Andrew Wiles

Born: April 11, 1953

Cambridge, England

by

Diane Neal

Gulf Coast Community College

March, 2000

#### Introduction

Andrew Wiles is a world-renowned English mathematician who received his fame in recent years. In 1993 Wiles solved a math problem that other mathematicians had been trying to solve for the past 350 years. He found a proof for Fermat’s last theorem. In finding this proof, Wiles not only laid a 17th century problem to rest, but fulfilled his life-long dream. In the words of Andrew Wiles…

…Fermat was my childhood passion. There is no problem that will mean the same to me.

Andrew Wiles was born on April 11, 1953 in Cambridge, England.  He lived there throughout his childhood.  It was in Cambridge that Andrew was introduced to what would become his life’s ambition.  Even as a child Andrew enjoyed doing math problems. He loved doing the problems at school so much that he took them home and made new ones of his own. He also enjoyed solving mathematical riddles from puzzle-books that he found in his local library.  When Wiles was 10 years old, he came across a book in the library entitled The Last Problem by Eric Temple Bell. This book contained a problem with no solution.  Andrew was so intrigued by this problem that it became a personal challenge for him to solve it.  Wiles remembers how he felt when he first encountered Fermat’s last theorem…

It looked so simple and yet the great mathematicians in history couldn’t solve it.  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.

Proving Fermat’s last theorem would become Andrew Wiles’ passion and life’s ambition.  The problem dates back to 1637 when Pierre de Fermat, a 17th century mathematician, jotted a theorem in the margin of his copy of the ancient Greek text, Arithmetica of Diophantus.  Along with his theorem which states…

Fermat wrote that he had a remarkable proof, but the margin was too small to contain it. If Fermat did indeed have a solution, he never wrote it down.   This was the only remaining theorem of Fermat’s that had not yet been proven or disproven and is thereby known as Fermat’s last theorem. This problem would intrigue, challenge, and frustrate mathematicians for the next 350 years.  Andrew Wiles was no exception.  However, he possessed such a passionate determination for solving Fermat’s problem that he would not give up until he ultimately achieved success.

Andrew Wiles’ fascination with this problem is accredited for inspiring his interest in mathematics that would lead him to his life’s work as a number theorist.  Wiles received his formal education in mathematics from Merton College in Oxford where he earned his B.A. in 1974 and from Clare College in Cambridge where he earned a Master in Arts in1977 and then a Ph.D. in 1980.  In 1981 he worked at the Institute for Advanced Study in Princeton and was appointed a professor the following year.

While working on his doctorate at Cambridge University, Wiles decided to set aside working on Fermat’s last theorem for a while.  He said in an interview by NOVA…

"… The problem with working on Fermat is that you could spend years getting nothing so when I went to Cambridge my professor, John Coates, was working on Iwasawa theory of elliptic curves and I started working with him."

Wiles did not realize that his research on elliptic curves would later prove to be helpful to him in solving Fermat’s last theorem.

In the summer of 1986 everything would change for Andrew Wiles. He would again embark on his quest to solve Fermat’s last theorem.  A friend casually mentioned to Andrew that Ken Ribet had proved a link between Taniyama-Shimura conjecture about elliptic curves and Fermat’s last theorem.  At that moment Wiles knew that to prove Fermat, all he had to do was to prove Taniyama-Shimura.

Wiles decided to work in total isolation. He knew that Fermat sparked so much interest that he would not be able to give it his undivided attention if anyone knew what he was working on. The only person that he told was his wife, Nada. Andrew told her about Fermat’s last theorem while they were on their honeymoon.  However, I m sure she did not realize the impact it would have on their lives. For the next 7 years Wiles would wake up with the problem, have it in his head all day, and go to bed with it at night. He totally inundated himself in finding a proof for the Taniyama-Shimura conjecture and, consequently, Fermat’s last theorem.  The only time he was able to relax was when he was with his children.  Wiles said …

"…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."

Finally in the spring of 1993, Andrew Wiles had a break-through and found a way to prove that all curves are modular and thereby prove Fermat’s last theorem. He asked a fellow professor at Princeton, Nick Katz, to help him test his proof. In order to keep a low profile, he disguised his proof in a course of lectures, which Katz attended.  Eventually Nick Katz was the only one left in the audience. No one else could follow the complex proof; especially without knowing it’s purpose.  The lectures revealed no errors. The 150-page proof seemed to work beautifully.

Andrew decided to announce his proof at a conference in Cambridge. He signed up to give a series of lectures on Elliptic curves and modular forms.  By his final lecture there was much talk about whether or not he was leading up to a proof of Fermat’s last theorem.  He gave a dramatic build-up, wrote the equation to Fermat’s last theorem on the blackboard and simply said…I solved it.  I think I’ll stop here.  It was a wonderful feeling for Wiles to have finally solved his problem.  The audience gave him a standing ovation.

It was not until a few months later that Andrew would find out that there was a flaw in his proof.  Ironically, Nick Katz found the error, the man who had earlier helped Wiles check his proof. It is a shame that Katz did not find the flaw at that stage of the game rather than after Wiles had announced his proof to the world. Wiles spent the next year working harder than ever to iron out the flaw.  He received some help from a former student, Richard Taylor.  However, Andrew was alone in his office when had the incredible revelation to switch to a different number family of curves that would make his problem work.  Finally the torment of working under the spotlight was over.

In October of 1994, Andrew Wiles was accredited for solving Fermat’s last theorem and giving the Taniyama-Shimura conjecture the title of a theorem.  He received many honors for his achievement. In 1994 he was appointed Eugene Higgins Professor of Mathematics at Princeton.  His paper, Modular elliptic curves and Fermat’s last theorem, appeared in the Annals of Mathematics in 1995.  Wiles was awarded the Shock Prize in Mathematics and the Prix Fermat for this ingenious piece of work.  In 1996 he received the Wolf Prize and the Macarthur Fellowship.  Wiles was also honored with a special silver plaque given by the International Mathematical Union in 1998.

Although Andrew Wiles has received these many honors for his achievement of solving Fermat’s last theorem, he described his greatest reward in saying…

"…There is no other problem that will mean the same to me.  I had this very rare privilege of being able to pursue in my adult life what had been my childhood dream.  I know it’s a rare privilege but if, if one can do this it’s more rewarding than anything one can imagine."

Today Andrew Wiles remains on the faculty at Princeton University.  He is involved in research and gives many lectures.  He claims that his mind is at rest since he solved Fermat’s last theorem and fulfilled his dream.  Wiles will undoubtedly work on and perhaps solve other mathematical problems in his lifetime, but nothing will ever be as special to him as Fermat’s last theorem.

#### References

1. The Proof, a film on video by NOVA.
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1. “Andrew Wiles Receives Special Tribute from International Mathematical Union.”  Princeton-News Aug.  27, 1998.
1. “Fermat’s last theorem.”  Encyclopedia Britannica. www.britannica.com
1. “Wiles, Andrew John" Encyclopedia Britannica. www.britannica.com
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1.  “Wiles, Andrew.” Compton’s Encyclopedia Online v 3.0 copyright 1998. The Learning Company, Inc.
1.  Adams, Susan.  “Solving the Ultimate Puzzle.” Forbes Magazine.  January 12, 1998.  http://www.forbes.com/forbes/98/0112/6101281s1.htm
1. “The Romance of Fermat’s Last Theorem.” Boston University Conference.Aug. 9-18, 1995.http://rendezvous.com/tangledweb/conferences/fermat/romance.html
1. “Fermat’s Last Theorem.”  (picture of Fermat and Wiles.)  Horizon.           http://win-www.uia.ac.be/u/fgeerts/fermint.html.

11.  “Andrew John Wiles.” School of  Mathematics and Statistics, University of St.

Andrews, Scotland.

12.  “The Proof-Solving Fermat: Andrew Wiles.” NOVA Online.