British number theorist Andrew Wiles has received the Abel Prize for his solution to Fermat’s last theorem — a problem that stumped. This book will describe the recent proof of Fermat’s Last The- orem by Andrew Wiles, aided by Richard Taylor, for graduate students and faculty with a. “I think I’ll stop here.” This is how, on 23rd of June , Andrew Wiles ended his series of lectures at the Isaac Newton Institute in Cambridge. The applause, so.
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This article is the winner ahdrew the schools category of the Plus new writers award Students were asked to write about the life and work of a mathematician of their choice. There is a problem that not even the collective mathematical genius of almost years could solve. When the ten-year-old Andrew Wiles read about it in his local Cambridge library, he dreamt of solving the problem that had haunted so many great mathematicians.
Little did he or the rest fermqt the world know that he would succeed I had to solve it. The story of the problem that would seal Wiles’ place in history begins in when Pierre de Fermat made a deceptively simple conjecture.
He stated that if is any whole number greater than 2, then there are no three whole numbersand other than zero that satisfy the equation Note that ifthen whole number solutions do exist, for exampleand. Fermat claimed to have proved this statement but that the “margin [was] too narrow to contain” it. It is the seeming simplicity of ajdrew problem, coupled with Fermat’s claim to have proved it, which has captured the hearts of so many mathematicians.
Andrew Wiles was born in Cambridge, England on April 11 At the age of andrsw he began to attempt to prove Fermat’s last theorem using textbook methods.
He then moved on to looking at the work of others who had attempted to prove the conjecture. The problem was that to prove the general form of the conjecture, it does not help to prove individual cases; infinity minus something is still infinity. Wiles had to try a different approach in order to solve the problem. It was while at Cambridge that he worked with John Coates on the arithmetic of elliptic curves. Elliptic curves are confusingly not much like an ellipse or a curve!
They are defined by points in the plane whose co-ordinates and satisfy an equation of the form where and are constants, and vermat are usually doughnut-shaped. When Wiles began studying elliptic curves they were thworem area of mathematics unrelated to Fermat’s last theorem. But hheorem was soon to change. Since the s the Taniyama-Shimura conjecture had stated that every elliptic curve can be matched to a modular form — a mathematical object that is symmetrical in an infinite number of ways.
Then in the summer of Andrw Ribet, building on work of Gerhard Frey, established a link between Fermat’s last theorem, elliptic curves and the Taniyama-Shimura conjecture. By showing a link between these three vastly different areas Ribet had changed the course of Wiles’ life forever. If such an elliptic curve existed, then the Taniyama-Shimura conjecture would be false.
Looking at this from a wioes perspective we can see that if the Taniyama-Shimura tjeorem could be proved to be true, then the curve could not exist, hence Fermat’s last theorem must be true.
So to prove Fermat’s last theorem, Wiles had to prove the Taniyama-Shimura conjecture. Proving the Taniyama-Shimura conjecture was an enormous task, one that many mathematicians considered impossible.
Wiles decided that the only way he could prove it would be to work in secret at his Princeton home. He still performed his lecturing duties at the university but no longer attended conferences or told anyone what he was working on. This led many to believe he had finished as a mathematician; simply run out of ideas. After six years working alone, Wiles felt he had almost proved the conjecture.
But he needed help from a friend called Nick Katz to examine one part of the proof. No problems were found and the moment to announce the proof came later that year at the Isaac Newton Institute in Cambridge. Unfortunately for Wiles this was not the end of the story: The flaw in the proof cannot be simply explained; however without rectifying the error, Fermat’s last theorem would remain unsolved.
After a year of effort, partly in collaboration with Richard Taylor, Wiles managed to fix the problem by merging two approaches. Both of the approaches were on their own inadequate, but together they were perfect. So it came to andre that after years and 7 years of one man’s undivided attention that Fermat’s last theorem was finally solved.
His interest in this particular problem was sparked by reading the andrw Fermat’s last theorem by Simon Singh, which gives a great insight into the history of the theorem for those who want to know more. Neil hopes to study maths at university inwhere he is looking forward to tackling some problems of his own. In his spare time he enjoys lazt football and has a season ticket for Sheffield Wednesday Football Club.
Andrew Wiles and Fermat’s last theorem |
Plus would like to thank the London Mathematical Society and the Maths, Stats and Operational Research Network, as well as the journal Nature for their kind support of this competition. This is a nice libro. I think however, that its continuation will soon be written somewhere else or the same Singh, who knows?
It seems to be the only direct proof currently existing. I see you have posted your comment in a few places about Gallo, yet no search seems to turn up any information about this extraordinary man who proved FLT in 6 pages. Perhaps you could help us all by posting a specific reference to where it may be found or even better a link? My guess at the “marvelous proof” claimed by Fermat is as follows: Let us imagine solid unit cubes of side unity to represent the number ‘1’. Then ‘x’ of these would represent the number ‘x’ and let us imagine these are placed in a linear array.
We can then place ‘y’ of these unit cubes to represent the number ‘y’. The cube of ‘y’ can be similarly contructed and placed alongside the cube of ‘x’. FLT asserts that the sum of the cubes of ‘x’ and ‘y’ cannot be equal to another cube, say of ‘z’. Then the exponent 5 for ‘x’ and ‘y’ would be represented by square arrays of the cubes of ‘x’ and ‘y’.
Similarly for exponent 5. Finally, the exponent 6 for ‘x’ and ‘y’ will turn the square arrays of cubes into “super-cubes”!! Please tell me if this holds water or is there a flaw in my reasoning? Skip to main content. A family of elliptic curves. Animation courtesy Aleksandar T. Griffiths on March 6, Fermat’s Last Ahdrew has been proved in less than words in the February issue of M