J, + (,.. :-i .. : f"t, .• r , , " r. -~ ~, .L-__' • , r·r t-,-\ 'C' '". " \'i r ,- '," ,, , c 1 -l,-, -t°,,1 ., 1 , • r A' - " -" " '- ~IC , ,~L 1 - + " 1.' .1. ]:' ( " ~' ., 1r- ( 1:'.4- j '~' s cJ f t {) i t:~ s tu to tLe discovery of elect::-:-o, ,B.cr.etisrr; by Oersted t m d because of the eLcouracement 01 his frier.d Alexmlder von I:u:;,bol t. cr ti <:10 --- t 1. c ar: :::,.,- \I'r: (' .~.-'- ...."'. rt 'I .~ 1 r -~ .- . +'1 ,--4- ~-, o -, -. " r,l' r- .~ o- r- t - ,. n ,- J_ ~ .... - . ., . . -r,"f- - . ~ ,., " r ," -, " ~ ,- <.j'-- (.r; r' . ' , 1,._, .,4 • ., ~ ,~ \ C' ",-r ) • ~- n,. ?' ~. t1 : - ..~". "" , r- ~. 0 .1.- '.• .., _, ,r c;,. ", _,{, ( 1 .LT _~ tc c..I The (~oublc ,;i r 10 '.·Ii: order to i eli!~ir:ate cr.~· L<.ir CLlrr2: ts, ar t: ~, r ( j +-. .1 • "7'1 J. I ( ~., ...., :.r . _f'~. \. -" 1 /',,,,(,- + l r ., , r ,. ~ -.! .. 1:'~ ,.....~-,- r.'.~ ~ .... ~ ,. - :' ... ~.~, T .- (' •. _," 1 (" t. 1 ~ .-./., "'j -, J. - , , 1-~1 ...... ,J -'r,-,' .- , ",,' 1 --,. "Y' ( . "1', " r ' .'.. - l." " (~t, -i' t-' .. -, t r" --!': ., 1 ~ _,,, 1" .l• .! t U.' - u: :" I "' : , ,. , .1.- ~ " 'r I ,. ;. :. ., , ,. J.. L vi 1 ., L" _~ J ..J ... 1 l- -. 1 -i " f • 1. J. " " ., . + " .... _0 ,- " ~ ! j 1 . . "- .~ .. ...... ,-. II c +: ..-.... ,1_ " \. I ~ r. .1 (" , ~.' r"- -. (".....:·,r -i. +~ 1 ,. -"Y' ~ ,(: \1 ,'Y _~ , , ',-' (' r '"1 ' l' 1 j ;- :2• ..:;. - .L - 1 _._,~_(_. .;.;...:.-,-.,..:"'_-.;.. . ..:'..:~ L " -. (- " r :...l.. ' ,~.J , r G.. ",1' -1- ,- , r i -+." : d .. , , .... .-i ,.,t r-, t', 1""''--' .L '.,.• l ,-,-0: 1-,---- 'i I ;:" r-l ..t,~ {' 1-;.,", l~ 1---. ~j1 d r, .1 --,1--:.'-' -,-' ( \ + ,J- .-.-..,,.. ...... ..n ..i\...l ..L .... _ . _ .. . '.' 0 .:; ': D:Lo··trjc ( , 1.1 C·' ~." ' L 1-· r J~ ?" 0, .L ?" " o. J • , .J. " + ,,0 "~ L ! , _ . , ,~ V r' cf "i " "J ' 1 ~- i c t :i j - . f~ 1 (~i v: :~ ~ L(" • t' . - r (~ , ~,. ~_, +l -,.t' •. J,. L, y-,... , .1 2.-10 "'! ·.. C -~." •• +' ~ "1 "-.- { • ..,: •.:i"; r .~ 1_ 'r· J , tr '-. ~ ~ -~-> ." -or • . " -, . . 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