Andrew Wiles

Sir Andrew John Wiles KBE FRS (born 11 April 1953)[1] is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize[6] and the 2017 Copley Medal by the Royal Society.[3] He was appointed Knight Commander of the Order of the British Empire in 2000, and in 2018, was appointed the first Regius Professor of Mathematics at Oxford.[7] Wiles is also a 1997 MacArthur Fellow.

Andrew Wiles

Andrew wiles1-3.jpg
Wiles at the 61st birthday conference for Pierre Deligne at the Institute for Advanced Study in 2005
Andrew John Wiles

(1953-04-11) 11 April 1953 (age 69)[1]
EducationKing's College School, Cambridge
The Leys School[1]
Alma mater
Known forProving the Taniyama–Shimura conjecture for semistable elliptic curves, thereby proving Fermat's Last Theorem
Proving the main conjecture of Iwasawa theory
Scientific career
ThesisReciprocity Laws and the Conjecture of Birch and Swinnerton-Dyer (1979)
Doctoral advisorJohn Coates[4][5]
Doctoral students

Education and early lifeEdit

Wiles was born on 11 April 1953[8] in Cambridge, England, the son of Maurice Frank Wiles (1923–2005) and Patricia Wiles (née Mowll). From 1952–1955, his father worked as the chaplain at Ridley Hall, Cambridge, and later became the Regius Professor of Divinity at the University of Oxford.[1]

Wiles began his formal schooling in Nigeria, while living there as a very young boy with his parents. However, according to letters written by his parents, for at least the first several months after he was supposed to be attending classes, he refused to go. From that fact, Wiles himself concluded that he wasn't in his earliest years enthusiastic about spending time in academic institutions. He trusts the letters, though he couldn't remember himself a time when he didn't enjoy solving mathematical problems.[9] This information can be found in the first three minutes of a video interview with Wiles at the YouTube channel named "The Abel Prize."

Wiles attended King's College School, Cambridge,[10] and The Leys School, Cambridge.[11] Wiles states that he came across Fermat's Last Theorem on his way home from school when he was 10 years old. He stopped at his local library where he found a book The Last Problem, by Eric Temple Bell, about the theorem.[12] Fascinated by the existence of a theorem that was so easy to state that he, a ten-year-old, could understand it, but that no one had proven, he decided to be the first person to prove it. However, he soon realised 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.[13]

Career and researchEdit

In 1974, Wiles earned his bachelor's degree in mathematics at Merton College, Oxford.[1] Wiles's graduate research was guided by John Coates, beginning in the summer of 1975. Together they 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.[14]

In 1980, Wiles earned a PhD while at Clare College, Cambridge.[5] After a stay at the Institute for Advanced Study in Princeton, New Jersey, in 1981, Wiles became a Professor of Mathematics at Princeton University.[15]

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. From 1994 to 2009, Wiles was a Eugene Higgins Professor at Princeton. He rejoined Oxford in 2011 as Royal Society Research Professor.[15]

In May 2018, Wiles was appointed Regius Professor of Mathematics at Oxford, the first in the university's history.[7]

Proof of Fermat's Last TheoremEdit

Starting in mid-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's own specialist area.[16][17]

The conjecture was seen by contemporary mathematicians as important, but extraordinarily difficult or perhaps impossible to prove.[18]: 203–205, 223, 226  For example, Wiles's ex-supervisor John Coates stated that it seemed "impossible to actually prove",[18]: 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]."[18]: 223 

Despite this, Wiles, with his from-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.[18]: 226  He dedicated all of his research time to this problem for over six 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.[18]: 229–230 

In June 1993, he presented his proof to the public for the first time at a conference in Cambridge.

He gave a lecture a day on Monday, Tuesday and Wednesday with the title "Modular Forms, Elliptic Curves and Galois Representations". There was no hint in the title that Fermat's last theorem would be discussed, Dr. Ribet said. ... Finally, at the end of his third lecture, Dr. Wiles concluded that he had proved a general case of the Taniyama conjecture. Then, seemingly as an afterthought, he noted that that meant that Fermat's last theorem was true. Q.E.D.[19]

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 May 1995 in a dedicated issue of the Annals of Mathematics.[20][21]

Awards and honoursEdit

Andrew Wiles in front of the statue of Pierre de Fermat in Beaumont-de-Lomagne in 1995, Fermat's birthplace in southern France

Wiles's proof of Fermat's Last Theorem has stood up to the scrutiny of the world's other mathematical experts. Wiles was interviewed for an episode of the BBC documentary series Horizon[22] about Fermat's Last Theorem. This was broadcast as an episode of the PBS science television series Nova with the title "The Proof".[12] His work and life are also described in great detail in Simon Singh's popular book Fermat's Last Theorem.

Wiles has been awarded a number of major prizes in mathematics and science:

Wiles's 1987 certificate of 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.[24]


  1. ^ a b c d e f Anon (2017). "Wiles, Sir Andrew (John)". Who's Who. (online Oxford University Press ed.). A & C Black, an imprint of Bloomsbury Publishing plc. doi:10.1093/ww/9780199540884.013.39819. (Subscription or UK public library membership required.) (subscription required)
  2. ^ a b Castelvecchi, Davide (2016). "Fermat's last theorem earns Andrew Wiles the Abel Prize". Nature. 531 (7594): 287. Bibcode:2016Natur.531..287C. doi:10.1038/nature.2016.19552. PMID 26983518.
  3. ^ a b c "Mathematician Sir Andrew Wiles FRS wins the Royal Society's prestigious Copley Medal". The Royal Society. Retrieved 27 May 2017.
  4. ^ a b Andrew Wiles at the Mathematics Genealogy Project  
  5. ^ a b Wiles, Andrew John (1978). Reciprocity laws and the conjecture of birch and swinnerton-dyer. (PhD thesis). University of Cambridge. OCLC 500589130. EThOS
  6. ^ "2016: Sir Andrew J. Wiles". Retrieved 22 July 2022.{{cite web}}: CS1 maint: url-status (link)
  7. ^ a b "Sir Andrew Wiles appointed first Regius Professor of Mathematics at Oxford". News & Events. University of Oxford. 31 May 2018. Retrieved 1 June 2018.
  8. ^ "Andrew Wiles". 20 January 2012.
  9. ^ {{cite Interview with Andrew Wiles| url=}
  10. ^ "Alumni". King's College School, Cambridge. Retrieved 1 February 2022.
  11. ^ "Old Leysian Prof Sir Andrew Wiles wins the Copley Medal". The Leys & St Faith's Schools Foundation. 2 November 2017. Retrieved 1 February 2022.
  12. ^ a b "Andrew Wiles on Solving Fermat". WGBH. Retrieved 16 March 2016.
  13. ^ Chang, Sooyoung (2011). Academic Genealogy of Mathematicians. p. 207. ISBN 9789814282291.
  14. ^ a b "Andrew Wiles". National Academy of Sciences. Retrieved 16 March 2016.
  15. ^ a b c d e O'Connor, John J.; Robertson, Edmund F. (September 2009). "Andrew John Wiles Biography". MacTutor History of Mathematics archive. Retrieved 1 February 2022.
  16. ^ Brown, Peter (28 May 2015). "How Math's Most Famous Proof Nearly Broke". Nautilus. Retrieved 16 March 2016.
  17. ^ Broad, William J. (31 January 2022). "Profiles in Science - The Texas Oil Heir Who Took On Math's Impossible Dare - James M. Vaughn Jr., wielding a fortune, argues that he brought about the Fermat breakthrough after the best and brightest had failed for centuries to solve the puzzle". The New York Times. Retrieved 2 February 2022.
  18. ^ a b c d e Simon Singh (1997). Fermat's Last Theorem. ISBN 1-85702-521-0
  19. ^ Kolata, Gina (24 June 1993). "At Last, Shout of 'Eureka!' In Age-Old Math Mystery". The New York Times. Retrieved 21 January 2013.
  20. ^ Wiles, Andrew (May 1995). "Issue 3". Annals of Mathematics. 141: 1–551. JSTOR i310703.
  21. ^ "Are mathematicians finally satisfied with Andrew Wiles's proof of Fermat's Last Theorem? Why has this theorem been so difficult to prove?". Scientific American. 21 October 1999. Retrieved 16 March 2016.
  22. ^ "BBC TWO, Horizon Fermat's Last Theorem". BBC. 16 December 2010. Retrieved 12 June 2014.
  23. ^ "Sir Andrew Wiles KBE FRS". London: Royal Society. Archived from the original on 17 November 2015. Retrieved 1 February 2022. One or more of the preceding sentences incorporates text from the website where: All text published under the heading 'Biography' on Fellow profile pages is available under Creative Commons Attribution 4.0 International License.
  24. ^ a b "EC/1989/39: Wiles, Sir Andrew John". The Royal Society. Retrieved 16 March 2016.
  25. ^ "Andrew J. Wiles". American Academy of Arts & Sciences. Retrieved 10 December 2021.
  26. ^ a b c Wiles Receives 2005 Shaw Prize. American Mathematical Society. Retrieved 16 March 2016.
  27. ^ "NAS Award in Mathematics". National Academy of Sciences. Archived from the original on 29 December 2010. Retrieved 13 February 2011.
  28. ^ Wiles Receives Ostrowski Prize. American Mathematical Society. Retrieved 16 March 2016.
  29. ^ "1997 Cole Prize, Notices of the AMS" (PDF). American Mathematical Society. Archived (PDF) from the original on 9 October 2022. Retrieved 13 April 2008.
  30. ^ Paul Wolfskehl and the Wolfskehl Prize. American Mathematical Society. Retrieved 16 March 2016.
  31. ^ "APS Member History". Retrieved 10 December 2021.
  32. ^ "Andrew J. Wiles Awarded the "IMU Silver Plaque"". American Mathematical Society. 11 April 1953. Retrieved 12 June 2014.
  33. ^ "Andrew Wiles Receives Faisal Prize" (PDF). American Mathematical Society. Archived (PDF) from the original on 9 October 2022. Retrieved 12 June 2014.
  34. ^ "Premio Pitagora" (in Italian). University of Calabria. Archived from the original on 15 January 2014. Retrieved 16 March 2016.
  35. ^ "JPL Small-Body Database Browser". NASA. Retrieved 11 May 2009.
  36. ^ "No. 55710". The London Gazette (Supplement). 31 December 1999. p. 34.
  37. ^ "Mathematical Institute". University of Oxford. Archived from the original on 13 January 2016. Retrieved 16 March 2016.
  38. ^ "British mathematician Sir Andrew Wiles gets Abel math prize". The Washington Post. Associated Press. 15 March 2016. Archived from the original on 15 March 2016.
  39. ^ Sheena McKenzie, CNN (16 March 2016). "300-year-old math question solved, professor wins $700k – CNN". CNN. {{cite news}}: |author= has generic name (help)
  40. ^ "A British mathematician just won a $700,000 prize for solving this fascinating centuries-old math problem 22 years ago". Business Insider. Retrieved 19 March 2016.
  41. ^ Iyengar, Rishi. "Andrew Wiles Wins 2016 Abel Prize for Fermat's Last Theorem". Time. Retrieved 19 March 2016.

External linksEdit