Sir Andrew John Wiles KBE FRS (born 11 April 1953) is a British 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 by the Royal Society. He was appointed Knight Commander of the Order of the British Empire in 2000, and in 2018 was appointed as the first Regius Professor of Mathematics at Oxford.
Sir Andrew Wiles
Andrew John Wiles
11 April 1953
|Education||King's College School, Cambridge|
The Leys School
|Known for||Proving the Taniyama–Shimura Conjecture for semistable elliptic curves, thereby proving Fermat's Last Theorem|
Proving the main conjecture of Iwasawa theory
|Thesis||Reciprocity Laws and the Conjecture of Birch and Swinnerton-Dyer (1979)|
|Doctoral advisor||John Coates|
Wiles was born on 11 April  1953 in Cambridge, England, the son of Maurice Frank Wiles (1923–2005), the Regius Professor of Divinity at the University of Oxford, 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.
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 about the theorem. 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.
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. After a stay at the Institute for Advanced Study in Princeton, New Jersey in 1981, Wiles became a Professor of Mathematics at Princeton University. In 1985–86, Wiles was a Guggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the École Normale Supérieure. From 1988 to 1990, Wiles was a Royal Society Research Professor at the University of Oxford, and then he returned to Princeton. From 1994 - 2009, Wiles was a Eugene Higgins Professor at Princeton. He rejoined Oxford in 2011 as Royal Society Research Professor. In May 2018 he was appointed Regius Professor of Mathematics at Oxford, the first in the university's history.
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 on the main conjecture of Iwasawa theory over the rational numbers, and soon afterward, he generalised this result to totally real fields.
His biographical page at Princeton University's website states that "Andrew has few equals in terms of his impact on modern number theory. Many of the world’s very best young number theorists received their Ph.D.'s under Andrew ... and many of these are today leaders and professors at top institutions around the world".
Starting in mid-1986, based on successive progress of the previous few years of Gerhard Frey, Jean-Pierre Serre and Ken Ribet, it became clear that Fermat's Last Theorem could be proven as a corollary of a limited form of the modularity theorem (unproven at the time and then known as the "Taniyama–Shimura–Weil conjecture"). The modularity theorem involved elliptic curves, which was also Wiles's own specialist area.
The conjecture was seen by contemporary mathematicians as important, but extraordinarily difficult or perhaps impossible to prove.:203–205, 223, 226 For example, Wiles's ex-supervisor John Coates states that it seemed "impossible to actually prove",: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].":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.: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.: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.
In August 1993, it was discovered that the proof contained a flaw in one area. Wiles tried and failed for over a year to repair his proof. According to Wiles, the crucial idea for circumventing, rather than closing this area, came to him on 19 September 1994, when he was on the verge of giving up. Together with his former student Richard Taylor, he published a second paper which circumvented the problem and thus completed the proof. Both papers were published in May 1995 in a dedicated issue of the Annals of Mathematics.
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 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. His work and life are also described in great detail in Simon Singh's popular book Fermat's Last Theorem.
Wiles has been awarded a number of major prizes in mathematics and science:
Wiles's 1987 certificate of election to the Royal Society reads:
Andrew Wiles is almost unique amongst number-theorists in his ability to bring to bear new tools and new ideas on some of the most intractable problems of number theory. His finest achievement to date has been his proof, in joint work with Mazur, of the "main conjecture" of Iwasawa theory for cyclotomic extensions of the rational field. This work settles many of the basic problems on cyclotomic fields which go back to Kummer, and is unquestionably one of the major advances in number theory in our times. Earlier he did deep work on the conjecture of Birch and Swinnerton-Dyer for elliptic curves with complex multiplication – one offshoot of this was his proof of an unexpected and beautiful 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.
All text published under the heading 'Biography' on Fellow profile pages is available under Creative Commons Attribution 4.0 International License." --"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)
The 2014 Brentwood Borough Council election took place on 22 May 2014 to elect members of Brentwood Borough Council in England. This was on the same day as other local elections.9999 Wiles
9999 Wiles, provisional designation 4196 T-2, is a Koronian asteroid from the outer region of the asteroid belt, approximately 6 to 7 kilometers in diameter. It was named after British mathematician Andrew Wiles.Brian Conrad
Brian Conrad (born November 20, 1970), is an American mathematician and number theorist, working at Stanford University. Previously, he taught at the University of Michigan and at Columbia University.
Conrad and others proved the modularity theorem, also known as the Taniyama-Shimura Conjecture. He proved this in 1999 with Christophe Breuil, Fred Diamond and Richard Taylor, while holding a joint postdoctoral position at Harvard University and the Institute for Advanced Study in Princeton, New Jersey.
Conrad received his bachelor's degree from Harvard in 1992, where he won a prize for his undergraduate thesis. He did his doctoral work under Andrew Wiles and went on to receive his Ph.D. from Princeton University in 1996 with a dissertation entitled Finite Honda Systems And Supersingular Elliptic Curves. He was also featured as an extra in Nova's The Proof.
His identical twin brother Keith Conrad, also a number theorist, is a professor at the University of Connecticut.Broom Bridge
Broom Bridge (Irish: Droichead Broome), also called Broome Bridge, and sometimes Brougham Bridge, is a bridge along Broombridge Road which crosses the Royal Canal in Cabra, Dublin, Ireland. Broome Bridge is named after William Broome, one of the directors of the Royal Canal company who lived nearby. It is famous for being the location where Sir William Rowan Hamilton first wrote down the fundamental formula for quaternions on 16 October 1843, which is to this day commemorated by a stone plaque on the northwest corner of the underside of the bridge. After being spoiled by the action of vandals and some visitors, the plaque was moved to a different place, higher, under the railing of the bridge.
The text on the plaque reads:
Here as he walked by
on the 16th of October 1843
Sir William Rowan Hamilton
in a flash of genius discovered
the fundamental formula for
i² = j² = k² = ijk = −1
& cut it on a stone of this bridge.
Given the historical importance of the bridge with respect to mathematics, mathematicians from all over the world have been known to take part in the annual commemorative walk from Dunsink Observatory to the site. Attendees have included Nobel Prize winners Murray Gell-Mann, Steven Weinberg and Frank Wilczek, and mathematicians Sir Andrew Wiles, Sir Roger Penrose and Ingrid Daubechies. The 16 October is sometimes referred to as Broomsday (in reference to Broome Bridge) and as a nod to the literary commemorations on 16 June (Bloomsday in honour of James Joyce).Centre for Mathematical Sciences (Cambridge)
The Centre for Mathematical Sciences (CMS) at the University of Cambridge houses the university's Faculty of Mathematics, the Isaac Newton Institute, and the Betty and Gordon Moore Library. It is situated on Wilberforce Road, formerly a St John's College playing field, and has been leased by St John's to the University as such is part of its expansion into West Cambridge.
The Isaac Newton Institute was opened in 1992. Andrew Wiles announced his proof of Fermat's Last Theorem on 23 June 1993. The rest of the site was designed by Edward Cullinan architects and Buro Happold and construction under project manager Davis Langdon was completed in 2003. It consists of 340 offices in 7 'pavilions', arranged in a parabola around a 'central core' with lecture rooms, common space, and a grass-covered roof, as well as a gatehouse. The design won awards including the British Construction Industry Major Project Award 2003, the David Urwin Design Award 2003, the Royal Fine Art Commission Trust Specialist Award 2003 and the RIBA Award 2003.Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States. CMI's scientific activities are managed from the President's office in Oxford, United Kingdom. The institute is "dedicated to increasing and disseminating mathematical knowledge." It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998 through the sponsorship of Boston businessman Landon T. Clay. Harvard mathematician Arthur Jaffe was the first president of CMI.
While the institute is best known for its Millennium Prize Problems, it carries out a wide range of activities, including a postdoctoral program (ten Clay Research Fellows are supported currently), conferences, workshops, and summer schools.Conjecture
In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found. Conjectures such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (which was a conjecture until proven in 1995 by Andrew Wiles) have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.Elliptic curve
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form
which is non-singular; that is, the curve has no cusps or self-intersections. (When the coefficient field has characteristic 2 or 3, the above equation is not quite general enough to comprise all non-singular cubic curves; see § Elliptic curves over a general field below.)
Formally, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is an abelian variety – that is, it has a multiplication defined algebraically, with respect to which it is an abelian group – and O serves as the identity element. Often the curve itself, without O specified, is called an elliptic curve; the point O is often taken to be the curve's "point at infinity" in the projective plane.
If y2 = P(x), where P is any polynomial of degree three in x with no repeated roots, the solution set is a nonsingular plane curve of genus one, an elliptic curve. If P has degree four and is square-free this equation again describes a plane curve of genus one; however, it has no natural choice of identity element. More generally, any algebraic curve of genus one, for example from the intersection of two quadric surfaces embedded in three-dimensional projective space, is called an elliptic curve, provided that it has at least one rational point to act as the identity.
Using the theory of elliptic functions, it can be shown that elliptic curves defined over the complex numbers correspond to embeddings of the torus into the complex projective plane. The torus is also an abelian group, and in fact this correspondence is also a group isomorphism.
Elliptic curves are especially important in number theory, and constitute a major area of current research; for example, they were used in the proof, by Andrew Wiles, of Fermat's Last Theorem. They also find applications in elliptic curve cryptography (ECC) and integer factorization.
An elliptic curve is not an ellipse: see elliptic integral for the origin of the term. Topologically, a complex elliptic curve is a torus.Euler system
In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by Kolyvagin (1990) in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper Kolyvagin (1988) and the work of Thaine (1988). Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product.
Euler systems can be used to construct annihilators of ideal class groups or Selmer groups, thus giving bounds on their orders, which in turn has led to deep theorems such as the finiteness of some Tate-Shafarevich groups. This led to Karl Rubin's new proof of the main conjecture of Iwasawa theory, considered simpler than the original proof due to Barry Mazur and Andrew Wiles.Fermat's Last Theorem
In number theory Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known to have infinitely many solutions since antiquity.This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The proof was described as a 'stunning advance' in the citation for his Abel Prize award in 2016. The proof of Fermat's Last Theorem also proved much of the modularity theorem and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques.
The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof, it was in the Guinness Book of World Records as the "most difficult mathematical problem", one of the reasons being that it has the largest number of unsuccessful proofs.Fermat's Last Theorem (book)
Fermat's Last Theorem is a popular science book (1997) by Simon Singh. It tells the story of the search for a proof of Fermat's last theorem, first conjectured by Pierre de Fermat in 1637, and explores how many mathematicians such as Évariste Galois had tried and failed to provide a proof for the theorem. Despite the efforts of many mathematicians, the proof would remain incomplete until as late as 1995, with the publication of Andrew Wiles' proof of the Theorem. The book is the first mathematics book to become a Number One seller in the United Kingdom, whilst Singh's documentary The Proof, on which the book was based, won a BAFTA in 1997.In the United States, the book was released as Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. The book was released in the United States in October 1998 to coincide with the US release of Singh's documentary The Proof about Wiles's proof of Fermat's Last Theorem.Fred Diamond
Fred Irvin Diamond (born November 19, 1964) is a mathematician, known for his role in proving the modularity theorem for elliptic curves. His research interest is in modular forms and Galois representations.
Diamond received his B.A. from the University of Michigan in 1984, and received his Ph.D. in mathematics from Princeton University in 1988 as a doctoral student of Andrew Wiles. He has held positions at Brandeis University and Rutgers University, and is currently a professor at King's College London.Diamond is the author of several research papers, and is also a coauthor along with Jerry Shurman of A First Course in Modular Forms, in the Graduate Texts in Mathematics series published by Springer-Verlag.List of alumni of Clare College, Cambridge
The following is a list of alumni of Clare College, Cambridge, a constituent college of the University of Cambridge.Mathematical Institute, University of Oxford
The Mathematical Institute is the mathematics department at the University of Oxford, England. It forms one of the twelve departments of the Mathematical, Physical and Life Sciences Division in the University. The department is located between Somerville College and Green Templeton College on Woodstock Road, next to the Faculty of Philosophy.Modularity theorem
In mathematics, the modularity theorem (formerly called the Taniyama–Shimura conjecture or the Taniyama–Shimura–Weil conjecture) states that elliptic curves over the field of rational numbers are related to modular forms. Andrew Wiles proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's last theorem. Later, Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor extended Wiles' techniques to prove the full modularity theorem in 2001. The modularity theorem is a special case of more general conjectures due to Robert Langlands. The Langlands program seeks to attach an automorphic form or automorphic representation (a suitable generalization of a modular form) to more general objects of arithmetic algebraic geometry, such as to every elliptic curve over a number field. Most cases of these extended conjectures have not yet been proved. However, Freitas, Le Hung & Siksek (2015) proved that elliptic curves defined over real quadratic fields are modular.Peter Sarnak
Peter Clive Sarnak (born 18 December 1953) is a South African-born mathematician with dual South-African and American nationalities. He has been Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Andrew Wiles, and is an editor of the Annals of Mathematics. He is known for his work in analytic number theory. Sarnak is also on the permanent faculty at the School of Mathematics of the Institute for Advanced Study. He also sits on the Board of Adjudicators and the selection committee for the Mathematics award, given under the auspices of the Shaw Prize.Rolf Schock Prizes
The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm, Sweden, in 1993, and since 2005 are awarded every three years. Each recipient currently receives SEK 400,000 (ca. US$ 60,000). A similar prize is the Kyoto Prize in Arts and Philosophy, established by the Inamori Foundation. It is considered the equivalent of the Nobel Prize in Philosophy.
The Prizes are awarded in four categories and decided by committees of three of the Swedish Royal Academies:
Logic and Philosophy (decided by the Royal Swedish Academy of Sciences)
Mathematics (decided by the Royal Swedish Academy of Sciences)
Visual Arts (decided by the Royal Swedish Academy of Arts)
Musical Arts (decided by the Royal Swedish Academy of Music)Wiles
Wiles is a surname. Notable people with the surname include:
Adam Wiles (born 1984), real name of Scottish singer, songwriter, DJ, and producer Calvin Harris
Andrew Wiles, British mathematician who proved Fermat's Last Theorem
Archie Wiles, cricketer from Trinidad
Billy Wiles, American wrestler
Irving Ramsey Wiles, United States artist
Jason Wiles, actor, director and producer
John Wiles, British television producer
Lemuel M. Wiles (1826–1905), American landscape painter.
Maurice Wiles, British theologian, father of Andrew Wiles
Mary Kate Wiles, American film, TV and YouTube actor
Michele Wiles, principal dancer at American Ballet Theatre
Simon Wiles, English footballer
Siouxsie Wiles, microbiologist and science communicatorWiles's proof of Fermat's Last Theorem
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were almost universally considered inaccessible to proof by contemporaneous mathematicians, meaning that they were believed to be impossible to prove using current knowledge.Wiles first announced his proof on Wednesday 23 June 1993 at a lecture in Cambridge entitled "Modular Forms, Elliptic Curves and Galois Representations". However, in September 1993 the proof was found to contain an error. One year later on Monday 19 September 1994, in what he would call "the most important moment of [his] working life", Wiles stumbled upon a revelation that allowed him to correct the proof to the satisfaction of the mathematical community. The corrected proof was published in 1995.Wiles' proof uses many techniques from algebraic geometry and number theory, and has many ramifications in these branches of mathematics. It also uses standard constructions of modern algebraic geometry, such as the category of schemes and Iwasawa theory, and other 20th-century techniques which were not available to Fermat.
Together, the two papers which contain the proof are 129 pages long, and consumed over seven years of Wiles's research time. John Coates described the proof as one of the highest achievements of number theory, and John Conway called it the proof of the [20th] century. Wiles' path to proving Fermat's Last Theorem, by way of proving the modularity theorem for the special case of semistable elliptic curves, established powerful modularity lifting techniques and opened up entire new approaches to numerous other problems. For solving Fermat's Last Theorem, he was knighted, and received other honours such as the 2016 Abel Prize. When announcing that Wiles had won the Abel Prize, the Norwegian Academy of Science and Letters described his achievement as a "stunning proof".