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Andrew Wiles

January 01, 1970

Sir Andrew John Wiles KBE FRS (born 11 April 1953) is an English mathematician and a 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 was awarded the 2016 Abel Prize and the 2017 Copley Medal and for which he was appointed a Knight Commander of the Order of the British Empire in 2000.[1] In 2018, Wiles was appointed the first Regius Professor of Mathematics at Oxford.[4] Wiles is also a 1997 MacArthur Fellow.

Sir Andrew Wiles
KBE FRS
Wiles in 2005
Born
Andrew John Wiles

(1953-04-11) 11 April 1953 (age 71)
Cambridge, England
NationalityBritish
EducationKing's College School, Cambridge
The Leys School
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
Awards
Scientific career
FieldsMathematics
Institutions
ThesisReciprocity Laws and the Conjecture of Birch and Swinnerton-Dyer (1979)
Doctoral advisorJohn Coates[2][3]
Doctoral students

Wiles was born in Cambridge to theologian Maurice Frank Wiles and his wife Patricia. While spending much of his childhood in Nigeria, Wiles developed an interest in mathematics and in Fermat's Last Theorem in particular. After moving to Oxford and graduating from there in 1974, he worked on unifying Galois representations, elliptic curves and modular forms, starting with Barry Mazur’s generalizations of Iwasawa theory. In the early 1980s, Wiles moved to Princeton University from Cambridge and worked on expanding out and applying Hilbert modular forms. In 1986, upon reading Ken Ribet’s seminal work on Fermat’s Last Theorem, Wiles set out to prove the modularity theorem for semistable elliptic curves, which implied Fermat’s Last Theorem. By 1993, he had been able to prove Fermat’s Last Theorem, though a flaw was discovered. After an insight on 19 September 1994, Wiles and his student Richard Taylor were able to circumvent the flaw, and published the results in 1995, to widespread acclaim.

In proving Fermat’s Last Theorem, Wiles developed new tools for mathematicians to begin unifying disparate ideas and theorems. His former student Taylor along with three other mathematicians were able to prove the full modularity theorem by 2000, using Wiles’ work. Upon receiving the Abel Prize in 2016, Wiles reflected on his legacy, expressing his belief that he did not just prove Fermat's Last Theorem, but pushed the whole of mathematics as a field towards the Langlands program of unifying number theory.[5]

Education and early life edit

Wiles was born on 11 April 1953 in Cambridge, England, the son of Maurice Frank Wiles (1923–2005) and Patricia Wiles (née Mowll). From 1952 to 1955, his father worked as the chaplain at Ridley Hall, Cambridge, and later became the Regius Professor of Divinity at the University of Oxford.[6]

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 in his earliest years, he was not enthusiastic about spending time in academic institutions. He trusts the letters, though he could not remember a time when he did not enjoy solving mathematical problems.[7]

Wiles attended King's College School, Cambridge,[8] and The Leys School, Cambridge.[9] 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.[10] 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.[11]

Career and research edit

In 1974, Wiles earned his bachelor's degree in mathematics at Merton College, Oxford.[6] 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 generalised this result to totally real fields.[12][13]

In 1980, Wiles earned a PhD while at Clare College, Cambridge.[3] After a stay at the Institute for Advanced Study in Princeton, New Jersey, in 1981, Wiles became a Professor of Mathematics at Princeton University.[14]

In 1985–86, Wiles was a Guggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the École Normale Supérieure.

In 1987, Wiles was elected to the Royal Society. At that point according to his election certificate, he had been working "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".[12]

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.[14]

In May 2018, Wiles was appointed Regius Professor of Mathematics at Oxford, the first in the university's history.[4]

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 and Ken Ribet, it became clear that Fermat's Last Theorem (the statement that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2) 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, and stated that all such curves have a modular form associated with them.[15][16] These curves can be thought of as mathematical objects resembling solutions for a torus’ surface, and if Fermat's Last Theorem were false and solutions existed, “a peculiar curve would result”. A proof of the theorem therefore would involve showing that such a curve would not exist.[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 

Wiles’ research involved creating a proof by contradiction of Fermat's Last Theorem, which Ribet in his 1986 work had found to have an elliptic curve and thus an associated modular form if true. Starting by assuming that the theorem was incorrect, Wiles then contradicted the Taniyama–Shimura–Weil conjecture as formulated under that assumption, with Ribet's theorem (which stated that if n were a prime number, no such elliptic curve could have a modular form, so no odd prime counterexample to Fermat's equation could exist), and Wiles also proved that the conjecture applied to the special case known as the semistable elliptic curves to which Fermat's equation was tied; in other words, Wiles had found that the Taniyama–Shimura–Weil conjecture was true in the case of Fermat's equation, and Ribet's finding, that the conjecture holding for semistable elliptic curves could mean Fermat's Last Theorem is true, prevailed, thus proving Fermat's Last Theorem.[19][20][21]

In June 1993, he presented his proof to the public for the first time at a conference in Cambridge. Gina Kolata of The New York Times summed up the presentation as follows:

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.[17]

In August 1993, it was discovered that the proof contained a flaw in several areas, related to properties of the Selmer group and use of a tool called an Euler system.[22] 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. According to Eric W. Weisstein, the circumvention involved "replacing elliptic curves with Galois representations, reducing the problem to a class number formula, solving that problem, and tying up loose ends", all using Iwasawa theory to fix "results from Matthias Flach based on ideas from Victor Kolyvagin", and letting Iwasawa's and Flach's approaches strengthen each other.[21][22][23] Together with his former student Richard Taylor, he published a second paper which contained the circumvention and thus completed the proof. Both papers were published in May 1995 in a dedicated issue of the Annals of Mathematics.[24][25]

Legacy edit

Wiles’ work has been used in many fields of mathematics. Notably, in 1999, his former student Richard Taylor and three other mathematicians built upon Wiles’ proof to prove the full modularity theorem.[26]

In 2016, upon receiving the Abel Prize, Wiles said about his proof of Fermat's Last Theorem, “The methods that solved it opened up a new way of attacking one of the big webs of conjectures of contemporary mathematics called the Langlands Program, which as a grand vision tries to unify different branches of mathematics. It’s given us a new way to look at that.”[5]

Awards and honours edit

 
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[27] about Fermat's Last Theorem. This was broadcast as an episode of the PBS science television series Nova with the title "The Proof".[10] 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:

References edit

  1. ^ a b c "Mathematician Sir Andrew Wiles FRS wins the Royal Society's prestigious Copley Medal". The Royal Society. Retrieved 27 May 2017.
  2. ^ a b Andrew Wiles at the Mathematics Genealogy Project  
  3. ^ 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.
  4. ^ 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.
  5. ^ a b Sample, Ian (15 March 2016). "Abel prize won by Oxford professor for Fermat's Last Theorem proof". the Guardian. Retrieved 20 November 2023.
  6. ^ a b c Anon (2017). "Wiles, Sir Andrew (John )". Who's Who (online Oxford University Press ed.). Oxford: A & C Black. doi:10.1093/ww/9780199540884.013.39819. (Subscription or UK public library membership required.)
  7. ^ "Interview with Andrew Wiles". YouTube. The Abel Prize. 10 March 2023. Retrieved 15 November 2023.
  8. ^ "Alumni". King's College School, Cambridge. Retrieved 1 February 2022.
  9. ^ "Old Leysian Prof Sir Andrew Wiles wins the Copley Medal". The Leys & St Faith's Schools Foundation. 2 November 2017. Retrieved 1 February 2022.
  10. ^ a b "Andrew Wiles on Solving Fermat". WGBH. November 2000. Retrieved 16 March 2016.
  11. ^ Chang, Sooyoung (2011). Academic Genealogy of Mathematicians. World Scientific. p. 207. ISBN 9789814282291.
  12. ^ a b c . The Royal Society. Archived from the original on 13 July 2015. Retrieved 16 March 2016.
  13. ^ a b "Andrew Wiles". National Academy of Sciences. Retrieved 16 March 2016.
  14. ^ 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.
  15. ^ Brown, Peter (28 May 2015). . Nautilus. Archived from the original on 15 March 2016. Retrieved 16 March 2016.
  16. ^ 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.
  17. ^ a b Kolata, Gina (24 June 1993). . The New York Times. Archived from the original on 20 November 2023. Retrieved 21 January 2013.
  18. ^ a b c d e Simon Singh (1997). Fermat's Last Theorem. ISBN 1-85702-521-0
  19. ^ Stevens, Glenn (n.d.), An Overview of the Proof of Fermat's Last Theorem (PDF), Boston University
  20. ^ Boston, Nick (Spring 2003), Proof of Fermat's Last Theorem (PDF), University of Wisconsin–Madison
  21. ^ a b "Fermat's Last Theorem / Useful Notes". TV Tropes. 2023. Retrieved 20 November 2023.
  22. ^ a b Weisstein, Eric W. (14 May 2004). "Fermat's Last Theorem -- from Wolfram MathWorld". Wolfram Research, Inc. Retrieved 20 November 2023.
  23. ^ Weisstein, Eric W. (26 September 2009). "Taniyama-Shimura Conjecture -- from Wolfram MathWorld". Wolfram Research, Inc. Retrieved 20 November 2023.
  24. ^ Wiles, Andrew (May 1995). "Issue 3". Annals of Mathematics. 141: 1–551. JSTOR i310703.
  25. ^ "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.
  26. ^ Devlin, Keith (21 July 1999). "Beyond Fermat's last theorem". the Guardian. Retrieved 20 November 2023.
  27. ^ "BBC TWO, Horizon Fermat's Last Theorem". BBC. 16 December 2010. Retrieved 12 June 2014.
  28. ^ . 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 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.
  29. ^ "Andrew J. Wiles". American Academy of Arts & Sciences. Retrieved 10 December 2021.
  30. ^ a b c Wiles Receives 2005 Shaw Prize. American Mathematical Society. Retrieved 16 March 2016.
  31. ^ . National Academy of Sciences. Archived from the original on 29 December 2010. Retrieved 13 February 2011.
  32. ^ Wiles Receives Ostrowski Prize. American Mathematical Society. Retrieved 16 March 2016.
  33. ^ "1997 Cole Prize, Notices of the AMS" (PDF). American Mathematical Society. Archived (PDF) from the original on 9 October 2022. Retrieved 13 April 2008.
  34. ^ Paul Wolfskehl and the Wolfskehl Prize. American Mathematical Society. Retrieved 16 March 2016.
  35. ^ "APS Member History". search.amphilsoc.org. Retrieved 10 December 2021.
  36. ^ "Andrew J. Wiles Awarded the "IMU Silver Plaque"". American Mathematical Society. 11 April 1953. Retrieved 12 June 2014.
  37. ^ "Andrew Wiles Receives Faisal Prize" (PDF). American Mathematical Society. Archived (PDF) from the original on 9 October 2022. Retrieved 12 June 2014.
  38. ^ (in Italian). University of Calabria. Archived from the original on 15 January 2014. Retrieved 16 March 2016.
  39. ^ "JPL Small-Body Database Browser". NASA. Retrieved 11 May 2009.
  40. ^ "No. 55710". The London Gazette (Supplement). 31 December 1999. p. 34.
  41. ^ . University of Oxford. Archived from the original on 13 January 2016. Retrieved 16 March 2016.
  42. ^ 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.
  43. ^ . The Washington Post. Associated Press. 15 March 2016. Archived from the original on 15 March 2016.
  44. ^ McKenzie, Sheena (16 March 2016). "300-year-old math question solved, professor wins $700k – CNN". CNN.
  45. ^ "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.
  46. ^ Iyengar, Rishi. "Andrew Wiles Wins 2016 Abel Prize for Fermat's Last Theorem". Time. Retrieved 19 March 2016.

External links edit

  • Profile from Oxford
  • Profile from Princeton 5 November 2021 at the Wayback Machine

January 01, 1970
andrew, wiles, andrew, john, wiles, born, april, 1953, english, mathematician, royal, society, research, professor, university, oxford, specialising, number, theory, best, known, proving, fermat, last, theorem, which, awarded, 2016, abel, prize, 2017, copley, . Sir Andrew John Wiles KBE FRS born 11 April 1953 is an English mathematician and a 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 was awarded the 2016 Abel Prize and the 2017 Copley Medal and for which he was appointed a Knight Commander of the Order of the British Empire in 2000 1 In 2018 Wiles was appointed the first Regius Professor of Mathematics at Oxford 4 Wiles is also a 1997 MacArthur Fellow Sir Andrew WilesKBE FRSWiles in 2005BornAndrew John Wiles 1953 04 11 11 April 1953 age 71 Cambridge EnglandNationalityBritishEducationKing s College School CambridgeThe Leys SchoolAlma materUniversity of Oxford MA University of Cambridge PhD Known forProving the Taniyama Shimura conjecture for semistable elliptic curves thereby proving Fermat s Last TheoremProving the main conjecture of Iwasawa theoryAwardsWhitehead Prize 1988 Rolf Schock Prize 1995 Ostrowski Prize 1995 Fermat Prize 1995 Wolf Prize 1995 6 Royal Medal 1996 NAS Award in Mathematics 1996 Foreign Associate of the National Academy of Sciences 1996 Cole Prize 1997 MacArthur Fellowship 1997 Wolfskehl Prize 1997 IMU Silver Plaque 1998 King Faisal International Prize in Science 1998 Shaw Prize 2005 Abel Prize 2016 Copley Medal 2017 1 De Morgan Medal 2019 Scientific careerFieldsMathematicsInstitutionsUniversity of Oxford Princeton UniversityThesisReciprocity Laws and the Conjecture of Birch and Swinnerton Dyer 1979 Doctoral advisorJohn Coates 2 3 Doctoral studentsManjul Bhargava Brian Conrad Ehud de Shalit Fred Diamond Ritabrata Munshi Karl Rubin Christopher Skinner Richard Taylor 2 Vinayak Vatsal Wiles was born in Cambridge to theologian Maurice Frank Wiles and his wife Patricia While spending much of his childhood in Nigeria Wiles developed an interest in mathematics and in Fermat s Last Theorem in particular After moving to Oxford and graduating from there in 1974 he worked on unifying Galois representations elliptic curves and modular forms starting with Barry Mazur s generalizations of Iwasawa theory In the early 1980s Wiles moved to Princeton University from Cambridge and worked on expanding out and applying Hilbert modular forms In 1986 upon reading Ken Ribet s seminal work on Fermat s Last Theorem Wiles set out to prove the modularity theorem for semistable elliptic curves which implied Fermat s Last Theorem By 1993 he had been able to prove Fermat s Last Theorem though a flaw was discovered After an insight on 19 September 1994 Wiles and his student Richard Taylor were able to circumvent the flaw and published the results in 1995 to widespread acclaim In proving Fermat s Last Theorem Wiles developed new tools for mathematicians to begin unifying disparate ideas and theorems His former student Taylor along with three other mathematicians were able to prove the full modularity theorem by 2000 using Wiles work Upon receiving the Abel Prize in 2016 Wiles reflected on his legacy expressing his belief that he did not just prove Fermat s Last Theorem but pushed the whole of mathematics as a field towards the Langlands program of unifying number theory 5 Contents 1 Education and early life 2 Career and research 2 1 Proof of Fermat s Last Theorem 2 2 Legacy 3 Awards and honours 4 References 5 External linksEducation and early life editWiles was born on 11 April 1953 in Cambridge England the son of Maurice Frank Wiles 1923 2005 and Patricia Wiles nee Mowll From 1952 to 1955 his father worked as the chaplain at Ridley Hall Cambridge and later became the Regius Professor of Divinity at the University of Oxford 6 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 in his earliest years he was not enthusiastic about spending time in academic institutions He trusts the letters though he could not remember a time when he did not enjoy solving mathematical problems 7 Wiles attended King s College School Cambridge 8 and The Leys School Cambridge 9 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 10 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 11 Career and research editIn 1974 Wiles earned his bachelor s degree in mathematics at Merton College Oxford 6 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 generalised this result to totally real fields 12 13 In 1980 Wiles earned a PhD while at Clare College Cambridge 3 After a stay at the Institute for Advanced Study in Princeton New Jersey in 1981 Wiles became a Professor of Mathematics at Princeton University 14 In 1985 86 Wiles was a Guggenheim Fellow at the Institut des Hautes Etudes Scientifiques near Paris and at the Ecole Normale Superieure In 1987 Wiles was elected to the Royal Society At that point according to his election certificate he had been working 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 12 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 14 In May 2018 Wiles was appointed Regius Professor of Mathematics at Oxford the first in the university s history 4 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 and Ken Ribet it became clear that Fermat s Last Theorem the statement that no three positive integers a b and c satisfy the equation an bn cn for any integer value of n greater than 2 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 and stated that all such curves have a modular form associated with them 15 16 These curves can be thought of as mathematical objects resembling solutions for a torus surface and if Fermat s Last Theorem were false and solutions existed a peculiar curve would result A proof of the theorem therefore would involve showing that such a curve would not exist 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 Wiles research involved creating a proof by contradiction of Fermat s Last Theorem which Ribet in his 1986 work had found to have an elliptic curve and thus an associated modular form if true Starting by assuming that the theorem was incorrect Wiles then contradicted the Taniyama Shimura Weil conjecture as formulated under that assumption with Ribet s theorem which stated that if n were a prime number no such elliptic curve could have a modular form so no odd prime counterexample to Fermat s equation could exist and Wiles also proved that the conjecture applied to the special case known as the semistable elliptic curves to which Fermat s equation was tied in other words Wiles had found that the Taniyama Shimura Weil conjecture was true in the case of Fermat s equation and Ribet s finding that the conjecture holding for semistable elliptic curves could mean Fermat s Last Theorem is true prevailed thus proving Fermat s Last Theorem 19 20 21 In June 1993 he presented his proof to the public for the first time at a conference in Cambridge Gina Kolata of The New York Times summed up the presentation as follows 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 17 In August 1993 it was discovered that the proof contained a flaw in several areas related to properties of the Selmer group and use of a tool called an Euler system 22 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 According to Eric W Weisstein the circumvention involved replacing elliptic curves with Galois representations reducing the problem to a class number formula solving that problem and tying up loose ends all using Iwasawa theory to fix results from Matthias Flach based on ideas from Victor Kolyvagin and letting Iwasawa s and Flach s approaches strengthen each other 21 22 23 Together with his former student Richard Taylor he published a second paper which contained the circumvention and thus completed the proof Both papers were published in May 1995 in a dedicated issue of the Annals of Mathematics 24 25 Legacy edit Wiles work has been used in many fields of mathematics Notably in 1999 his former student Richard Taylor and three other mathematicians built upon Wiles proof to prove the full modularity theorem 26 In 2016 upon receiving the Abel Prize Wiles said about his proof of Fermat s Last Theorem The methods that solved it opened up a new way of attacking one of the big webs of conjectures of contemporary mathematics called the Langlands Program which as a grand vision tries to unify different branches of mathematics It s given us a new way to look at that 5 Awards and honours edit nbsp 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 27 about Fermat s Last Theorem This was broadcast as an episode of the PBS science television series Nova with the title The Proof 10 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 1988 6 Elected a Fellow of the Royal Society FRS in 1989 28 12 Elected member of the American Academy of Arts and Sciences 1994 29 Schock Prize 1995 14 Fermat Prize 1995 30 Wolf Prize in Mathematics 1995 6 14 Elected a Foreign Associate of the National Academy of Sciences 1996 13 NAS Award in Mathematics from the National Academy of Sciences 1996 31 Royal Medal 1996 30 Ostrowski Prize 1996 32 Cole Prize 1997 33 MacArthur Fellowship 1997 Wolfskehl Prize 1997 34 see Paul Wolfskehl Elected member of the American Philosophical Society 1997 35 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 36 King Faisal Prize 1998 37 Clay Research Award 1999 14 Premio Pitagora Croton 2004 38 Shaw Prize 2005 30 The asteroid 9999 Wiles was named after Wiles in 1999 39 Knight Commander of the Order of the British Empire 2000 40 The building at the University of Oxford housing the Mathematical Institute is named after Wiles 41 Abel Prize 2016 42 43 44 45 46 Copley Medal 2017 1 References edit a b c Mathematician Sir Andrew Wiles FRS wins the Royal Society s prestigious Copley Medal The Royal Society Retrieved 27 May 2017 a b Andrew Wiles at the Mathematics Genealogy Project nbsp 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 Sir Andrew Wiles appointed first Regius Professor of Mathematics at Oxford News amp Events University of Oxford 31 May 2018 Retrieved 1 June 2018 a b Sample Ian 15 March 2016 Abel prize won by Oxford professor for Fermat s Last Theorem proof the Guardian Retrieved 20 November 2023 a b c Anon 2017 Wiles Sir Andrew John Who s Who online Oxford University Press ed Oxford A amp C Black doi 10 1093 ww 9780199540884 013 39819 Subscription or UK public library membership required Interview with Andrew Wiles YouTube The Abel Prize 10 March 2023 Retrieved 15 November 2023 Alumni King s College School Cambridge Retrieved 1 February 2022 Old Leysian Prof Sir Andrew Wiles wins the Copley Medal The Leys amp St Faith s Schools Foundation 2 November 2017 Retrieved 1 February 2022 a b Andrew Wiles on Solving Fermat WGBH November 2000 Retrieved 16 March 2016 Chang Sooyoung 2011 Academic Genealogy of Mathematicians World Scientific p 207 ISBN 9789814282291 a b c EC 1989 39 Wiles Sir Andrew John The Royal Society Archived from the original on 13 July 2015 Retrieved 16 March 2016 a b Andrew Wiles National Academy of Sciences Retrieved 16 March 2016 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 Brown Peter 28 May 2015 How Math s Most Famous Proof Nearly Broke Nautilus Archived from the original on 15 March 2016 Retrieved 16 March 2016 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 a b Kolata Gina 24 June 1993 At Last Shout of Eureka In Age Old Math Mystery The New York Times Archived from the original on 20 November 2023 Retrieved 21 January 2013 a b c d e Simon Singh 1997 Fermat s Last Theorem ISBN 1 85702 521 0 Stevens Glenn n d An Overview of the Proof of Fermat s Last Theorem PDF Boston University Boston Nick Spring 2003 Proof of Fermat s Last Theorem PDF University of Wisconsin Madison a b Fermat s Last Theorem Useful Notes TV Tropes 2023 Retrieved 20 November 2023 a b Weisstein Eric W 14 May 2004 Fermat s Last Theorem from Wolfram MathWorld Wolfram Research Inc Retrieved 20 November 2023 Weisstein Eric W 26 September 2009 Taniyama Shimura Conjecture from Wolfram MathWorld Wolfram Research Inc Retrieved 20 November 2023 Wiles Andrew May 1995 Issue 3 Annals of Mathematics 141 1 551 JSTOR i310703 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 Devlin Keith 21 July 1999 Beyond Fermat s last theorem the Guardian Retrieved 20 November 2023 BBC TWO Horizon Fermat s Last Theorem BBC 16 December 2010 Retrieved 12 June 2014 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 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 Andrew J Wiles American Academy of Arts amp Sciences Retrieved 10 December 2021 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 Archived PDF from the original on 9 October 2022 Retrieved 13 April 2008 Paul Wolfskehl and the Wolfskehl Prize American Mathematical Society Retrieved 16 March 2016 APS Member History search amphilsoc org Retrieved 10 December 2021 Andrew J Wiles Awarded the IMU Silver Plaque American Mathematical Society 11 April 1953 Retrieved 12 June 2014 Andrew Wiles Receives Faisal Prize PDF American Mathematical Society Archived PDF from the original on 9 October 2022 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 Supplement 31 December 1999 p 34 Mathematical Institute University of Oxford Archived from the original on 13 January 2016 Retrieved 16 March 2016 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 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 McKenzie Sheena 16 March 2016 300 year old math question solved professor wins 700k CNN CNN 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 Wins 2016 Abel Prize for Fermat s Last Theorem Time Retrieved 19 March 2016 External links editAndrew Wiles at Wikipedia s sister projects nbsp Media from Commons nbsp Quotations from Wikiquote nbsp Data from Wikidata Profile from Oxford Profile from Princeton Archived 5 November 2021 at the Wayback Machine Retrieved from https en wikipedia org w index php title Andrew Wiles amp oldid 1223256470, wikipedia, wiki, book, books, library,

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