Customer Reviews

Notes on Fermat's Last Theorem (Canadian Mathematical Society Series of Monographs and Advanced Texts)

5 star:		(4)
4 star:		(0)
3 star:		(0)
2 star:		(2)
1 star:		(3)

 

 

This is grossly inaccurately advertised. In the introduction the author states that high school math plus an acquaintance with a first course in linear algebra is sufficient to understand the general flow. This is silly at best.

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.

The book is a bit confusing until you get into it.

The proof of Fermat's Last Theorem by Andrew Wiles has generated a great interest in number theory and mathematics in general. Alf's book is a huge intellectual meal!

For the reader with a casual interest, read the recent article in Scientific American or watch the NOVA program on PBS. This book gets at the heart of the mathematical issues that made Fermat's Last Theorem such a stimulus for mathematics research for the last 350 years.

Van der Porteen has a nerdish style that is partially explained by his biography. Still, the book was an enjoyable stretch for me, and I am glad he put forth the effort!

The cover says this book can be understood by anyone with a basic math background and an interest in formulas. Don't believe it! By only the second chapter, the author assumes, without any real explanation, that you know what a euclidean field is and how continued fractions relate to matrices. The presentation strikes me as arrogant; there are far too many gaps to be filled in by the reader. Maybe I'm dumb, but I did somehow manage to stumble through MIT with 16 straight A's in my undergraduate math courses, and spent three years in graduate school studying number theory. The author should have taken more time to explain, and skipped a lot of the sideshows and self-promotion. If I could return this book I would. I give it a 3 only because the appendices are more fun than the main text.

Look: I am a professor of mathematics (retired) and I did not understand much of the technicalities in this book. So the criticisms by other reviewers that the book was too difficult are correct. It is not an account for the lay person, although if read correctly, a lay person can still get a lot out of browsing through it, because the technical mathematics is peppered with so much history and anecdotes about the living mathematicians involved, plus the marvelous humor of the author, that a lay person could enjoy it greatly with the proper attitude.

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.

This is a splendid book. Covering advanced material yet remaining accessible to beginners is a difficult task, and van der Poorten succeeds admirably. Not only that, it's humorous, light-hearted, and in general a pleasure to read. I highly recommend it to anybody who wants more than a popular treatment of FLT yet doesn't have the background in algebraic number theory and algebraic geometry necessary to comprehend more advanced treatments. Come to think of it, I recommend it to anybody interested in mathematics at all. If you approach it with the understanding that all simplifications of advanced technical topics require accepting a bit of arm waving, I can pretty much guarentee that you'll love it.

Although the author comes over as arrogant, I am, after several years, warming to this book. With concentration and very careful reading I have found that much can be gained from it. It is humorous, witty and iconoclastic. Reading a page here and a paragraph there, I have learned what Mordell's theorem is, almost understood a single paragraph proof of the prime number theorem, and more maths besides.

It is however heavy going and the lectures and notes are in a concentrated form. The cover says the book assumes only one year of university maths. I really doubt this is enough math for this book. So beware.

I quite agree with the reviewer from Massachusetts.
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.

The following claim is way off the mark: "Assumes only one year of university mathematics background even for the more advanced topics."

The text will be usefull to graduate students who want to know what motivates the ideas used in the proof. As such the book is a usefull addition to the literature.

I was expecting a book that clearly and concisely explained the principle behind Fermat's Last Theorem and Andrew Wiles proof. This book does not provide that and I was greatly disappointed.

If the publisher had printed the notes of one of Alf van der Poorten's students, they may have had a better book.

This book has no flow and is unreadable. If there is a connection between the random collection of one paragraph descriptions of mathematical oddities found is this book, then I am at a loss to find it.

I too would have liked my money back.

Andrew Wiles publish a book and save us from these awful amateurish renditions!