Andrew Wiles

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Sir Andrew Wiles
Andrew wiles1-3.jpg
Wiles at the 61st Birthday conference for P. Deligne (Institute for Advanced Study, 2005).
Born Andrew John Wiles
(1953-04-11) 11 April 1953 (age 61)[1]
Cambridge, England
Nationality British
Fields Mathematics
Institutions
Alma mater
Thesis Reciprocity Laws and the Conjecture of Birch and Swinnerton-Dyer (1979)
Doctoral advisor John Coates[2]
Doctoral students
Known for Proving the Taniyama–Shimura Conjecture for semistable elliptic curves, thereby proving Fermat's Last Theorem
Proving the main conjecture of Iwasawa theory
Notable awards Whitehead Prize (1988)
Ostrowski Prize (1995)
Fermat Prize (1995)
Wolf Prize (1995/6)
Royal Medal (1996)
Cole Prize (1997)
IMU Silver Plaque (1998)
King Faisal International Prize in Science (1998)
Shaw Prize (2005)

Sir Andrew John Wiles, KBE, FRS (born 11 April 1953)[1] is a British mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is most notable for proving Fermat's Last Theorem.[3][4][5][6][7][8][9][10]

Early life and education[edit]

Wiles is the son of Maurice Frank Wiles (1923–2005), the Regius Professor of Divinity at the University of Oxford[1] and Patricia Wiles (née Mowll). His father worked as the Chaplain at Ridley Hall, Cambridge, for the years 1952–55. Wiles was born in Cambridge, England, in 1953, and he attended King's College School, Cambridge, and The Leys School, Cambridge.

Wiles states that he came across Fermat's Last Theorem on his way home from school when he was 10 years old. He stopped by his local library where he found a book about the theorem.[11] Fascinated by the existence of a theorem that was so easy to state that he, a ten-year old, could understand it, but nobody had proven it, he decided to be the first person to prove it. However, he soon realized that his knowledge was too limited, so he abandoned his childhood dream, until it was brought back to his attention at the age of 33 by Ken Ribet's 1986 proof of the epsilon conjecture, which Gerhard Frey had previously linked to Fermat's famous equation.

Mathematical career[edit]

Wiles earned his bachelor's degree in mathematics in 1974 after his study at Merton College, Oxford, and a Ph.D. in 1980, after his research at Clare College, Cambridge. After a stay at the Institute for Advanced Study in New Jersey in 1981, Wiles became a professor at Princeton University. In 1985–86, Wiles was a Guggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the École Normale Supérieure. From 1988 to 1990, Wiles was a Royal Society Research Professor at the University of Oxford, and then he returned to Princeton. He rejoined Oxford in 2011 as Royal Society Research Professor.

Wiles's graduate research was guided by John Coates beginning in the summer of 1975. Together these colleagues worked on the arithmetic of elliptic curves with complex multiplication by the methods of Iwasawa theory. He further worked with Barry Mazur on the main conjecture of Iwasawa theory over the rational numbers, and soon afterward, he generalized this result to totally real fields.

The proof of Fermat's Last Theorem[edit]

Starting in the summer of 1986, based on successive progress of the previous few years of Gerhard Frey, Jean-Pierre Serre and Ken Ribet, it became clear that Fermat's Last Theorem could be proven as a corollary of a limited form of the modularity theorem (unproven at the time and then known as the "Taniyama–Shimura-Weil conjecture"). The modularity theorem involved elliptic curves, which was also Wiles' own specialist area.

The conjecture was seen by contemporary mathematicians as important, but extraordinarily difficult or perhaps inaccessible to proof.[12]:203–205, 223, 226 For example, Wiles' ex-supervisor John Coates states that it seemed "impossible to actually prove",[12]:226 and Ken Ribet considered himself "one of the vast majority of people who believed [it] was completely inaccessible", adding that "Andrew Wiles was probably one of the few people on earth who had the audacity to dream that you can actually go and prove [it]." [12]:223

Despite this, Wiles, who had had a childhood fascination with Fermat's Last Theorem, decided to undertake the challenge of proving the conjecture at least to the extent needed for Frey's curve.[12]:226 He dedicated all of his research time to this problem for over 6 years in near-total secrecy, covering up his efforts by releasing prior work in small segments as separate papers and confiding only in his wife.[12]:229–230 In 1993, he presented his proof to the public for the first time at a conference in Cambridge.[13] In August 1993 it was discovered that the proof contained a flaw in one area. Wiles tried and failed for over a year to repair his proof. According to Wiles, the crucial idea for circumventing, rather than closing this area, came to him on 19 September 1994 when he was on the verge of giving up. Together with his former student Richard Taylor, he published a second paper which circumvented the problem and thus completed the proof. Both papers were published in 1995 in a special volume of the Annals of Mathematics.

Recognition by the media[edit]

His proof of Fermat's Last Theorem has stood up to the scrutiny of the world's mathematical experts. Wiles was interviewed for an episode of the BBC documentary series Horizon[7] that focused on Fermat's Last Theorem. This was renamed "The Proof", and it was made an episode of the Public Broadcasting Service's science television series Nova.[14] He has been a foreign member of the U.S. National Academy of Sciences since 1996.

Awards and honours[edit]

Andrew Wiles before the statue of Pierre de Fermat in Beaumont-de-Lomagne (October 1995)

Wiles has been awarded several major prizes in mathematics and science:

Wiles nomination for election to the Royal Society reads:

Andrew Wiles is almost unique amongst number-theorists in his ability to bring to bear new tools and new ideas on some of the most intractable problems of number theory. His finest achievement to date has been his proof, in joint work with Mazur, of the "main conjecture" of Iwasawa theory for cyclotomic extensions of the rational field. This work settles many of the basic problems on cyclotomic fields which go back to Kummer, and is unquestionably one of the major advances in number theory in our times. Earlier he did deep work on the conjecture of Birch and Swinnerton-Dyer for elliptic curves with complex multiplication - one offshoot of this was his proof of an unexpected and beautiful generalization of the classical explicit reciprocity laws of Artin-Hasse-Iwasawa. Most recently, he has made new progress on the construction of l-adic representations attached to Hilbert modular forms, and has applied these to prove the "main conjecture" for cyclotomic extensions of totally real fields - again a remarkable result since none of the classical tools of cyclotomic fields applied to these problems.[15]

In popular culture[edit]

References[edit]

  1. ^ a b c d e "WILES, Sir Andrew (John)". Who's Who 2014, A & C Black, an imprint of Bloomsbury Publishing plc, 2014; online edn, Oxford University Press. (subscription required)
  2. ^ a b Andrew Wiles at the Mathematics Genealogy Project
  3. ^ O'Connor, John J.; Robertson, Edmund F., "Andrew Wiles", MacTutor History of Mathematics archive, University of St Andrews .
  4. ^ "Wiles's bibliography" (PDF). Retrieved 2014-06-12. 
  5. ^ Andrew Wiles from the Scopus bibliographic database.
  6. ^ Mazur, B.; Wiles, A. (1984). "Class fields of abelian extensions of Q". Inventiones Mathematicae 76 (2): 179. doi:10.1007/BF01388599. 
  7. ^ a b "BBC TWO, Horizon Fermat's Last Theorem". Bbc.co.uk. 2010-12-16. Retrieved 2014-06-12. 
  8. ^ Wiles, A. (1988). "On ordinary ?-adic representations associated to modular forms". Inventiones Mathematicae 94 (3): 529. doi:10.1007/BF01394275. 
  9. ^ Coates, J.; Wiles, A. (1977). "On the conjecture of Birch and Swinnerton-Dyer". Inventiones Mathematicae 39 (3): 223. doi:10.1007/BF01402975. 
  10. ^ List of publications from Microsoft Academic Search
  11. ^ "NOVA | Andrew Wiles on Solving Fermat". Pbs.org. Retrieved 2014-06-12. 
  12. ^ a b c d e Fermat's Last Theorem, Simon Singh, 1997, ISBN 1-85702-521-0
  13. ^ Kolata, Gina (24 June 1993). "At Last, Shout of 'Eureka!' In Age-Old Math Mystery". The New York Times. Retrieved 21 January 2013. 
  14. ^ "NOVA Online: The Proof". WGBH. 1997. Archived from the original on 1 May 2006. Retrieved 2006-05-03. 
  15. ^ a b "EC/1989/39: Wiles, Sir Andrew John". London: The Royal Society. Archived from the original on 2014-05-26. 
  16. ^ "NAS Award in Mathematics". National Academy of Sciences. Archived from the original on 29 December 2010. Retrieved 13 February 2011. 
  17. ^ Wiles Receives NAS Award in Mathematics July 1996
  18. ^ Wiles Receives Ostrowski Prize June 1996
  19. ^ Correction 1998
  20. ^ "1997 Cole Prize, Notices of the AMS" (PDF). Archived from the original on 8 April 2008. Retrieved 2008-04-13. 
  21. ^ Paul Wolfskehl and the Wolfskehl Prize October 1997
  22. ^ "Andrew J. Wiles Awarded the "IMU Silver Plaque"". Ams.org. 1953-04-11. Retrieved 2014-06-12. 
  23. ^ Andrew Wiles receives special tribute August 28, 1998
  24. ^ "Andrew Wiles Receives Faisal Prize" (PDF). Retrieved 2014-06-12. 
  25. ^ "Premio Pitagora". Lami.unical.it. Retrieved 2014-06-12. 
  26. ^ Wiles Receives 2005 Shaw Prize September 2005
  27. ^ "JPL Small-Body Database Browser". Retrieved 2009-05-11. 
  28. ^ The London Gazette: (Supplement) no. 55710. p. 34. 31 December 1999.
  29. ^ [1][dead link]

External links[edit]