Wiles, Andrew John

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Andrew John Wiles

In 1995,Andrew John Wiles(April 11, 1953 - ) succeeded in proving the 350 year-old Fermats !ast

"heorem (F!"), and suddenly the unassuming #nglish mathematician

$ecame a cele$rity% A&ter Fermats death, the &ollo'ing marginal note 'as

&ound in his copy o& achets edition o& the complete 'ors o&

*iophantus+ "o divide a cu$e into t'o cu$es, a &ourth po'er, or in

general any po'er 'hatever a$ove the second, into t'o po'ers o& the

same denomination, is impossi$le, and I have assuredly &ound an

admira$le proo& o& this, $ut the margin is too narro' to contain it% .ith

these 'ords Fermat set the mathematical 'orld on a long uncharted voyage to discover a proo& o& his

claim% In modern notation, F!" asserts that there do not e/ist positive integersx,y,zand nsuch that

xn yn zn 'hen n2 %

For centuries mathematicians 'ere una$le either to prove or disprove Fermats statement% 4any

talented mathematicians struggled 'ith the pro$lem% In the 1thcentury, !eonhard #uler revie'ed

Fermats 'or on num$er theory and proved most o& the latters assertions% #uler noted that Fermat had

provided a proo& o& his theorem in the case 'hen n 6, and #uler sho'ed ho' to prove the assertion

&or n 3%7ome thought they had solved the general case $ut 'ere mistaen, 'hile mathematicians lie

8auss and il$ert claimed they had $etter things to do 'ith their time than 'aste it on such a triviality,

liely to result in &ailure any'ay% 4any mathematicians o'ed their reputation, at least in part, to the

advances they made 'hile 'oring on the pro$lem%

.iles, $orn at :am$ridge, $ecame a'are o& F!" 'hen at ten years o& age he &ound a discussion o& it

and its history in a li$rary $oo% e decided then and there that one day he 'ould solve the pro$lem%

.iles earned a %A% at 4erton :ollege, ;/&ord in 19


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in 190% is thesis, supervised $y =ohn :oates, 'as not concerned 'ith F!", $ut 'as a 'or on the

theory o& elliptic curves, 'hich 'ould later prove to have a connection 'ith his avo'ed goal% .hile

completing his doctorate, .iles 'as a =unior >esearch &ello' at :lare :ollege and also a en?amin

@eirce Assistant @ro&essor at arvard% In 191, he moved to the Institute &or Advanced 7tudy and the

ne/t year 'as appointed a pro&essor at @rinceton niversity% In 1996, he $ecame #ugene iggins

@ro&essor o& 4athematics at @rinceton%

"he &inal chapter in the long history o& F!" $egan in 1955 'hen -year-old Butaa "aniyama posed a

pro$lem at an international con&erence on alge$raic num$er theory held in "oyo% "hree years later

"aniyama committed suicide and his 'or 'as taen up $y his close &riend 8oro 7himura% "he result,

no'n as the "aniyama-7himura con?ecture, esta$lishes an important connection $et'een elliptic

curves, studied in alge$raic geometry, and modular &orms, 'hich are certain &unctions investigated in

num$er theory% #lliptic curves are not ellipses $ut *iophantine eCuations o& the &orm

y Ax3Bx Cx D

7uch eCuations 'ere &ound among Fermats 'or% "he "aniyama-7himura con?ecture e&&ectively

claims that every rational elliptic curve is a modular &orm in disguise%

In 196, 8erhard Frey o& 8ermany suggested that i& the "aniyama-7himura con?ecture 'ere true, then

so 'ould F!"% "he ne/t year Denneth >i$et o& the niversity o& :ali&ornia at ereley proved the

connection% .hen .iles proved a special case o& the "aniyama-7himura con?ecture, it 'as strong

enough to remove Fermats !ast "heorem &rom the rans o& unsolved mathematical pro$lems%

In 1993, .iles gave a series o& lectures, 'hose su$?ect 'as not announced, at the Isaac Ee'ton

Institute at :am$ridge% In his &inal lecture, $e&ore an over&lo'ing cro'd o& spectators 'ho could tell

'here .iles 'as going, he announced his proo&% At the end o& his tal, .iles 'rote on the $oard+ I


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thin Ill stop here% "his 'as the culmination o& seven years 'or &or .iles, in 'hich he concentrated

solely on &inding a proo&% ut the announcement 'as premature and 'as not &ollo'ed $y a pu$lication

o& the details o& his proo&% .hen his results 'ere 'ritten up &or pu$lication, a su$tle error 'as

discovered% .hile this 'as a terri$le $lo', he 'ent $ac to his research 'ith his &ormer student >ichard

"aylor &or another 1 months, $e&ore 'ell, let .iles spea &or himsel&+

G suddenly, totally une/pectedly, I had this incredi$le revelation% It 'as the most

important in my 'oring li&e% Eothing I ever do again G it 'as so

indescri$a$ly $eauti&ul, it 'as so simple and so elegant, and I ?ust stared in dis$elie&

&or t'enty minutes, then during the day I 'aled round the department% Id eep

coming $ac to my des to see i& it 'as still there - it 'as still there%

"his time the proo& stood, $ut it too the mathematical 'orld t'o additional years to veri&y it, a&ter his

original manuscript,Modular elliptic curves and Fermats Last Theorem, and the .iles-"aylor

correction 'as pu$lished in theAnnals of Mathematics in 4ay 1995% In 1999 :hristophe reuil, rian

:onrad, Fred *iamond and "aylor gave a proo& o& the &ull "aniyama-7himura con?ecture%

.ith .iles triumph came many honors% e 'as a'arded the 7choc @riHe in 4athematics &rom the

>oyal 7'edish Academy o& 7ciences and the @ri/ Fermat &rom the niversit @aul 7a$atier% In 199J,

he received the .ol& @riHe and 'as elected as a &oreign mem$er to the Eational Academy o& 7ciences

o& the nited 7tates, receiving its mathematics priHe% ;n =une


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and hold it he did, at various times &rom 1960 to 19J1%

Quotation of the Day:@ure mathematicians ?ust love a challenge% "hey love unsolved pro$lems%

.hen doing maths theres this great &eeling% Bou start 'ith a pro$lem that ?ust mysti&ies you% Bou cant

understand it, its so complicated, you ?ust cant mae head nor tail o& it% ut then 'hen you &inally

resolve it, you have this incredi$le &eeling o& ho' $eauti&ul it is, no' it all &its together so elegantly%

4ost deceptive are the pro$lems 'hich loo easy, and yet they turn out to $e incredi$ly intricate%

Fermat is the most $eauti&ul e/ample o& this% It ?ust looed as though it had to have a solution and, o&

course, its very special $ecause Fermat said that he had a solution% Andre' .iles

Documents

Wiles, Andrew John