I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.
I loved doing problems in school. I'd take them home and make up new ones of my own.
But the best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem -- Fermat's Last Theorem.
Here was a problem, that I, a ten year old, could understand and I knew from that moment that I would never let it go. I had to solve it.
I realized that anything to do with Fermat's Last Theorem generates too much interest.
I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.
Young children simply aren't interested in Fermat. They just want to hear a story and they're not going to let you do anything else.
Fermat couldn't possibly have had this proof.
I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.
But what has made this problem special for amateurs is that there's a tiny possibility that there does exist an elegant 17th-century proof.
Sir
Andrew John Wiles KBEThe Most Excellent Order of the British Empire is an order of chivalry established on 4 June 1917 by George V of the United Kingdom. The Order comprises five classes in civil and military divisions...
FRS (born 11 April 1953) is a British
mathematicianA mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and a
Royal SocietyThe Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
Research Professor at Oxford University, specializing in
number theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. He is most famous for
proving Fermat's Last TheoremWiles's proof of Fermat's Last Theorem is a proof of the modularity theorem for semistable elliptic curves released by Andrew Wiles, which, together with Ribet's theorem, provides a proof for Fermat's Last Theorem. Wiles first announced his proof in June 1993 in a version that was soon recognized...
.
Early life and education
Wiles is the son of
Maurice Frank WilesMaurice Frank Wiles was a Regius Professor of Divinity at Oxford University for 21 years, from 1970 to 1991.-Miracles:...
(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, CambridgeRidley Hall is a theological college located in Sidgwick Avenue in Cambridge in the United Kingdom, which trains intending ministers for the Church of England and other churches. It was founded in 1881 and named in memory of Nicholas Ridley, a leading protestant theologian of the sixteenth century...
, for the years 1952–55. Wiles was born in Cambridge, England, in 1953, and he attended King's College School, Cambridge, and The Leys School, Cambridge.
Wiles discovered Fermat's Last Theorem on his way home from school when he was 10 years old. He stopped by his local library where he found a book about the theorem. Puzzled by the fact that the statement of the theorem was so easy that he, a ten-year old, could understand it, he decided to be the first person to prove it. However, he soon realized that his knowledge of mathematics was too small, so he abandoned his childhood dream, until 1986, when he heard that
RibetKenneth Alan "Ken" Ribet is an American mathematician, currently a professor of mathematics at the University of California, Berkeley. His mathematical interests include algebraic number theory and algebraic geometry....
had proved
SerreJean-Pierre Serre is a French mathematician. He has made contributions in the fields of algebraic geometry, number theory, and topology.-Early years:...
's ε-conjecture and therefore established a link between Fermat's Last Theorem and the Taniyama-Shimura conjecture.
Wiles earned his
bachelor's degreeA bachelor's degree is usually an academic degree awarded for an undergraduate course or major that generally lasts for three or four years, but can range anywhere from two to six years depending on the region of the world...
in mathematics in 1974 after his study at
Merton College, OxfordMerton College is one of the constituent colleges of the University of Oxford in England. Its foundation can be traced back to the 1260s when Walter de Merton, chancellor to Henry III and later to Edward I, first drew up statutes for an independent academic community and established endowments to...
, and a
Ph.D.Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1980, after his research at
Clare College, CambridgeClare College is a constituent college of the University of Cambridge in Cambridge, England.The college was founded in 1326, making it the second-oldest surviving college of the University after Peterhouse. Clare is famous for its chapel choir and for its gardens on "the Backs"...
.
After a stay at the
Institute for Advanced StudyThe Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in
New JerseyNew Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...
in 1981, Wiles became a professor at
Princeton UniversityPrinceton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. In 1985–86, Wiles was a Guggenheim Fellow at the
Institut des Hautes Études ScientifiquesThe Institut des Hautes Études Scientifiques is a French institute supporting advanced research in mathematics and theoretical physics...
near Paris and at the
École Normale SupérieureThe École normale supérieure is one of the most prestigious French grandes écoles...
. From 1988 to 1990, Wiles was a
Royal SocietyThe Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
Research Professor at Oxford University, and then he returned to Princeton.
In October 2009 it was announced that Wiles would again become a Royal Society Research Professor at Oxford in 2011.
Mathematical career
Wiles's graduate research was guided by John Coates beginning in the summer of 1975. Together these colleagues worked on the arithmetic of
elliptic curveIn mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...
s with
complex multiplicationIn 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 In mathematics, complex multiplication is the...
by the methods of
Iwasawa theoryIn number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur...
. He further worked with
Barry Mazur-Life:Born in New York City, Mazur attended the Bronx High School of Science and MIT, although he did not graduate from the latter on account of failing a then-present ROTC requirement. Regardless, he was accepted for graduate school and received his Ph.D. from Princeton University in 1959,...
on the main conjecture of Iwasawa theory over the
rational numberIn mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...
s, and soon afterward, he generalized this result to totally real fields.
The proof of Fermat's Last Theorem
Starting in the summer of 1986, based on successive progress of the previous few years of
Gerhard FreyGerhard Frey is a German mathematician, known for his work in number theory. His Frey curve, a construction of an elliptic curve from a purported solution to the Fermat equation, was central to Wiles' proof of Fermat's Last Theorem....
,
Jean-Pierre SerreJean-Pierre Serre is a French mathematician. He has made contributions in the fields of algebraic geometry, number theory, and topology.-Early years:...
and Ken Ribet, Wiles realised that a proof of a limited form of the modularity theorem might then be in reach. He dedicated all of his research time to this problem in relative secrecy. In 1993, he presented his proof to the public for the first time at a conference in Cambridge. In August 1993, however, it turned out that the proof contained a gap. In desperation, Wiles tried to fill in this gap, but found out that the error he had made was a very fundamental one. According to Wiles, the crucial idea for circumventing, rather than closing this gap, came to him on 19 September 1994. Together with his former student
Richard Taylor-External links:**...
, he published a second paper which circumvented the gap and thus completed the proof. Both papers were published in 1995 in a special volume of the
Annals of MathematicsThe Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
.
Recognition by the media
His proof of
Fermat's Last TheoremIn number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
has stood up to the scrutiny of the world's mathematical experts. Wiles was interviewed for an episode of the
BBCThe British Broadcasting Corporation is a British public service broadcaster. Its headquarters is at Broadcasting House in the City of Westminster, London. It is the largest broadcaster in the world, with about 23,000 staff...
documentary series
Horizon that focused on Fermat's Last Theorem. This was renamed "The Proof", and it was made an episode of the
Public Broadcasting ServiceThe Public Broadcasting Service is an American non-profit public broadcasting television network with 354 member TV stations in the United States which hold collective ownership. Its headquarters is in Arlington, Virginia....
's science television series
NovaNova is a popular science television series from the U.S. produced by WGBH Boston. It can be seen on the Public Broadcasting Service in the United States, and in more than 100 other countries...
. He is a foreign member of the
United States National Academy of SciencesThe National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
since 1996. He remains a citizen of the United Kingdom.
Family
Wiles is married to Nada Canaan Wiles, who earned her Ph.D. in
microbiologyMicrobiology is the study of microorganisms, which are defined as any microscopic organism that comprises either a single cell , cell clusters or no cell at all . This includes eukaryotes, such as fungi and protists, and prokaryotes...
from
Princeton UniversityPrinceton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in
New JerseyNew Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...
, and they have three daughters: Clare, Kate and Olivia. He lives in Oxford.
Awards
Wiles has been awarded several major prizes in mathematics and science:
- Junior Whitehead Prize
The Whitehead Prize is awarded yearly by the London Mathematical Society to a mathematician working in the United Kingdom who is at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C...
of the LMS-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
(1988)
- Fellow of the Royal Society (1989)
- Schock Prize
The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock . The prizes were first awarded in Stockholm, Sweden, in 1993 and have been awarded every two years since...
(1995)
- Fermat Prize
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 analytic geometry* Number theory....
(1995)
- Wolf Prize
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts...
(1995/6)
- NAS Award in Mathematics
The NAS Award in Mathematics is awarded by the U.S. National Academy of Sciences "for excellence of research in the mathematical sciences published within the past ten years." It has been awarded every four years since 1988....
from the National Academy of Sciences (1996)
- Royal Medal
The Royal Medal, also known as The Queen's Medal, is a silver-gilt medal awarded each year by the Royal Society, two for "the most important contributions to the advancement of natural knowledge" and one for "distinguished contributions in the applied sciences" made within the Commonwealth of...
(1996)
- Ostrowski Prize
The Ostrowski Prize is a mathematics award given every other year by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands...
(1996)
- Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, 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 prize is named after Frank Nelson Cole, who...
(1997)
- Wolfskehl Prize (1997) – see Paul Wolfskehl
Paul Friedrich Wolfskehl , was an industrialist with an interest in mathematics. He bequeathed 100,000 marks to the first person to prove Fermat's Last Theorem.He was the younger of two sons of a rich Jewish banker, Joseph Carl Theodor Wolfskehl.His older brother, the jurist...
- A silver plaque from the International Mathematical Union
The International Mathematical Union is an international non-governmental organisation devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science and supports the International Congress of Mathematicians...
(1998) recognizing his achievements, in place of the Fields MedalThe Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, 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...
, which is restricted to those under 40 (Wiles was born in 1953 and proved the theorem in 1994)
- King Faisal Prize (1998)
- Clay Research Award
The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research...
(1999)
- Pythagoras Award (Croton, 2004)
- Shaw Prize
The Shaw Prize is an annual award first presented by the Shaw Prize Foundation in 2004. Established in 2002 in Hong Kong, it honours living "individuals, regardless of race, nationality and religious belief, who have achieved significant breakthrough in academic and scientific research or...
(2005)
Public honours
- The asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
9999 Wiles9999 Wiles is a C-type main belt asteroid. It orbits the Sun every 4.8 years.It was discovered by C. J. van Houten, I. van Houten-Groeneveld and T. Gehrels on September 29, 1973. Given the provisional designation 4196 T-2, it was renamed 9999 Wiles in honour of Andrew J. Wiles, who proved...
was named for Wiles in 1999.
- Wiles was appointed to the rank of Knight Commander of the Order of the British Empire
The Most Excellent Order of the British Empire is an order of chivalry established on 4 June 1917 by George V of the United Kingdom. The Order comprises five classes in civil and military divisions...
in the United Kingdom in 2000.
In popular culture
- Wiles was mentioned in an episode of Star Trek for his proof of Fermat's Last Theorem.
- He was also mentioned in Stieg Larsson
Karl Stig-Erland Larsson , who wrote professionally as Stieg Larsson, was a Swedish journalist and writer, born in Skelleftehamn outside Skellefteå. He is best known for writing the "Millennium series" of crime novels, which were published posthumously...
's second book of the Millennium trilogy The Girl Who Played With FireThe Girl Who Played with Fire is the second novel in the best-selling "Millennium series" by Swedish writer Stieg Larsson. It was published posthumously in Swedish in 2006 and in English in January 2009....
, and also the third, The Girl Who Kicked the Hornets' NestThe Girl Who Kicked the Hornets' Nest is the third and final novel in the best-selling "Millennium series"by Swedish writer Stieg Larsson.The novel is the sequel to The Girl Who Played with Fire....
. Wiles was credited with solving Fermat's Last Theorem when the female protagonist Lisbeth SalanderLisbeth Salander is a fictional character created by Swedish author and journalist Stieg Larsson. She is the heroine of Larsson's award-winning "Millennium series", first appearing in the novel The Girl with the Dragon Tattoo...
attempted to solve it.
- Tom Lehrer
Thomas Andrew "Tom" Lehrer is an American singer-songwriter, satirist, pianist, mathematician and polymath. He has lectured on mathematics and musical theater...
's song That's Mathematics mentions that Wiles "confirms what Fermat / Jotted down in that margin / Which could've used some enlargin'."
- Rock band BATS
Bats are a five piece band based in Dublin, Ireland. Formed in 2007, they are a blend of post-punk, hardcore and metal, with lyrics drawing heavily from science subject areas.The début EP Cruel Sea Scientist was released in 2007 on Armed Ambition...
has a song named after Wiles which describes his career.
External links