What was Fermat's Last Theorem?Date: 07/23/97 at 14:39:52 From: Steve Gardner Subject: Fermat's last theorem If it is not too much trouble, I wonder if you might take the time to explain Fermat's Last Theorem to me. I am an undergraduate in mathematics, early in my degree (I have little formal education in number theory; however, I am really interested in it). I know this is asking the impossible, but please keep the explanation at an easy level. As I said, I am early in my degree, so a somewhat superficial, qualitative answer would be perfect. Date: 07/23/97 at 15:48:58 From: Doctor Rob Subject: Re: Fermat's last theorem In the margin of his copy of a book by Diophantus, Pierre de Fermat wrote that it is possible to have a square be the sum of two squares, but that a cube can not be the sum of two cubes, nor a fourth power be a sum of two fourth powers, and so on. Further, he wrote that he had found a truly marvelous proof which the margin was too small to contain. In modern language, he was stating that the equation x^n + y^n = z^n has no solution in integers x, y, z > 0 and n > 2. Long after all the other statements made by Fermat had been either proved or disproved, this remained; hence it is called Fermat's *Last* Theorem (actually, Conjecture would be more accurate than Theorem). This conjecture was worked on by many famous mathematicians. Fermat himself proved this theorem for n = 4, and Leonhard Euler did n = 3. Special cases were dispatched one after another. New theories were developed to attack this problem, but all attempts at a general proof failed. They failed, that is, until this decade, when, building on work of many famous mathematicians, Prof. Andrew Wiles of Princeton University finally proved it. His method could not have been known to Fermat. Fermat's "truly marvelous proof" is now believed to have been faulty. Is this what you wanted? If not, write back with a better description of what you want, and we will try to comply. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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