Notes on Fermat's Last Theorem

Rating:
Summary: Neither recreational nor instructive
Review: 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. The book makes me want to take up number theory. Anyone out there want to finance me through further university studies?

Rating:
Summary: Not for the faint-hearted
Review: 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. The book makes me want to take up number theory. Anyone out there want to finance me through further university studies?

Rating:
Summary: Neither recreational nor instructive
Review: 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.

Rating:
Summary: A poorly written seemingly random collection of boring notes
Review: 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!

Rating:
Summary: Association of American Publishers Prize
Review: Notes on Fermat's Last Theorem was awarded the Professional/Scholarly Publishing 1996 Award for Excellence in Mathematics by the Association of American Publishers. See http://www.publishers.org/div/psp/winners.html

Rating:
Summary: It's readable even though it's reasonably serious math!

Review: The blurb says: An exciting introduction to number theory as reflected by the history of Fermat's Last Theorem.

By the way. Wiley hasn't been very competent. But they did make the book a beautiful cover. Wiley reprinted the book in early December. I have complained about it seemingly having been out of print.

I can add that the book has been enjoyed both by my mother-in-law [all mathematics omitted] and by Fields Medallists. Here's what some of the 'critics' say:

"The poetry far excels that normally found in math books". Hendrik W Lenstra.
"It sounds just like Alf ...". Win Wheeler (my mother-in-law)
"I love the book. Thanks for writing it. If you're ever in the Cotswolds come and stay". K B MD
"I don't normally write fan letters ...". Walter Feit
"I am now reading --- and enjoying very much --- your 'Notes on FLT' ...". Jean-Pierre Serre
"... it should be bedtime reading for every mathematician". Ram Murty

I think my favourite is Dr Kevin Barraclough's invitation; the Cotswolds are nice.

The blurb next claims:

This book displays the unique talents of author Alfred J van der Poorten in mathematical exposition for mathematicians. Here, mathematics' most famous problem and the ideas underlying its recent solution are presented in a way that appeals to the imagination and leads the reader through related areas of mathematics. The first book to focus on Fermat's Last Theorem since Andrew Wiles presented his celebrated proof, Notes on Fermat's Last Theorem surveys 350 years of mathematical history in an amusing collection of tidbits, anecdotes, footnotes, exercises, limericks, references, illustrations, and more.

Proving that one can both read mathematics and read about it, this thoroughly accessible treatment
Helps students and professionals develop a background in number theory and provides introductions to the various fields of mathematics that are touched upon
Offers insight into the exciting world of mathematical research
Covers a number of areas appropriate for classroom use
Assumes only a year or so of university mathematics even for the more advanced topics
Explains why Fermat surely did not have the proof to his theorem
Examines the efforts of mathematicians over the centuries to solve the problem
Shows how the pursuit of the theorem contributed to the greater development of mathematics

Around 1637, the French jurist Pierre de Fermat scribbled in the margin of his copy of Diophantus' Arithmetica what came to be known as Fermat's Last Theorem, the most famous question in mathematical history. Stating that it is impossible to split a cube into two cubes, or a fourth power into two fourth powers, or any higher power into two like powers, but not leaving behind the marvelous proof he claimed to have had, Fermat prompted three and a half centuries of mathematical enquiry which culminated only recently with the proof of Fermat's Last Theorem by Andrew Wiles.

This book represents the first serious treatment of Fermat's Last Theorem since Wiles' proof. It is based on a series of lectures give by the author to celebrate Wiles' achievement, with each chapter explaining a separate area of number theory as it pertains to Fermat's Last Theorem. Together, they provide a concise history of the problem as well as a brief discussion of Wiles' proof and its implications. Requiring little more than one year of university mathematics and a liking for formulas, this overview provides many useful tips and cites numerous references for those who desire more mathematical detail.

The book's most distinctive feature is its easy-to-read, humorous style, complete with examples, anecdotes, and some of the less well known mathematics underlying the newly discovered proof. In the author's own words, the book deals with "serious mathematics without being too serious about it". Alf van der Poorten demystifies mathematical research, offers an intuitive approach to the subject --- loosely suggesting various definitions and unexplained facts --- and invites the reader to fill in the missing links in some of the mathematical claims.

Let me not trouble you with the Table of Contents (why not look at the book's home page at http://www.mpce.mq.edu.au/~alf/NotesonFLT.html).

But do note that its appendices

Appendix A. Remarks on Fermat's Last Theorem
For those who only want to pretend to have looked at the rest of this book. 187--199

Appendix B. "The Devil and Simon Flagg", by Arthur Porges.
The devil fails where Wiles will succeed. 201--206

Appendix C. "Math Riots Prove Fun Incalculable", by Eric Zorn
Is the FLT truly as important as sport? 207--209

obviously are readable by anyone('s mother-in-law).


Rating:
Summary: Deep insights into Fermat's Last Theorem and mathemtics
Review: 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!

Rating:
Summary: Deep insights into Fermat's Last Theorem and mathemtics
Review: 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.

Rating:
Summary: Disappointing and definitely not accessible
Review: 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.

Rating:
Summary: An illuminating and fascinating introduction to FLT
Review: 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.