His history is entertaining and completely readable to the layperson, often including simple examples to illustrate principles and the details hardly ever. Many believe fermat proved his last theorem for n 4, which was. Note that we proved fermat s last theorem in a different way than usual, namely we proved it for a specific couple of numbers a b, for all the powers, in contrast to proving it for a specific power n and all the numbers a b. We show that if the first case of fermat s last theorem is false for prime exponent p then p2 divides qp q for all primes q theorem of the title. There are deep and subtle connections between number theory.
In this paper we show an alternative perspective on fermat s last theorem using notions of classical geometry, trigonometry, reductio ad absurdum, and simple but nonobvious mathematical tricks. Fermat s last theorem by simon singh fourth estate, 1997. Aczel made this great book to show us how such a simple theorem. Aczel attempts to convey the mystery and history of theoretical mathematics in this book around fermat s last theorem.
This book will describe the recent proof of fermat s last theorem by andrew wiles, aided by richard taylor, for graduate students and faculty with a reasonably broad background in algebra. However, trying to blast through some 2000 years of theoretical mathematics in a way that the average reader can understand is a pretty tall order. Note that as a corollary to this theorem we see that fermat s last theorem is true for n 4 k. The famous theorem is known as fermats last theorem, and states. The last person i investigated was carl friedrich gauss 17771855.
Shirali and others published the story of fermats last theorem find, read and cite all the research you need on researchgate. Indeed, part of its achievement is the way it succeeds in combining. Simon singh also produced a rather good tv documentary on it for horizon, a rare example of maths being made the subject of a tv programme. Simple, elegant, and utterly impossible to prove, fermats last theorem captured. I think it is highly improbable that fermat had a simple proof. Shirali and others published the story of fermat s last theorem find, read and cite all the research you need on researchgate. Manindra agarwal iit kanpur fermat s last theorem december 2005 10 30. The paper of taylor and wiles does not close this gap but circumvents it. One of his contributions was the idea of congruence arithmetic. Eulers proof of fermats last theorem for n 3 is incorrect. This seminar discusses the relation between elliptic curves and fermat s last theorem from several points of view, but gives fewer details about the argument of 25 than the present summary. Between its publication and andrew wiless eventual solution over 350 years later, many mathematicians and amateurs.
The purpose of the conference, and indeed this book, is to introduce and explain the many ideas and techniques used by wiles in his proof, and to explain how his result can be combined with ribets theorem and ideas of frey and serre to show, at long last, that fermat s last theorem is true. Arieh shenkman, israel i some philosophical aspects. Pdf the story of fermats last theorem researchgate. The leading thought throughout the derivation is illustrated in fig. We wish to know how many rational points lie on this curve.
Publication date 1996 topics fermat s last theorem publisher. Without loss of generality, z may be assumed to be even. New proof of fermat s little theorem the proof that follows relies on taylors theorem or the binomial theorem. Wiles still remembers how he felt the moment he was introduced to the last theorem. This is a simple consequence of the laws of modular arithmetic. As one can ima this book is a very brief history of a significant part of the mathematics that is presented in the perspective of one of the most difficult mathematical problems fermat s last. The shimurataniyama conjecture is part of a more general philosophy. When one supercube made up of unit cubes is subtracted from a. The proof of the fermat s last theorem will be derived utilizing such a geometrical representation of integer numbers raised to an integer power. This conjecture was worked on by many famous mathematicians. As fermat did for the case n 4, euler used the technique of in nite descent. Prove that the sum of two cubes cannot be a cube, i. His books blend historical anecdote, character studies, and hard science.
Denoting x, y, z are respectively the lengths of the edges of the distinct three ndimensional cubes, then the above proposition becomes. Is there any hope of an elementary proof of fermats last. The ndimensional cubea new way to prove the fermats. I would recommend starting out with edwards book fermat s last theorem, for analysis of euclids proof of n3. Wiless proof of fermats last theorem is a proof by british mathematician andrew wiles of a. 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 reasonably broad background in algebra. The book was a history of fermat s last theorem, a mathematical problem that had plagued mathematicians since the 17th century.
A balanced book that succeeds in giving the reader a general idea of the mathematics involved. Nigel boston university of wisconsin madison the proof. The only case of fermat s last theorem for which fermat actually wrote down a proof is for the case n 4. Despite the efforts of many mathematicians, the proof would remain incomplete until as. I found this very useful as an example of applications of gaussian integers and eisenstein integers. Chicago manual of style, and the american psychological association apa. The book itself is a short and relatively easy read. Wiles gerd faltings t he proof of the conjecture mentioned in the title was finally completed in september of 1994. Some of the proofs of fermat s little theorem given below depend on two simplifications the first is that we may assume that a is in the range 0. It looked so simple, and yet all the great mathematicians in history couldnt solve it. This section explains what the theorem is, who invented it and who eventually proved it.
Fermats last theorem simple english wikipedia, the free. This paper gives a proof on fermat s last theorem flt for n 3 by firstly reducing the fermat s equation to a cubic equation of one variable and then using tschirnhaus transformation to reduce it to a depressed cubic. Professor who solved fermats last theorem wins maths. Rational points on curves let fx,y 0 be a curve of degree n with rational coe. Ribenboim is one of the top experts about fermat s last theorem and he is to praised for putting these beautiful proofs down. Fermat s last theorem is a popular science book 1997 by simon singh. It says that then there are no triples when a, b and c are integers greater than or equal to one meaning that if n is more than two, a, b and c cannot be natural numbers. Fermat s last theorem talks about what happens when the 2 changes to a bigger whole number. A mistake is much more likely given how many mathematicians since then have made suc. In particular, this finally yields a proof of fermats last theorem. Aczel does a thorough job of describing the problems behind fermat s last theorem including the history of mathematical discoveries that lead to the final solution of the proof in 1993. One of three must be even, whereas the other two are odd.
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