- Hardcover: 240 pages
- Publisher: Wiley-Interscience; 1st edition (February 16, 1996)
- Language: English
- ISBN-10: 0471062618
- ISBN-13: 978-0471062615
- Product Dimensions: 6.4 x 0.9 x 9.6 inches
- Shipping Weight: 1.4 pounds (View shipping rates and policies)
- Average Customer Review: 11 customer reviews
- Amazon Best Sellers Rank: #3,102,340 in Books (See Top 100 in Books)
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Notes on Fermat's Last Theorem (Canadian Mathematical Society Series of Monographs and Advanced Texts) 1st Edition
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Have you ever wanted a math book that you could dip into like a favorite, inspired novel? One in which every page has a delicious quote, a provoking viewpoint, or a novel insight? A book that when read for the third time still makes you think or smile? A book that you can't put down, finding yourself reading on, even when you only picked it up to check on one little fact? This is Van der Poorten's polished, eccentric, opinionated, and inspiring Notes on Fermat's Last Theorem. We need more mathematics books like this.
...Finally, let me repeat that Van der Poorten's monograph is a wonderful mathematics book, which dares to breach the stylistic barriers that usually impede understanding. It encompasses a lot of material, from elementary to very deep, but remains accessible. I expect it will turn a lot of people on to number theory and arithmetic geometry, and indeed the beauty of mathematics as a whole. -- American Mathematical Monthly A Publication of the American Mathematical Society
From the Publisher
This is one of the first books to deal with Fermat's theorem and its proof discovered by Andrew Wiles, including a succinct discussion of Wiles' proof and its implications. Each chapter explains a separate area of number theory as it pertains to Fermat's last theorem and combined, presents a concise history of the theorem. The engaging writing style makes the text accessible for non-math students.
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There are other books about FLT written specifically for non-mathematicians. They pretend to explain what Wiles did, but that is practically impossible to do in any meaningful way. If you want to go that route, try "Fearless Symmetry" by Ash and Gross. If you think you understand the last chapters in it, maybe you are mathematically talented after all!
I rave about this book because, in addition to some technical information I am trained enough to understand, the author conveyed the incredible drama of Wiles' achievement so well, especially in contrast to the failures over hundreds of years of many expert mathematicians (well, they did have partial successes - Kummer, Vandiver, Faltings et al - but those were not front page news for the New York Times). And what added to that drama was Wiles' initial failure, an irredeemable gap in his first proof; fortunately he found a different method leading to a correct proof with the help of Taylor. Also, having read Wiles' final correct paper in the Annals of Mathematics (and not understanding it), I saw that he generously acknowledged all the preceding results and techniques by so many other fine mathematicians upon which his work was based. In other words, although Wiles deserves all the acclaim he has received, it still was primarily an achievement over a long period of time of a whole group of very able mathematicians who have not been knighted like Wiles. He is more like the player who wins the most valuable player award for the team that wins the Super Bowl or the World Series - it was the whole team that won, not just that player.
I highly recommend this book - yes, especially for those trained in mathematics, but also for those willing to read it just for the human interest aspects supplementing all that math., a great story told brilliantly.
The contents are loosely related lectures introducing (and only introducing - this isn't a summary of Wiles' proof) topics in number theory necessary for proving FLT. Each lecture is followed by "Notes and Remarks" often containing more advanced material that is lengthier than the lecture itself. While this separation is good in itself, the lectures still require math far beyond high school and in some cases require graduate work. Lecture 4 starts with a cyclotomic field that is a concept well beyond high school. Lecture 8 starts with the Riemann zeta function that, despite the fact that a high school student can understand it as an infinite series, requires for its appreciation a mathematical sophistication that is not reached until graduate school. Lecture 12 contains the phrase "As regards the zeta function, the trick turns out to be to notice that ... is in fact holomorphic", so one must understand "holomorphic". Note 3 of lecture 13 refers to a residue that, as a topic in complex analysis, is unheard of in high school. Algebraic number fields, the Riemann sphere, poles of complex functions and more all make their appearance, albeit briefly. I truly picked these examples just by opening the book at random multiple times. Woe to the reader who is lacking these topics and more besides.
Pleasure to the reader with the background and, far more importantly, the mathematical sophistication to appreciate this book. As a set of lectures its character is quite different from a number theory textbook. Its audience is small but will no doubt be enthusiastic.
I bought this book in the hope that I could get enough (indices to the) information necessary to understand Wiles' proof of FLT contirbuted to Annals of Mathematics some ten years ago.
The book has simply turned out to be junk for me: it does not provide any enlightenment as to the undestanding of the proof, nor does it offer any recreational delight (supposed? by Poorten himself.) As many reviewers have pointed out, "arrogance" is the exact word to describe the attitude of the authour.
I too would like to have the money re-imbursed.
The bottom line is, if you would like to understand the proof, do not buy this book but follow the "beaten path": study algebra, algebraic number theory, class field theory, modular forms and elliptic curves. I know this sounds (and is) demanding, but it is not impossible since many good textbooks on each subject have appeared these ten years.
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The proof of Fermat's Last Theorem by Andrew Wiles has generated a great interest in number theory and mathematics in...Read more