Can you picture yourself working for seven years in solitude and secrecy on a problem that has stumped the world's best mathematicians for centuries? Imagine, if you can, that your work is crowned with success, and that overnight you become a worldwide celebrity. Then, after a few months, your peers point out a hole in your argument. Back to your solitary pondering, only this time you cannot escape the glare of publicity! This nightmare predicament was the reality Andrew Wiles found himself in for a whole year following his initial announcement of success. Miraculously, just as he was ready to finally admit defeat, he had a flash of insight on how he could overcome the remaining obstacle and complete his proof. Pierre de Fermat (1601-1665) was a legendary French mathematician,
but he would hardly still be remembered by laymen, had it not been for
his famous scribbling in 1637. In the margin of his copy of an ancient
Greek text (Diophant's The theorem is deceptively simple: For more than 350 years, all the best mathematicians (and countless amateurs) tried in vain to re-discover the proof that Fermat claimed to have found. Over time doubts have grown, tempered by the knowledge that Fermat was a mathematical genius, and that he had the habit of offering his discoveries as challenges to his colleagues. Wiles' proof could not have been found by Fermat, but we cannot dismiss Fermat's claim with complete certainty. Simon Singh's spellbinding book describes Wiles' lonely
struggle to find a proof, his false success, his setback, and his final
victory against all odds. You do not need a background in mathematics to enjoy the book. Although
I have a degree in engineering physics, I must admit that I do not have
the faintest idea of what a statement such as I find the account of Wiles' personal struggle at least as fascinating
as the puzzle itself. What did he actually
It appears that Wiles is an intensely private person. Born in Cambridge, he had been dreaming of finding a proof of Fermat's Theorem since he was 10. He became a professor at Princeton University in the United states in the 1980s. He got married shortly after embarking on his intellectual odyssey and told his wife about his obsession during their honeymoon. They had two children, and his family gave him all the comfort and recreation he needed. He knew that his colleagues would not leave him alone if he told them the true nature of his research, and he felt that he needed to work with total concentration, without any distraction. During the latter stages of his work, he must also have feared that someone might leapfrog him and attain victory by building on his ideas. — Shortly before publication he did confide in a trusted colleague who helped him examine the proof. As for the nature of his work, he has likened it to stumbling around in a dark room in an unfamiliar mansion. Gradually you get some sense of where the furniture is, and how various objects feel to the touch. After six months you find the light switch and everything becomes clear! Then you move on to the next darkened room... One can only try to imagine the emotional rollercoaster Wiles must
have been on in 1993-94. First a series of lectures at Cambridge University
before an elite audience in an electrified atmosphere, culminating in
Wiles' simply writing Fermat's formula on the blackboard and saying:
I am reminded of Harry Martinson's
How certain can we be that there are no additional holes in Wiles' proof? The probability should be rather low, now that it has been out for 15 years, and has attracted great interest from the most eminent experts in the field. Fermat's Theorem is much more than a historical curiosity, because whole branches of mathematics have sprouted from investigations related to the Theorem. — Regrettably, perhaps, mathematics has advanced so far that only the experts can express an opinion about a proof with any claim to credibility. Gone forever are the simple days when mathematical proofs could be demonstrated to schoolchildren, e.g. that the square root of two cannot be a rational number, or that there must be an infinite number of primes. In the same vein, it may be even more difficult to pass judgment on mathematical theorems proven with the assistance of computers. (Wiles did not use one.) For instance, there is a theorem which says that any map, no matter how complex, requires no more than four colors to ensure that regions with a common border are assigned different colors. To a layman, it is surprising that this simple theorem was not proved to be true until 1976, using a computer to check 1936 different configurations. Checking the proof "by hand" seems impractical. Instead the proof must involve checking the programming of the computer itself. (This aspect is discussed in ref. 7 below.) — And before long, computers may well turn into more than mere assistants in finding mathematical proofs, with staggering implications!
1. Fermat's Last Theorem
(1996). A documentary
film. 45 min. 2. An interview with Andrew Wiles. 3. Wikipedia article on Fermat, with many links. 4. Wikipedia article on Fermat's Last Theorem, with many links. 5. Wikipedia overview of Wiles' proof of Fermat's Last Theorem, with many links. 6. Wiles'
1995 article in Annals of Mathematics: "Modular Elliptic Curves
and Fermat's Last Theorem". Highly technical. Unreadable to most
of us, but it has a certain charm... 7. 2005 Web
article by Wim H. Hesselink. |
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Last
edited or checked June 5, 2013. Broken links fixed March 16, 2018
and February 14, 2024. |

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