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Sir Andrew John Wiles KBE FRS (born 11 April 1953[1]) is a British mathematician and a Royal Society
Royal Society
Research Professor at the University of Oxford, specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he received the 2016 Abel Prize.[2][6][7] Wiles has received numerous other honours, including the Copley Medal, the Royal Society's highest honour, in 2017.

Contents

1 Education and early life 2 Career and research

2.1 Proof of Fermat's Last Theorem 2.2 Awards and honours

3 References

Education and early life[edit] Wiles was born in 1953 in Cambridge, England, 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 attended King's College School, Cambridge, and The Leys School, Cambridge.[8]

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Wiles states that he came across Fermat's Last Theorem
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.[9] 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.[10] Career and research[edit] Wiles earned his bachelor's degree in mathematics in 1974 at Merton College, Oxford, and a PhD in 1980 as a graduate student of Clare College, Cambridge.[5] After a stay at the Institute for Advanced Study in Princeton, New Jersey
Princeton, 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
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.[11] 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
Barry Mazur
on the main conjecture of Iwasawa theory over the rational numbers, and soon afterward, he generalised this result to totally real fields.[12] Proof of Fermat's Last Theorem[edit] Main article: Wiles's proof of Fermat's Last Theorem Starting in mid-1986, based on successive progress of the previous few years of Gerhard Frey, Jean-Pierre Serre
Jean-Pierre Serre
and Ken Ribet, it became clear that Fermat's Last Theorem
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.[13] The conjecture was seen by contemporary mathematicians as important, but extraordinarily difficult or perhaps impossible to prove.[14]:203–205, 223, 226 For example, Wiles's ex-supervisor John Coates states that it seemed "impossible to actually prove",[14]:226 and Ken Ribet
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]."[14]: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.[14]: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.[14]: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.[15]

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 volume of the Annals of Mathematics.[16] Awards and honours[edit]

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

Wiles's proof of Fermat's Last Theorem
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
BBC
documentary series Horizon[17] that focused on Fermat's Last Theorem. This was renamed "The Proof", and it was made an episode of the US Public Broadcasting Service's science television series Nova.[9] 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:

Junior Whitehead Prize of the London Mathematical Society
London Mathematical Society
(1988)[1] Elected a Fellow of the Royal Society
Fellow of the Royal Society
(FRS) in 1989[18][19] Schock Prize (1995)[11] Fermat Prize (1995)[20] Wolf Prize in Mathematics (1995/6)[11] NAS Award in Mathematics from the National Academy of Sciences (1996)[21] Royal Medal
Royal Medal
(1996)[20] Ostrowski Prize (1996)[22] Cole Prize (1997)[23] Wolfskehl Prize
Wolfskehl Prize
(1997)[24] – see Paul Wolfskehl A silver plaque from the International Mathematical Union (1998) recognising his achievements, in place of the Fields Medal, which is restricted to those under 40 (Wiles was 41 when he proved the theorem in 1994)[25] King Faisal Prize (1998)[26] Clay Research Award (1999)[11] Pythagoras Award (Croton, 2004)[27] Shaw Prize
Shaw Prize
(2005)[20] The asteroid 9999 Wiles
9999 Wiles
was named after Wiles in 1999.[28] Knight Commander of the Order of the British Empire
Knight Commander of the Order of the British Empire
(2000)[29] The building at the University of Oxford
University of Oxford
housing the Mathematical Institute is named after Wiles.[30] Abel Prize
Abel Prize
(2016)[2][6][7][31][32] Copley Medal (2017)[3]

Wiles's 1987 certificate of election to the Royal Society
Royal Society
reads:

Andrew Wiles
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 generalisation 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.[19]

References[edit]

^ a b c d e Anon (2017) WILES, Sir Andrew (John). ukwhoswho.com. Who's Who (online Oxford University Press
Oxford University Press
ed.). A & C Black, an imprint of Bloomsbury Publishing plc. doi:10.1093/ww/9780199540884.013.39819.  (subscription required) ^ a b c Castelvecchi, Davide (2016). "Fermat's last theorem earns Andrew Wiles
Andrew Wiles
the Abel Prize". Nature. 531 (7594): 287–287. doi:10.1038/nature.2016.19552. PMID 26983518.  ^ a b "Mathematician Sir Andrew Wiles
Andrew Wiles
FRS wins the Royal Society's prestigious Copley Medal". The Royal Society. Retrieved 27 May 2017.  ^ a b Andrew Wiles
Andrew Wiles
at the Mathematics Genealogy Project ^ a b Wiles, Andrew John (1978). Reciprocity laws and the conjecture of birch and swinnerton-dyer. lib.cam.ac.uk (PhD thesis). University of Cambridge. OCLC 500589130. EThOS uk.bl.ethos.477263.  ^ a b "British mathematician Sir Andrew Wiles
Andrew Wiles
gets Abel math prize". The Washington Post. Associated Press. 15 March 2016. Archived from the original on 15 March 2016. CS1 maint: BOT: original-url status unknown (link) ^ a b Sheena McKenzie, CNN (16 March 2016). "300-year-old math question solved, professor wins $700k - CNN". CNN.  ^ "Cambridge-born mathematician awarded top prize for solving centuries-old numerical problem". Cambridge
Cambridge
News. Retrieved 16 March 2016. [dead link] ^ a b " Andrew Wiles
Andrew Wiles
on Solving Fermat". WGBH. Retrieved 16 March 2016.  ^ Chang, Sooyoung (2011). Academic Genealogy of Mathematicians. p. 207. ISBN 9789814282291.  ^ a b c d O'Connor, John J.; Robertson, Edmund F. (September 2009). "Wiles Biography". MacTutor History of Mathematics archive. Retrieved 16 March 2016.  ^ "Andrew Wiles". National Academy of Sciences. Retrieved 16 March 2016.  ^ Brown, Peter (28 May 2015). "How Math's Most Famous Proof Nearly Broke". Nautilus. Retrieved 16 March 2016.  ^ a b c d e Simon Singh
Simon Singh
(1997). Fermat's Last Theorem. ISBN 1-85702-521-0 ^ Kolata, Gina (24 June 1993). "At Last, Shout of 'Eureka!' In Age-Old Math Mystery". The New York Times. Retrieved 21 January 2013.  ^ "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.  ^ " BBC
BBC
TWO, Horizon Fermat's Last Theorem". BBC. 16 December 2010. Retrieved 12 June 2014.  ^ "Sir Andrew Wiles
Andrew Wiles
KBE FRS". London: Royal Society. Archived from the original on 17 November 2015.  One or more of the preceding sentences incorporates text from the royalsociety.org website where:

All text published under the heading 'Biography' on Fellow profile pages is available under Creative Commons Attribution 4.0 International License." --" Royal Society
Royal Society
Terms, conditions and policies". Archived from the original on 25 September 2015. Retrieved 9 March 2016. CS1 maint: BOT: original-url status unknown (link)

^ a b "EC/1989/39: Wiles, Sir Andrew John". The Royal Society. Retrieved 16 March 2016.  ^ a b c Wiles Receives 2005 Shaw Prize. American Mathematical Society. Retrieved 16 March 2016. ^ "NAS Award in Mathematics". National Academy of Sciences. Archived from the original on 29 December 2010. Retrieved 13 February 2011.  ^ Wiles Receives Ostrowski Prize. American Mathematical Society. Retrieved 16 March 2016. ^ "1997 Cole Prize, Notices of the AMS" (PDF). American Mathematical Society. Retrieved 13 April 2008.  ^ Paul Wolfskehl
Paul Wolfskehl
and the Wolfskehl Prize. American Mathematical Society. Retrieved 16 March 2016. ^ "Andrew J. Wiles Awarded the "IMU Silver Plaque"". American Mathematical Society. 11 April 1953. Retrieved 12 June 2014.  ^ " Andrew Wiles
Andrew Wiles
Receives Faisal Prize" (PDF). American Mathematical Society. Retrieved 12 June 2014.  ^ "Premio Pitagora" (in Italian). University of Calabria. Archived from the original on 15 January 2014. Retrieved 16 March 2016.  ^ "JPL Small-Body Database Browser". NASA. Retrieved 11 May 2009.  ^ "No. 55710". The London Gazette
The London Gazette
(Supplement). 31 December 1999. p. 34.  ^ "Mathematical Institute". University of Oxford. Retrieved 16 March 2016.  ^ "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.  ^ Iyengar, Rishi. " Andrew Wiles
Andrew Wiles
Wins 2016 Abel Prize
Abel Prize
for Fermat's Last Theorem". Time. Retrieved 19 March 2016. 

v t e

Abel Prize
Abel Prize
laureates

Jean-Pierre Serre
Jean-Pierre Serre
(2003) Michael Atiyah
Michael Atiyah
/ Isadore Singer
Isadore Singer
(2004) Peter Lax
Peter Lax
(2005) Lennart Carleson
Lennart Carleson
(2006) S. R. Srinivasa Varadhan
S. R. Srinivasa Varadhan
(2007) John G. Thompson
John G. Thompson
/ Jacques Tits
Jacques Tits
(2008) Mikhail Gromov (2009) John Tate
John Tate
(2010) John Milnor
John Milnor
(2011) Endre Szemerédi
Endre Szemerédi
(2012) Pierre Deligne
Pierre Deligne
(2013) Yakov Sinai
Yakov Sinai
(2014) John Forbes Nash Jr.
John Forbes Nash Jr.
/ Louis Nirenberg
Louis Nirenberg
(2015) Andrew Wiles
Andrew Wiles
(2016) Yves Meyer
Yves Meyer
(2017) Robert Langlands
Robert Langlands
(2018)

v t e

Rolf Schock Prize laureates

Logic and philosophy

Willard Van Orman Quine
Willard Van Orman Quine
(1993) Michael Dummett
Michael Dummett
(1995) Dana Scott
Dana Scott
(1997) John Rawls
John Rawls
(1999) Saul Kripke
Saul Kripke
(2001) Solomon Feferman (2003) Jaakko Hintikka
Jaakko Hintikka
(2005) Thomas Nagel
Thomas Nagel
(2008) Hilary Putnam
Hilary Putnam
(2011) Derek Parfit (2014) Ruth Millikan (2017)

Mathematics

Elias M. Stein
Elias M. Stein
(1993) Andrew Wiles
Andrew Wiles
(1995) Mikio Sato (1997) Yuri I. Manin
Yuri I. Manin
(1999) Elliott H. Lieb
Elliott H. Lieb
(2001) Richard P. Stanley
Richard P. Stanley
(2003) Luis Caffarelli (2005) Endre Szemerédi
Endre Szemerédi
(2008) Michael Aschbacher (2011) Yitang Zhang
Yitang Zhang
(2014) Richard Schoen
Richard Schoen
(2017)

Musical arts

Ingvar Lidholm
Ingvar Lidholm
(1993) György Ligeti
György Ligeti
(1995) Jorma Panula
Jorma Panula
(1997) Kronos Quartet
Kronos Quartet
(1999) Kaija Saariaho
Kaija Saariaho
(2001) Anne Sofie von Otter
Anne Sofie von Otter
(2003) Mauricio Kagel
Mauricio Kagel
(2005) Gidon Kremer
Gidon Kremer
(2008) Andrew Manze
Andrew Manze
(2011) Herbert Blomstedt
Herbert Blomstedt
(2014) Wayne Shorter
Wayne Shorter
(2017)

Visual arts

Rafael Moneo
Rafael Moneo
(1993) Claes Oldenburg
Claes Oldenburg
(1995) Torsten Andersson (1997) Herzog & de Meuron (1999) Giuseppe Penone
Giuseppe Penone
(2001) Susan Rothenberg (2003) SANAA
SANAA
/ Kazuyo Sejima
Kazuyo Sejima
+ Ryue Nishizawa (2005) Mona Hatoum (2008) Marlene Dumas
Marlene Dumas
(2011) Anne Lacaton / Jean-Philippe Vassal (2014) Doris Salcedo
Doris Salcedo
(2017)

v t e

Laureates of the Wolf Prize in Mathematics

1970s

Israel Gelfand
Israel Gelfand
/ Carl L. Siegel (1978) Jean Leray
Jean Leray
/ André Weil
André Weil
(1979)

1980s

Henri Cartan
Henri Cartan
/ Andrey Kolmogorov
Andrey Kolmogorov
(1980) Lars Ahlfors
Lars Ahlfors
/ Oscar Zariski
Oscar Zariski
(1981) Hassler Whitney
Hassler Whitney
/ Mark Krein
Mark Krein
(1982) Shiing-Shen Chern
Shiing-Shen Chern
/ Paul Erdős
Paul Erdős
(1983/84) Kunihiko Kodaira
Kunihiko Kodaira
/ Hans Lewy
Hans Lewy
(1984/85) Samuel Eilenberg
Samuel Eilenberg
/ Atle Selberg
Atle Selberg
(1986) Kiyosi Itô
Kiyosi Itô
/ Peter Lax
Peter Lax
(1987) Friedrich Hirzebruch
Friedrich Hirzebruch
/ Lars Hörmander
Lars Hörmander
(1988) Alberto Calderón
Alberto Calderón
/ John Milnor
John Milnor
(1989)

1990s

Ennio de Giorgi / Ilya Piatetski-Shapiro (1990) Lennart Carleson
Lennart Carleson
/ John G. Thompson
John G. Thompson
(1992) Mikhail Gromov / Jacques Tits
Jacques Tits
(1993) Jürgen Moser
Jürgen Moser
(1994/95) Robert Langlands
Robert Langlands
/ Andrew Wiles
Andrew Wiles
(1995/96) Joseph Keller / Yakov G. Sinai (1996/97) László Lovász
László Lovász
/ Elias M. Stein
Elias M. Stein
(1999)

2000s

Raoul Bott
Raoul Bott
/ Jean-Pierre Serre
Jean-Pierre Serre
(2000) Vladimir Arnold
Vladimir Arnold
/ Saharon Shelah
Saharon Shelah
(2001) Mikio Sato / John Tate
John Tate
(2002/03) Grigory Margulis
Grigory Margulis
/ Sergei Novikov (2005) Stephen Smale
Stephen Smale
/ Hillel Furstenberg (2006/07) Pierre Deligne
Pierre Deligne
/ Phillip A. Griffiths / David B. Mumford (2008)

2010s

Dennis Sullivan
Dennis Sullivan
/ Shing-Tung Yau
Shing-Tung Yau
(2010) Michael Aschbacher / Luis Caffarelli (2012) George Mostow / Michael Artin
Michael Artin
(2013) Peter Sarnak
Peter Sarnak
(2014) James G. Arthur (2015) Richard Schoen
Richard Schoen
/ Charles Fefferman
Charles Fefferman
(2017) Alexander Beilinson
Alexander Beilinson
/ Vladimir Drinfeld (2018)

Agriculture Arts Chemistry Mathematics Medicine Physics

v t e

Shaw Prize
Shaw Prize
laureates

Astronomy

Jim Peebles
Jim Peebles
(2004) Geoffrey Marcy
Geoffrey Marcy
and Michel Mayor
Michel Mayor
(2005) Saul Perlmutter, Adam Riess
Adam Riess
and Brian Schmidt
Brian Schmidt
(2006) Peter Goldreich
Peter Goldreich
(2007) Reinhard Genzel
Reinhard Genzel
(2008) Frank Shu
Frank Shu
(2009) Charles Bennett, Lyman Page
Lyman Page
and David Spergel (2010) Enrico Costa and Gerald Fishman (2011) David Jewitt and Jane Luu
Jane Luu
(2012) Steven Balbus
Steven Balbus
and John Hawley (2013) Daniel Eisenstein, Shaun Cole and John Peacock (2014) William Borucki (2015) Ronald Drever, Kip Thorne
Kip Thorne
and Rainer Weiss
Rainer Weiss
(2016) Simon White
Simon White
(2017)

Life science and medicine

Stanley Norman Cohen, Herbert Boyer, Kan Yuet-wai and Richard Doll (2004) Michael Berridge (2005) Xiaodong Wang (2006) Robert Lefkowitz
Robert Lefkowitz
(2007) Ian Wilmut, Keith Campbell and Shinya Yamanaka
Shinya Yamanaka
(2008) Douglas Coleman and Jeffrey Friedman (2009) David Julius (2010) Jules Hoffmann, Ruslan Medzhitov and Bruce Beutler
Bruce Beutler
(2011) Franz-Ulrich Hartl and Arthur Horwich (2012) Jeffrey Hall, Michael Rosbash
Michael Rosbash
and Michael Young (2013) Kazutoshi Mori and Peter Walter
Peter Walter
(2014) Bonnie Bassler and Everett Peter Greenberg (2015) Adrian Bird
Adrian Bird
and Huda Zoghbi
Huda Zoghbi
(2016) Ian R. Gibbons
Ian R. Gibbons
and Ronald Vale (2017)

Mathematical science

Shiing-Shen Chern
Shiing-Shen Chern
(2004) Andrew Wiles
Andrew Wiles
(2005) David Mumford
David Mumford
and Wu Wenjun (2006) Robert Langlands
Robert Langlands
and Richard Taylor (2007) Vladimir Arnold
Vladimir Arnold
and Ludvig Faddeev
Ludvig Faddeev
(2008) Simon Donaldson
Simon Donaldson
and Clifford Taubes
Clifford Taubes
(2009) Jean Bourgain
Jean Bourgain
(2010) Demetrios Christodoulou
Demetrios Christodoulou
and Richard S. Hamilton
Richard S. Hamilton
(2011) Maxim Kontsevich
Maxim Kontsevich
(2012) David Donoho (2013) George Lusztig (2014) Gerd Faltings
Gerd Faltings
and Henryk Iwaniec
Henryk Iwaniec
(2015) Nigel Hitchin
Nigel Hitchin
(2016) János Kollár and Claire Voisin
Claire Voisin
(2017)

v t e

Fellows of the Royal Society
Royal Society
elected in 1989

Fellows

Brian Anderson Kenneth Bagshawe John M. Ball Adrian Bird Roger Blandford Arthur Cain Mark Child Alwyn Davies Peter Goddard Michael Green Brian Heap Geoffrey Hewitt Derek Hull Julian Hunt Richard Hynes Michael James Francis Kelly John Lawton Gilbert George Lonzarich Andrew David McLachlan Michael A. Moore Kim Nasmyth Paul Nurse Robert Ladislav Parker Geoff Parker Richard Peto Warren R. Roper John Martin Rowell Ian John Russell John Philip Simons Charles Roger Slack Marshall Stoneham Roger C. Thomas Anne Treisman Kenneth Wade Patrick David Wall Rob Webster Thomas Summers West Andrew Wiles Ian Robert Young

Statute 12

Edward Shackleton, Baron Shackleton

Foreign

Nicole Marthe Le Douarin Paul Erdős Kenichi Fukui Edward B. Lewis Barbara McClintock Edward Mills Purcell

Authority control

WorldCat Identities VIAF: 85443439 LCCN: n97052585 ISNI: 0000 0001 1075 0153 GND: 12010105X SUDOC: 112043631 MGP: 9

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