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For the French mathematician known for work in the area of elliptic curves, see André Weil. In Mathematics, an elliptic curve is a smooth, projective Algebraic curve of genus one on which there is a specified point O André Weil should not be confused with two other mathematicians with similar names Hermann Weyl (1885-1955 who made substantial contributions
Andrew Wiles
Sir Andrew John Wiles
Sir Andrew John Wiles
Born April 11, 1953 (1953-04-11) (age 55)
Cambridge, England
Residence United Kingdom
United States
Nationality British
Fields Mathematics
Institutions Princeton University
Alma mater Oxford University
Cambridge University
Doctoral advisor John Coates
Doctoral students Manjul Bhargava
Brian Conrad
Karl Rubin
Chris Skinner
Richard Taylor
Known for Proving Fermat's Last Theorem
Notable awards Wolf Prize (1995)
Royal Medal (1996)
Fermat Prize (1995)
Shaw Prize (2005)

Sir Andrew John Wiles KBE FRS (born April 11, 1953)[1] is a British mathematician and a professor at Princeton University, specialising in number theory. Events 491 - Flavius Anastasius becomes Byzantine Emperor, with the name of Anastasius I. Year 1953 ( MCMLIII) was a Common year starting on Thursday (link will display full calendar of the Gregorian calendar. The city of Cambridge (ˈkeɪmbrɪdʒ is a university town and the administrative centre of the county of Cambridgeshire, England England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located The United States of America —commonly referred to as the The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Princeton University is a private Coeducational research university located in Princeton, New Jersey. Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval The University of Oxford (informally "Oxford University" or simply "Oxford" located in the city of Oxford, Oxfordshire, England is the The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the A doctorate is an Academic degree that indicates the highest level of academic achievement John Coates may refer to John Coates (tenor (1865&ndash1941 English tenor John Coates (mathematician (born 1945 Australian mathematician Manjul Bhargava ( मञ्जुल भार्गव) (born in 1974 in Hamilton, Ontario, Canada) is a professor of Mathematics Brian Conrad (b November 20, 1970, New York City) is an American Mathematician and number theorist, working at Richard Taylor (born Richard Lawrence Taylor 19 May 1962) is a British Mathematician working in the field of Number theory Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like The Royal Medals of the Royal Society of London, also as The Queen's Medals were established by King George IV. The Fermat prize of mathematical Research rewards research works in fields where the contributions of Pierre de Fermat have been decisive The Shaw Prize, established by Sir Run Run Shaw (邵逸夫 b 1907 a leader in the media industry in Hong Kong and a long-time Philanthropist Knight is the English term for a social position originating in the Middle Ages. The Most Excellent Order of the British Empire is a British Order of chivalry established on 4 June 1917 by King George V. The Royal Society of London for the Improvement of Natural Knowledge, known simply as The Royal Society, is a Learned society for science that was founded in 1660 Events 491 - Flavius Anastasius becomes Byzantine Emperor, with the name of Anastasius I. Year 1953 ( MCMLIII) was a Common year starting on Thursday (link will display full calendar of the Gregorian calendar. The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located A mathematician is a person whose primary area of study and research is the field of Mathematics. Princeton University is a private Coeducational research university located in Princeton, New Jersey. Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes He is most famous for proving Fermat's Last Theorem. Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like

Contents

Early work

Andrew Wiles was born in Cambridge, England in 1953 and attended King's College School, Cambridge (where his maths teacher, David Higginbottom first introduced Fermat's Last Theorem to him) and The Leys School, Cambridge; and earned his BA degree in 1974 after study at Merton College, Oxford, and a Ph.D. in 1980 after research at Clare College, Cambridge. The city of Cambridge (ˈkeɪmbrɪdʒ is a university town and the administrative centre of the county of Cambridgeshire, England Year 1953 ( MCMLIII) was a Common year starting on Thursday (link will display full calendar of the Gregorian calendar. The Leys School is a co-educational British public school (privately funded and independent)—it is a boarding and day school for over 520 pupils A bachelor's degree is usually an Undergraduate Academic degree awarded for a course or major that generally lasts for three four or in some cases and Year 1974 ( MCMLXXIV) was a Common year starting on Tuesday (link will display full calendar of the 1974 Gregorian calendar. See also Wardens of Merton College Oxford. Merton College is also the name of a college in the London Borough of Merton. "PhD" redirects here for other uses see PhD (disambiguation. Year 1980 ( MCMLXXX) was a Leap year starting on Tuesday (link displays the 1980 Gregorian calendar) Clare College is a college of the University of Cambridge, the second oldest surviving college after Peterhouse. His graduate research was guided by John Coates beginning in the summer of 1975. John Henry Coates, FRS (born 26 January 1945) is a Mathematician who holds (since 1986 the position of Sadleirian Professor of Pure Mathematics Year 1975 ( MCMLXXV) was a Common year starting on Wednesday (link will display full calendar of the Gregorian calendar. Together they worked on the arithmetic of elliptic curves with complex multiplication by the methods of Iwasawa theory. In Mathematics, an elliptic curve is a smooth, projective Algebraic curve of genus one on which there is a specified point O In Mathematics, complex multiplication is the theory of Elliptic curves E that have an Endomorphism ring larger than the Integers and In Number theory, Iwasawa theory is a Galois module theory of Ideal class groups initiated by Kenkichi Iwasawa, in the 1950s as part of the He further worked with Barry Mazur on the main conjecture of Iwasawa theory over Q, and soon afterwards generalized this result to totally real fields. Barry Charles Mazur (born December 19, 1937) is a professor of mathematics at Harvard University. In Number theory, Iwasawa theory is a Galois module theory of Ideal class groups initiated by Kenkichi Iwasawa, in the 1950s as part of the In Number theory, a Number field K is called totally real if for each Embedding of K into the Complex numbers Taking approximately seven years to complete the work, Wiles was the first person to prove Fermat's Last Theorem, earning him a place in history. Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like

Solution of Fermat's Last Theorem

Andrew Wiles' most famous mathematical result is that all rational semistable elliptic curves are modular which, in particular, implies Fermat's Last Theorem. In Mathematics, the modularity theorem establishes an important connection between Elliptic curves over the field of Rational numbers and Modular forms Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like

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. Goro Shimura ( Japanese: 志村 五郎 Shimura Gorō; born 1930 in Hamamatsu Japan) is a Japanese Mathematician, and currently Yutaka Taniyama ( Japanese: 谷山 豊 Taniyama Yutaka; November 12, 1927 &ndash November 17, 1958) was a Japanese In the West it became well known through a paper by André Weil. André Weil should not be confused with two other mathematicians with similar names Hermann Weyl (1885-1955 who made substantial contributions With Weil giving conceptual evidence for it, it is sometimes called the Shimura-Taniyama-Weil conjecture. In Mathematics, the modularity theorem establishes an important connection between Elliptic curves over the field of Rational numbers and Modular forms It states that every rational elliptic curve is modular. In Number theory, the classical modular curve is an irreducible plane algebraic curve given by an equation Φn(x y=0 where The full conjecture was proven by Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor in 1998 using many of the methods that Andrew Wiles used in his 1995 published papers. Brian Conrad (b November 20, 1970, New York City) is an American Mathematician and number theorist, working at List of Publications On congruence modules associated to Λ-adic forms Compositio Mathematica 71 (1989 49–83 Richard Taylor (born Richard Lawrence Taylor 19 May 1962) is a British Mathematician working in the field of Number theory

Fermat's Last Theorem states that no nontrivial integer solutions exist for the equation: xn + yn = zn if n is an integer greater than two. Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like
____________________________________
The bridge between Fermat and Taniyama
If p is an odd prime and a, b, and c are positive integers such that ap+bp=cp, then a corresponding equation y² = x(x - ap)(x + bp) defines a hypothetical elliptic curve, called the Frey curve, which must exist if there is a counterexample to Fermat's Last Theorem. In Mathematics, an elliptic curve is a smooth, projective Algebraic curve of genus one on which there is a specified point O The epsilon conjecture is a statement in Number theory concerning properties of Galois representations associated with Modular forms It was proposed by Following on work by Yves Hellegouarch who first considered this curve, Frey pointed out that if such a curve existed it had peculiar properties, and suggested in particular that it might not be modular. Gerhard Frey (born 1944 is a German Mathematician, known for his work in Number theory. In Number theory and Algebraic geometry, a modular curve is a Riemann surface, or the corresponding Algebraic curve, constructed as a quotient

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 conjecture showing that Frey's idea that the Frey curve could not be modular was correct. Kenneth Alan "Ken" Ribet is an American Mathematician, currently a professor of mathematics at the University of California Berkeley. Barry Charles Mazur (born December 19, 1937) is a professor of mathematics at Harvard University. The epsilon conjecture is a statement in Number theory concerning properties of Galois representations associated with Modular forms It was proposed by In Number theory, the classical modular curve is an irreducible plane algebraic curve given by an equation Φn(x y=0 where In particular, this showed that a proof of the 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. Nicholas Michael Katz (born December 7, 1943) is an American Mathematician, working in the fields of Algebraic geometry, particularly 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

Awards

Wiles has been awarded several major prizes in mathematics and science

Other Biographical details

Wiles' father is Rev. The Shaw Prize, established by Sir Run Run Shaw (邵逸夫 b 1907 a leader in the media industry in Hong Kong and a long-time Philanthropist Prof. Maurice Frank Wiles (1923-2005), Regius Professor of Divinity at the University of Oxford[3] and his mother Patricia Wiles (née Mowll). Maurice Frank Wiles ( October 17, 1923 - June 3, 2005) was a Regius Professor of Divinity at Oxford University for 21 years His father worked as Chaplain at Ridley Hall Cambridge for the period 1952-55. Wiles is married to Nada Canaan Wiles[4], who has a PhD in microbiology from Princeton, and they have two daughters[1] Since 1994 he has been Eugene Higgins Professor at Princeton. Microbiology (from Greek grc μῑκρος mīkros, "small" grc βίος bios, " Life " and grc -λογία He is a Foreign member of the US National Academy of Sciences since 1996 (as he remains a British citizen)[1].

He is currently Chair of the Mathematics Department at Princeton[5].

References

Notes

  1. ^ a b c d e "WILES, Sir Andrew (John)", Who's Who, A & C Black, January 2007
  2. ^ 1997 Cole Prize, Notices of the AMS. Who's Who (2007 edition ISBN 978-0-7136-7527-6 is an annual British publication of biographies which vary in length (typically a single paragraph or Retrieved on 2008-04-13. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 1111 - Henry V is crowned Holy Roman Emperor. 1204 - The Fourth Crusade sacks Constantinople
  3. ^ WILES, Rev. Prof. Maurice Frank, Who Was Who, A & C Black, January 2007
  4. ^ The Sound of Math, Princeton Alumni Weekly. Retrieved on 2008-04-13. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 1111 - Henry V is crowned Holy Roman Emperor. 1204 - The Fourth Crusade sacks Constantinople
  5. ^ MathemaicsDepartment, Princeton University. Retrieved on 2008-04-19. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 1012 - Martyrdom of Alphege in Greenwich London. 1529 - At the Second Diet of Speyer

External links

Persondata
NAME Wiles, Andrew
ALTERNATIVE NAMES
SHORT DESCRIPTION Mathematician
DATE OF BIRTH April 11, 1953 (1953-04-11) (age 55)
PLACE OF BIRTH Cambridge, England
DATE OF DEATH
PLACE OF DEATH
The MacTutor History of Mathematics archive is an award-winning website maintained by John J A mathematician is a person whose primary area of study and research is the field of Mathematics. Events 491 - Flavius Anastasius becomes Byzantine Emperor, with the name of Anastasius I. Year 1953 ( MCMLIII) was a Common year starting on Thursday (link will display full calendar of the Gregorian calendar. The city of Cambridge (ˈkeɪmbrɪdʒ is a university town and the administrative centre of the county of Cambridgeshire, England England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland
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