Sir Andrew John Wiles (born April 11, 1953) is a British-American research mathematician at Princeton University, specialising in number theory. He attended The Leys School, Cambridge and then earned his BA degree from Merton College, Oxford in 1974 and Ph.D. from Clare College, Cambridge in 1980. His 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 Q, and soon afterwards generalised this result to totally real fields. His most famous mathematical result is that all rational semistable elliptic curves are modular which, in particular, implies Fermat's Last Theorem. Image File history File links No higher resolution available. ... April 11 is the 101st day of the year in the Gregorian calendar (102nd in leap years). ... 1953 (MCMLIII) was a common year starting on Thursday. ... Geography Status City (1951) Region East of England Admin. ... Motto (French) God and my right Anthem God Save the King (Queen) England() – on the European continent() – in the United Kingdom() Capital (and largest city) London (de facto) Official languages English (de facto) Unified  -  by Athelstan 967 AD  Area  -  Total 130,395 km²  50,346 sq mi  Population  -  2006 estimate... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Princeton University is a private coeducational research university located in Princeton, New Jersey, in the United States of America. ... The University of Oxford (usually abbreviated as Oxon. ... The University of Cambridge (often Cambridge University), located in Cambridge, England, is the second-oldest university in the English-speaking world and has a reputation as one of the worlds most prestigious universities. ... Professor John Henry Coates, FRS (born January 26, 1945) is a mathematician who holds (since 1986) the position of Sadleirian Professor (of pure mathematics) at the University of Cambridge in the United Kingdom. ... Manjul Bhargava is a Clay Research Fellow (July 1, 2000 to June 30, 2005), and a Visiting Fellow at Princeton University. ... Brian Conrad (b. ... Karl Rubin is currently (2006) the Thorp Professor of Mathematics at the University of California, Irvine. ... Richard Taylor (born 19 May 1962) is a British mathematician working in the field of number theory. ... Pierre de Fermats informal conjecture written in the margin of his book proved to be one of the most intriguing and enigmatic math problems ever devised. ... The Wolf Prize has been awarded annually since 1978 to living scientists and artists for achievements in the interest of mankind and friendly relations among peoples . ... The Royal Medals of the Royal Society of London were established by King George IV. They were further supported with certain changes to their conditions, by King William IV and Queen Victoria. ... The Fermat prize of mathematical research rewards research works in fields where the contributions of Pierre de Fermat have been decisive: Statements of Variational Principles Foundations of Probability and Analytical Geometry Number theory. ... In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ... André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century. ... April 11 is the 101st day of the year in the Gregorian calendar (102nd in leap years). ... 1953 (MCMLIII) was a common year starting on Thursday. ... Leonhard Euler, one of the greatest mathematicians of all time 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, in the United States of America. ... 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 of problems that arise from their study. ... The Leys School Stamp Building (formerly East House) (right) and Headmasters house(left) with the school chapel behind 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 aged between 11 and 18 years. ... A bachelors degree (Artium Baccalaureus, A.B. or B.A.) is usually an undergraduate academic degree awarded for a course or major that generally lasts for three, four, or in some cases and countries, five or six years. ... College name The House of Scholars of Merton Named after Walter de Merton Established 1264 Sister College Peterhouse Warden Prof. ... 1974 (MCMLXXIV) was a common year starting on Tuesday. ... Doctor of Philosophy, abbreviated Ph. ... Full name Clare College Motto - Named after Elizabeth de Clare Previous names University Hall (1326), Clare Hall (1338), Clare College (1856) Established 1326 Sister College(s) Oriel College St Hughs College Master Prof. ... Professor John Henry Coates, FRS (born January 26, 1945) is a mathematician who holds (since 1986) the position of Sadleirian Professor (of pure mathematics) at the University of Cambridge in the United Kingdom. ... 1975 (MCMLXXV) was a common year starting on Wednesday. ... In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ... In mathematics, complex multiplication is the theory of elliptic curves E that have an endomorphism ring larger than the integers; and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense (it roughly means that the action on the tangent space at... 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 theory of cyclotomic fields. ... Barry 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 theory of cyclotomic fields. ... In number theory , a number field K is called totally real if for each embedding of K into the complex numbers the image lies inside the real numbers. ... The Taniyama–Shimura theorem (also called the Modularity Theorem) establishes an important connection between elliptic curves, which are objects from algebraic geometry, and modular forms, which are certain periodic holomorphic functions investigated in number theory. ... Pierre de Fermats informal conjecture written in the margin of his book proved to be one of the most intriguing and enigmatic math problems ever devised. ...

Solution of Fermat's Last Theorem

Andrew 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. In the West it became well known through a paper by André Weil. With Weil giving conceptual evidence for it, it is sometimes called the Shimura-Taniyama-Weil conjecture. It states that every rational elliptic curve is modular. 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. Goro Shimura (志村 五郎, 1930 -) is a Japanese-American mathematician, and currently a professor of mathematics at Princeton University. ... A sketch of Yutaka Taniyama Yutaka Taniyama (Japanese: è°·å±± 豊 Taniyama Yutaka[1]; November 12, 1927 – November 17, 1958) was a Japanese mathematician, best known for conjecturing, in modern language, automorphic properties of L-functions of elliptic curves over any number field. ... André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century. ... The Taniyama–Shimura theorem (also called the modularity theorem) establishes an important connection between arithmetic of elliptic curves over rational numbers and modular forms, analytic objects of the 19th century mathematics, which are certain periodic holomorphic functions investigated in number theory. ... In number theory, the classical modular curve is an irreducible plane algebraic curve given by an equation Φn(x, y)=0, where for the j-invariant j(Ï„), x=j(n Ï„), y=j(Ï„) is a point on the curve. ... Brian Conrad (b. ... Fred Diamond (born November 19, 1964) is an American mathematician. ... Richard Taylor (born 19 May 1962) is a British mathematician working in the field of number theory. ...

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. 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. Pierre de Fermats informal conjecture written in the margin of his book proved to be one of the most intriguing and enigmatic math problems ever devised. ... In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ... In number theory, Serres epsilon conjecture stated a property of Galois representations associated with modular forms which was proven by Ken Ribet in the summer of 1986, in a significant step towards the proof of Fermats Last Theorem. ... Gerhard Frey is a German mathematician, known for his work in number theory. ... In mathematics, a modular curve is a Riemann surface, or corresponding algebraic curve, constructed as HΓ where H is the upper half-plane in the complex numbers, and Γ is a Fuchsian group acting on H, with Γ a subgroup of the modular group of integral 2×2 matrices. ... Kenneth Alan Ken Ribet is an American mathematician, currently a professor of mathematics at the University of California, Berkeley. ... Barry Mazur (born December 19, 1937) is a professor of mathematics at Harvard University. ... Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. ... In number theory, Serres epsilon conjecture stated a property of Galois representations associated with modular forms which was proven by Ken Ribet in the summer of 1986, in in a significant step towards the proof of Fermats Last Theorem. ... In number theory, the classical modular curve is an irreducible plane algebraic curve given by an equation Φn(x, y)=0, where for the j-invariant j(Ï„), x=j(n Ï„), y=j(Ï„) is a point on the curve. ... In mathematics, a semistable elliptic curve in diophantine geometry is an elliptic curve that has bad reduction only of multiplicative type. ...

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. 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. Nick Katz (Nicholas M. Katz) is an American mathematician, working in the fields of algebraic geometry, particularly on p-adic methods, monodromy and moduli problems, and number theory. ...

Cultural references

Wiles's work on Fermat's Last Theorem was commemorated (in fictional form) in the musical Fermat's Last Tango, written by Joanne Sydney Lessner and Joshua Rosenblum.[1]

Wiles and his work on Fermat's last theorem were mentioned in the Star Trek: Deep Space Nine episode "Facets". This also served as a correction for Fermat's last theorem being said to be unsolved in the earlier Star Trek: The Next Generation episode "The Royale". Space station Star Trek: Deep Space Nine (ST:DS9 or STDS9 or DS9 for short) is a science fiction television series produced by Paramount and set in the Star Trek universe. ... Facets is the penultimate episode in the third season of Star Trek: Deep Space Nine. ... The title as it appeared in most episodes opening credits. ... The Royale is the name of an episode from the second season of Star Trek: The Next Generation. ...

Wiles is mentioned in Tom Lehrer's song "That's Mathematics" Tom Lehrer in 1960. ...

Trivia

• Wiles has an Erdős number of 3
• He is married to Nada Canaan and has three children Clare, Kate and Olivia
• He enjoys playing golf at Princeton University's course Springdale
• Fellow, Royal Society (1989)

The Erdős number, honouring the late Hungarian mathematician Paul Erdős, one of the most prolific writers of mathematical papers, is a way of describing the collaborative distance, in regard to mathematical papers, between an author and Erdős. ... The premises of The Royal Society in London (first four properties only). ...

Awards

Wiles has been awarded several major prizes in mathematics:

• Schock Prize (1995)
• Cole Prize (1996) [2]
• National Academy of Sciences Award in Mathematics from the American Mathematical Society (1996) [3]
• Ostrowski Prize (1996) [4][5]
• Royal Medal (1996)
• Wolf Prize (1996)
• Wolfskehl Prize (1997) [6] - see Paul Wolfskehl
• A silver plaque from the International Mathematical Union (1998) recognizing his achievements, in place of the Fields Medal, which is restricted to those under 40 (Wiles was born in 1953 and proved the theorem in 1994). [7]
• King Faisal Prize (1998) [8]
• Clay Research Award (1999)
• Named Knight Commander of the Order of the British Empire (2000).
• Shaw Prize (2005) [9]

The Schock Prizes were instituted by the will of philosopher and artist Rolf Schock (1933-1986). ... The Cole Prize is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. ... The Royal Medals of the Royal Society of London were established by King George IV. They were further supported with certain changes to their conditions, by King William IV and Queen Victoria. ... Past winners of the Wolf Prize in Mathematics: 1978 Israel M. Gelfand, Carl L. Siegel 1979 Jean Leray, André Weil 1980 Henri Cartan, Andrei Kolmogorov 1981 Lars Ahlfors, Oscar Zariski 1982 Hassler Whitney, Mark Grigoryevich Krein 1983/4 Shiing S. Chern, Paul ErdÅ‘s 1984/5 Kunihiko Kodaira, Hans... Paul Friedrich Wolfskehl (1856-1906) was a mathematician born in Darmstadt. ... The International Mathematical Union is an international non-governmental organization devoted to international cooperation in the field of mathematics. ... The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years. ... This article or section does not adequately cite its references or sources. ... The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. ... The Most Excellent Order of the British Empire is a British order of chivalry established on 4 June 1917 by King George V. The Order includes five classes in civil and military divisions; in decreasing order of seniority, these are Knight Grand Cross or Dame Grand Cross (GBE) Knight Commander... The Shaw Prize is established by Sir Run Run Shaw (邵逸夫 1907–), a leader in the media industry in Hong Kong and a long-time philanthropist, to, in the official words, honor individuals, regardless of race, nationality and religious belief, who have achieved significant breakthrough in academic...

Quotations

Wikiquote has a collection of quotations related to:

Andrew Wiles

• "I think I'll stop here." -- immediately after presenting the proof of Fermat's Last Theorem, Cambridge, 23 June 1993

Image File history File links This is a lossless scalable vector image. ... Wikiquote is a sister project of Wikipedia, using the same MediaWiki software. ... June 23 is the 174th day of the year (175th in leap years) in the Gregorian calendar, with 191 days remaining. ... 1993 (MCMXCIII) was a common year starting on Friday of the Gregorian calendar and marked the Beginning of the International Decade to Combat Racism and Racial Discrimination (1993-2003). ...

References

• Princeton home page
• Andrew Wiles' bibliography
• Andrew Wiles (May 1995). "Modular elliptic curves and Fermat's Last Theorem". Annals of Mathematics 141 (3): 443-551. 
• Richard Taylor and Andrew Wiles (May 1995). "Ring-theoretic properties of certain Hecke algebras". Annals of Mathematics 141 (3): 553-572. 
• Gerd Faltings (1995). "The Proof of Fermat's last theorem by R. Taylor and A. Wiles". Notices of the AMS 42 (7): 743-746. 
• John Coates (July 1996). "Wiles Receives NAS Award in Mathematics". Notices of the AMS 43 (7): 760-763. 
• Singh, Simon (1997). Fermat's Enigma. ISBN 0-8027-1331-9. 
• Mozzochi, Charles (2000). The Fermat Diary. ISBN 0-8218-2670-0. 
• NOVA Online: The Proof. WGBH (1997). Retrieved on 2006-05-03.
• O'Connor, John J.; Edmund F. Robertson "Andrew Wiles". MacTutor History of Mathematics archive.  
• Bluff your way in Fermat's Last Theorem. Retrieved on 2006-05-03.
• Fermat's Last Tango. Retrieved on 2006-05-22.

Richard Taylor (born 19 May 1962) is a British mathematician working in the field of number theory. ... Gerd Faltings, June 2006 Gerd Faltings (born July 28, 1954 in Gelsenkirchen-Buer) is a German Lutheran mathematician known for his work in arithmetic algebraic geometry. ... The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ... Professor John Henry Coates, FRS (born January 26, 1945) is a mathematician who holds (since 1986) the position of Sadleirian Professor (of pure mathematics) at the University of Cambridge in the United Kingdom. ... Simon Singh Simon Lehna Singh (born 1964) is a British author with a doctorate in physics, who has specialized in writing about mathematical and scientific topics in an accessible manner. ... It has been suggested that this article be split into articles entitled WGBH-TV and WGBH (FM), accessible from a disambiguation page. ... For the Manfred Mann album, see 2006 (album). ... May 3 is the 123rd day of the year in the Gregorian calendar (124th in leap years). ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... For the Manfred Mann album, see 2006 (album). ... May 3 is the 123rd day of the year in the Gregorian calendar (124th in leap years). ... For the Manfred Mann album, see 2006 (album). ... May 22 is the 142nd day of the year (143rd in leap years) in the Gregorian calendar. ...

External links

• Andrew Wiles at the Mathematics Genealogy Project
• List of Publications