{{Infobox_Scientist
| name = Andrew Wiles
| image = Wiles.jpg
| caption = Sir Andrew John Wiles
| birth_date = {{Birth date and age|1953|4|11|mf=y}}
| birth_place = [[Cambridge]], [[England]]
| residence = [[United Kingdom]]<br>[[United States]]
| nationality = [[United Kingdom|British]]
| field = [[Mathematics]]
| work_institutions = [[Princeton University]]
| alma_mater = [[University of Oxford|Oxford University]]<br>[[University of Cambridge|Cambridge University]]
| doctoral_advisor = [[John Coates]]
| doctoral_students =
[[Manjul Bhargava]]<br>[[Brian Conrad]]<br>[[Karl Rubin]]<br>[[Chris Skinner]]<br>[[Richard Taylor (mathematician)|Richard Taylor]]<br><!--[[Fred Diamond]]<br>[[Luis Navas]]<br>[[James Parson]]<br>
[[Kartik Prasanna]]<br>[[Ravi Ramakrishna]]<br>[[Arash Rastegar]]<br>[[Vinayak Vatsal]]<br>[[Ehud de Shalit]]<br>[[Mirela Ciperiani]]-->
| known_for = [[Fermat's Last Theorem|Proving Fermat's Last Theorem]]
| prizes = [[Wolf Prize]] (1995)<br>[[Royal Medal]] (1996)<br>[[Fermat Prize]] (1995)<br>[[Shaw Prize]] (2005)
| Erdős number = 3
| religion =
| footnotes =
}}
{{for|the French mathematician with work in the area of [[elliptic curve]]s|André Weil}}
'''Sir Andrew John Wiles''', [[Order of the British Empire|KBE]] (born [[April 11]] [[1953]]) is a [[Briton|British]] [[mathematician|research mathematician]] at [[Princeton University]], specialising in [[number theory]]. He is most famous for proving [[Fermat's Last Theorem]].
==Early work==
Andrew Wiles was born in Cambridge, England in 1953 and attended [[The Leys School]], Cambridge and then earned his [[bachelor's degree|BA degree]] from [[Merton College, Oxford]] in [[1974]] and [[Doctor of Philosophy|Ph.D.]] from [[Clare College, Cambridge]] in 1980. His graduate research was guided by [[John Coates]] beginning in the summer of [[1975]]. Together they worked on the arithmetic of [[elliptic curve]]s with [[complex multiplication]] by the methods of [[Iwasawa theory]]. He further worked with [[Barry Mazur]] on the main conjecture of [[Iwasawa theory]] over '''Q''', and soon afterwards generalised this result to [[totally real field]]s.
==Solution of Fermat's Last Theorem==
Andrew Wiles' most famous mathematical result is that [[Taniyama–Shimura theorem|all rational semistable elliptic curves are modular]] which, in particular, implies [[Fermat's Last Theorem]].
Wiles was introduced to Fermat's Last Theorem at the age of ten. He tried to prove the theorem using textbook methods and later studied the work of mathematicians who had tried to prove it. When he began his graduate studies he stopped trying to prove it and began studying elliptic curves under the supervision of John Coates.
In the 1950s and 1960s a connection between elliptic curves and modular forms was conjectured by the Japanese mathematician [[Goro Shimura]] based on some ideas that [[Yutaka Taniyama]] posed. In the West it became well known through a paper by [[André Weil]]. With Weil giving conceptual evidence for it, it is sometimes called the [[Shimura–Taniyama theorem|Shimura-Taniyama-Weil conjecture]]. It states that every rational elliptic curve is [[classical modular curve|modular]]. The full conjecture was proven by [[Christophe Breuil]], [[Brian Conrad]], [[Fred Diamond]], and [[Richard Taylor (mathematician)|Richard Taylor]] in 1998 using many of the methods that Andrew Wiles used in his 1995 published papers.
{| cellpadding="2" style="width: 170px; float:left; border: solid 1px #ccc; margin: 0 1em 0 1em"
| [[Fermat's Last Theorem]] states that no nontrivial integer solutions exist for the equation: x<sup>n</sup> + y<sup>n</sup> = z<sup>n</sup> if n is an integer greater than two.
|-
|____________________________________
|-
| '''The bridge between Fermat and Taniyama'''
|-
| If p is an odd prime and a, b, and c are positive integers such that a<sup>p</sup>+b<sup>p</sup>=c<sup>p</sup>, then a corresponding equation y² = x(x - a<sup>p</sup>)(x + b<sup>p</sup>) defines a hypothetical [[elliptic curve]], called the [[Frey curve]], which must exist if there is a counterexample to Fermat's Last Theorem. Following on work by [[Yves Hellegouarch]] who first considered this curve, [[Gerhard Frey|Frey]] pointed out that if such a curve existed it had peculiar properties, and suggested in particular that it might not be [[modular curve|modular]].
|-
|}
A connection between Taniyama-Shimura and Fermat was made by [[Ken Ribet]], following on work by [[Barry Mazur]] and [[Jean-Pierre Serre]], with his proof of the [[epsilon theorem|epsilon conjecture]] showing that Frey's idea that the Frey curve could not be [[classical modular curve|modular]] was correct. In particular, this showed that a proof of the [[semistable elliptic curve|semistable]] case of the Taniyama-Shimura conjecture would imply Fermat's Last Theorem. Wiles made the decision that he would work exclusively on the Taniyama-Shimura conjecture shortly after he had learned that Ribet had proven the epsilon conjecture in 1986. While many mathematicians thought the Taniyama-Shimura conjecture was inaccessible, Wiles resolved to follow that approach.
When Wiles first began studying Taniyama-Shimura, he would casually mention Fermat to people, but he found that doing so created too much interest. He wanted to be able to work on his problem in a concentrated fashion, and if people were expressing too much interest then he would not have been able to focus on his problem. Consequently he let only [[Nicholas Katz]] know what he was working on. Wiles did not do any research that was not related to Taniyama-Shimura, though of course he did continue in his teaching duties at Princeton University; continuing to attend seminars, lecture undergraduates, and give tutorials.
==Cultural references==
* Wiles's work on Fermat's Last Theorem was commemorated (in fictional form) in the musical Fermat's Last Tango, written by Joanne Sydney Lessner and Joshua Rosenblum.[http://www.princeton.edu/~paw/web_exclusives/features/features_14.html]
* Wiles and his work on Fermat's last theorem were mentioned in the ''[[Star Trek: Deep Space Nine]]'' episode "[[Facets (DS9 episode)|Facets]]". This also served as a correction for Fermat's last theorem being said to be unsolved in the earlier ''[[Star Trek: The Next Generation]]'' episode "[[The Royale]]".
* Wiles is mentioned in [[Tom Lehrer]]'s song "That's Mathematics"
* Information about Wiles' proof of Fermat's Last Theorem appears in ''[[The Parrot's Theorem]]''
* Wiles was interviewed for an episode of BBC's documentary series ''[[Horizon (BBC TV series)|Horizon]]'', which focused on Fermat's Last Theorem
* One of two multiple choice questions, on a fake television quiz show watched in episode 15 of the anime series ''[[Lucky Star (manga)|Lucky Star]]'', concerns "Princeton's Sir Wiles", and asks which theorem he proved in 1994.
[[Image:Andrew wiles1-3.jpg|thumb|right|[[Andrew Wiles]]]]
==Awards==
Wiles has been awarded several major prizes in mathematics:
* [[Schock Prize]] (1995)
* [[Cole Prize]] (1996) [http://www.ams.org/notices/199703/comm-cole.pdf]
* National Academy of Sciences Award in Mathematics from the American Mathematical Society (1996) [http://www.ams.org/notices/199607/comm-wiles.pdf]
* Ostrowski Prize (1996) [http://www.ams.org/notices/199606/people.pdf][http://www.ams.org/notices/199807/fyi.pdf]
* [[Royal Medal]] (1996)
* [[Wolf Prize in Mathematics|Wolf Prize]] (1996)
* Wolfskehl Prize (1997) [http://www.ams.org/notices/199710/barner.pdf] - see [[Paul Wolfskehl]]
* A silver plaque from the [[International Mathematical Union]] (1998) recognizing his achievements, in place of the [[Fields Medal]], which is restricted to those under 40 (Wiles was born in 1953 and proved the theorem in 1994). [http://www.ams.org/featurecolumn/archive/wiles.html]
* [[King Faisal Foundation#King Faisal International Prize|King Faisal Prize]] (1998) [http://www.ams.org/notices/199805/comm-wiles.pdf]
* [[Clay Research Award]] (1999)
* Named [[Order of the British Empire|Knight Commander of the Order of the British Empire]] (2000).
* [[Shaw Prize]] (2005) [http://www.ams.org/notices/200508/comm-shaw.pdf]
{{wikiquote|Andrew Wiles}}
==References==
* [http://www.princeton.edu/pr/home/98/0828-wiles/hmcap.html Princeton home page]
* [http://www.math.princeton.edu/CV/WilesBIB.pdf Andrew Wiles' bibliography]
* {{cite journal | author = Andrew Wiles | year = 1995 | month = May | title = Modular elliptic curves and Fermat's Last Theorem | journal = Annals of Mathematics | volume = 141 | issue = 3 | pages = 443-551 | url = http://math.stanford.edu/~lekheng/flt/wiles.pdf }}
* {{cite journal | author = [[Richard Taylor (mathematician)|Richard Taylor]] and Andrew Wiles | year = 1995 | month = May | title = Ring-theoretic properties of certain Hecke algebras | journal = Annals of Mathematics | volume = 141 | issue = 3 | pages = 553-572 | url = http://math.stanford.edu/~lekheng/flt/taylor-wiles.pdf }}
* {{cite journal | author = [[Gerd Faltings]] | year = 1995 | title = The Proof of Fermat's last theorem by R. Taylor and A. Wiles | journal = Notices of the [[American Mathematical Society|AMS]] | volume = 42 | issue = 7 | pages = 743-746 | url = http://www.ams.org/notices/199507/faltings.pdf }}
* {{cite journal | author = [[John Coates]] | year = 1996 | month = July | title = Wiles Receives NAS Award in Mathematics | journal = Notices of the AMS | volume = 43 | issue = 7 | pages = 760-763 | url = http://www.ams.org/notices/199607/comm-wiles.pdf }}
* {{cite book|last=Singh|first=Simon|authorlink=Simon Singh|year=1997|title=Fermat's Enigma|id=ISBN 0-8027-1331-9}}
* {{cite book|last=Mozzochi|first=Charles|year=2000|title=The Fermat Diary|id=ISBN 0-8218-2670-0}}
* {{cite web|year=1997|url=http://www.pbs.org/wgbh/nova/proof/|title=[[NOVA (TV series)|NOVA Online]]: The Proof|publisher=[[WGBH]]|accessdate=2006-05-03}}
* {{MacTutor Biography|id=Wiles}}
* {{cite web|url=http://math.stanford.edu/~lekheng/flt/index.html|title=Bluff your way in Fermat's Last Theorem|accessdate=2006-05-03}}
* {{cite web|url=http://www.claymath.org/publications/Fermats_Last_Tango/|title=Fermat's Last Tango|accessdate=2006-05-22}}
==External links==
* {{MathGenealogy|id=9696}}
* [http://www.math.princeton.edu/CV/WilesBIB.pdf List of Publications]
{{Schock Prize laureates}}
{{Wolf Prize in Mathematics}}
{{Shaw Prize}}
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[[Category:1953 births]]
[[Category:20th century mathematicians]]
[[Category:21st century mathematicians]]
[[Category:Alumni of Clare College, Cambridge]]
[[Category:Alumni of Merton College, Oxford]]
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[[Category:Fellows of the Royal Society]]
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[[Category:Living people]]
[[Category:MacArthur Fellows]]
[[Category:Members and associates of the United States National Academy of Sciences]]
[[Category:Number theorists]]
[[Category:Princeton University faculty]]
[[Category:Rolf Schock Prize laureates]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Knights Commander of the Order of the British Empire]]
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