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Fermat's Last Theorem

Andrew Wiles has now proved Fermat's Last Theorem, but to most of us it's still as much of a mystery as it ever was. In Fermat's Last Theorem Amir Aczel gives us the background to this proof, describing the evolution of the mathematics involved, and the stories of mathematicians who have tried in the past to prove it but failed. Several convinced themselves that they had cracked it, only to have a fatal flaw discovered in their proof. The book is written in a non-technical way, with hardly any mathematical notation, and so it will appeal to the non-mathematical reader who wants to find out what all the fuss was about.

Simon Singh has written a book with the same title, and it's natural to compare the two. Well Aczel's is shorter, so it might appeal to someone wanting a less detailed read. The historical phase gives more information on the mathematicians involved than just their work related to FLT. Hence the book seems to wander around more than Singh's - one gets less of the idea of a thread running through the book.. There is more treatment of modular forms - their history, and simple descriptions, as well as the stories of Shimura, Taniyama and Weil. But in conclusion I would say that this book is aimed at those wanting an easy to read overview of FLT.

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Paperback 160 pages
ISBN: 0385319460
Salesrank: 479052
Weight:0.08 lbs

Published: 1997 Delta

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Paperback 160 pages
ISBN: 0385319460
Salesrank: 1134949
Weight:0.08 lbs

Published: 1997 Delta

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Paperback 160 pages
ISBN: 0385319460
Salesrank: 229725
Weight:0.08 lbs

Published: 1997 Delta

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Product Description
Over three hundred years ago, a French scholar scribbled a simple theorem in the margin of a book. It would become the world's most baffling mathematical mystery. Simple, elegant, and utterly impossible to prove, Fermat's Last Theorem captured the imaginations of amateur and professional mathematicians for over three centuries. For some it became a wonderful passion. For others it was an obsession that led to deceit, intrigue, or insanity. In a volume filled with the clues, red herrings, and suspense of a mystery novel, Dr. Amir Aczel reveals the previously untold story of the people, the history, and the cultures that lie behind this scientific triumph. From formulas devised for the farmers of ancient Babylonia to the dramatic proof of Fermat's theorem in 1993, this extraordinary work takes us along on an exhilarating intellectual treasure hunt. Revealing the hidden mathematical order of the natural world in everything from stars to sunflowers, Fermat's Last Theorem brilliantly combines philosophy and hard science with investigative journalism. The result: a real-life detective story of the intellect, at once intriguing, thought-provoking, and impossible to put down.

Product Description

Over three hundred years ago, a French scholar scribbled a simple theorem in the margin of a book.  It would become the world's most baffling mathematical mystery.

Simple, elegant, and utterly impossible to prove, Fermat's Last Theorem captured the imaginations of amateur and professional mathematicians for over three centuries.  For some it became a wonderful passion.  For others it was an obsession that led to deceit, intrigue, or insanity.  In a volume filled with the clues, red herrings, and suspense of a mystery novel, Dr.  Amir Aczel reveals the previously untold story of the people, the history, and the cultures that lie behind this scientific triumph.

From formulas devised for the farmers of ancient Babylonia to the dramatic proof of Fermat's theorem in 1993, this extraordinary work takes us along on an exhilarating intellectual treasure hunt.  Revealing the hidden mathematical order of the natural world in everything from stars to sunflowers, Fermat's Last Theorem brilliantly combines philosophy and hard science with investigative journalism.  The result: a real-life detective story of the intellect, at once intriguing, thought-provoking, and impossible to put down.

For me useful ***
I think the most telling thing about this book is that it is out of print and going used for $0.13 from sellers. One thing you learn about mathematics books is: if they are any good at all they hold their value, even used. The major thing the author does is show contempt for the reader by never giving any real equations. I find his end notes probably the most useful and they also show that he had insufficient background to write this book. For me the use of the book is the reference to the mathematicians who did the work historically. I'm disgusted that he never wrote out the modular form equation that is on what the whole proof rests. For that he is a cheat as an author: people aren't dumb and they don't need this level of dumb me down text.

For me useful ***

I think the most telling thing about this book is that
it is out of print and going used for $0.13 from sellers.
One thing you learn about mathematics books is:
if they are any good at all they hold their value, even used.
The major thing the author does is show contempt for the reader by
never giving any real equations. I find his end notes
probably the most useful and they also show that he had insufficient background to write this book. For me the use of the book is the reference
to the mathematicians who did the work historically.
I'm disgusted that he never wrote out the modular form
equation that is on what the whole proof rests.
For that he is a cheat as an author:
people aren't dumb and they don't need this level of dumb me down text.

No mathematical depth and it sometimes reads like a children's novel ***
This is one of the books that appeared in print shortly after the announcement was made that Andrew Wiles had found a proof of Fermat's Last Theorem. In many ways, the public reaction to the announcement was surprising; there was a great deal of interest in the problem and therefore, publishers rushed to get a popular book out on the subject. This book is one in the category of popular books, there is very little in the way of complicated mathematics and even then it is not really needed to understand the contents. Aczel weaves a complicated historical drama and often interjects verbiage more suited to a children's novel. For example, on page 133, there is the passage: "Wiles walked around the department for several hours. He didn't know whether he was awake or dreaming. Every once in a while, he would return to his desk to see if his fantastic finding was still there - and it was. He went home. " Many if not most of the greatest mathematicians of the ages are mentioned at some point in this book. While none of them are done in depth, there is enough for you to recognize the convoluted paths that solutions to complex problems often take. Furthermore mathematics is replete with "Aha!" moments where centuries of effort are suddenly distilled into a clear solution. Wiles had such a moment when he patched a serious hole in his original proof. If you are interested in a detailed explanation of what Fermat's Last Theorem is and how it was proven, you need to look elsewhere. However, if a superficial explanation is the point of your interest and can tolerate some occasional poetic license in the area of exaggeration, then this book will work for you.

No mathematical depth and it sometimes reads like a children's novel ***

This is one of the books that appeared in print shortly after the announcement was made that Andrew Wiles had found a proof of Fermat's Last Theorem. In many ways, the public reaction to the announcement was surprising; there was a great deal of interest in the problem and therefore, publishers rushed to get a popular book out on the subject.
This book is one in the category of popular books, there is very little in the way of complicated mathematics and even then it is not really needed to understand the contents. Aczel weaves a complicated historical drama and often interjects verbiage more suited to a children's novel. For example, on page 133, there is the passage:

"Wiles walked around the department for several hours. He didn't know whether he was awake or dreaming. Every once in a while, he would return to his desk to see if his fantastic finding was still there - and it was. He went home. "

Many if not most of the greatest mathematicians of the ages are mentioned at some point in this book. While none of them are done in depth, there is enough for you to recognize the convoluted paths that solutions to complex problems often take. Furthermore mathematics is replete with "Aha!" moments where centuries of effort are suddenly distilled into a clear solution. Wiles had such a moment when he patched a serious hole in his original proof.
If you are interested in a detailed explanation of what Fermat's Last Theorem is and how it was proven, you need to look elsewhere. However, if a superficial explanation is the point of your interest and can tolerate some occasional poetic license in the area of exaggeration, then this book will work for you.

350 Year Old Detective Story ****
In 1637 Pierre de Fermat scribbled some notes in a margin of a mathematics book and the world has been talking about it ever since. Was his "last theorem" ever real or did he simply invent a story to boost his ego? Perhaps we will never know, but three centuries later Prof. Andrew Wiles did provide the solution to the greatest mathematical conundrum in history (or at least the most famous). Some people argue that Prof. Wiles used a mathematics unknown to Fermat, but if the Egyptians could build the pyramids in a mere 23 years (a feat that would take us with all our modern technology more than a century, if the money and determination could even be acquired) perhaps the knowledge of Fermat was lost over the centuries as well. We are certainly rediscovering things ancient people knew, so who is to say Fermat did not have a solution? Though slow at times this is a fantastic detective story for anyone who loves mathematics (don't worry, you don't have to be a genius to enjoy it). A wonderful afternoon read.

350 Year Old Detective Story ****

In 1637 Pierre de Fermat scribbled some notes in a margin of a mathematics book and the world has been talking about it ever since. Was his "last theorem" ever real or did he simply invent a story to boost his ego? Perhaps we will never know, but three centuries later Prof. Andrew Wiles did provide the solution to the greatest mathematical conundrum in history (or at least the most famous). Some people argue that Prof. Wiles used a mathematics unknown to Fermat, but if the Egyptians could build the pyramids in a mere 23 years (a feat that would take us with all our modern technology more than a century, if the money and determination could even be acquired) perhaps the knowledge of Fermat was lost over the centuries as well. We are certainly rediscovering things ancient people knew, so who is to say Fermat did not have a solution?

Though slow at times this is a fantastic detective story for anyone who loves mathematics (don't worry, you don't have to be a genius to enjoy it). A wonderful afternoon read.

An Introductory Book ****
While I did enjoy this book, I believe that it only serves as an introductory preface to the theorem. It does present all of the main ideas, but it fails to provide a network with which to tie them all together. When used with another book, such as Fermats Enigma by Simon Singh, many of the ideas come together so that the reader can see where Andrew Wiles proof came from and how it works. I would recommend this book for those who have very little knowledge of the theorem and would like to know a general outline.

An Introductory Book ****

While I did enjoy this book, I believe that it only serves as an introductory preface to the theorem. It does present all of the main ideas, but it fails to provide a network with which to tie them all together. When used with another book, such as Fermats Enigma by Simon Singh, many of the ideas come together so that the reader can see where Andrew Wiles proof came from and how it works. I would recommend this book for those who have very little knowledge of the theorem and would like to know a general outline.

Interesting idea, wrong direction **
I think a book about the solution to Fermat's last theorem is an excellent idea. However, I think that this book ultimately fails because Aczel takes too much time discussing the history of the theorem and the developement of mathematics up until the point when the problem was solved in 1993. More than two centuries of mathematics is pigeon-holed into a book that is under 200 pages. In that respect, I think that the author was overly ambitious in his aim; it is simply impossible to explain topology in 3 or 4 pages. I would have rather seen the story approached from the human, rather than the math, side of things.

Interesting idea, wrong direction **

I think a book about the solution to Fermat's last theorem is an excellent idea. However, I think that this book ultimately fails because Aczel takes too much time discussing the history of the theorem and the developement of mathematics up until the point when the problem was solved in 1993. More than two centuries of mathematics is pigeon-holed into a book that is under 200 pages. In that respect, I think that the author was overly ambitious in his aim; it is simply impossible to explain topology in 3 or 4 pages. I would have rather seen the story approached from the human, rather than the math, side of things.

OK, But Not the Best Book on Fermat's Last Theorem **
I accidentally read this instead of the book my brother really recommended to me, Fermat's Enigma, by Simon Singh. (q.v.) I subsequently read Singh's book, and it is MUCH better than Aczel's. This book tells the story, but with a bland high school textbook style, and with too much emphasis on the gossipy politics involved. If you are, like me, a non-mathematician, I think you will enjoy the Singh book (which is based on the popular BBC TV special about FLT) much more than this one.

OK, But Not the Best Book on Fermat's Last Theorem **

I accidentally read this instead of the book my brother really recommended to me, Fermat's Enigma, by Simon Singh. (q.v.) I subsequently read Singh's book, and it is MUCH better than Aczel's. This book tells the story, but with a bland high school textbook style, and with too much emphasis on the gossipy politics involved. If you are, like me, a non-mathematician, I think you will enjoy the Singh book (which is based on the popular BBC TV special about FLT) much more than this one.

Very good history of Fermat's Last Theorem. ****
This book described the history of Fermat's last theorem. It also described the history of some of the theories that Andrew Wiles built upon to solve Fermat's last theorem. For example, it gives an in-depth account of how Wiles proved that all elliptic curves are modular, thus drawing the world closer to solving Fermat's last theorem. It is a must-read for anyone interested in high-level mathematics.

Very good history of Fermat's Last Theorem. ****

This book described the history of Fermat's last theorem. It also described the history of some of the theories that Andrew Wiles built upon to solve Fermat's last theorem. For example, it gives an in-depth account of how Wiles proved that all elliptic curves are modular, thus drawing the world closer to solving Fermat's last theorem. It is a must-read for anyone interested in high-level mathematics.

A journey into history ruined **
Unfortunately, Mr. Aczel has lost a golden opportunity to bring out the history of mathematics and mathematicians. His vignettes are enticing but ultimately perfunctory and unsatisfying. He fails to connect the dots in a meaningful way and so the mathematicians he portrays remain both unrelated to each other and mere sketches.

A journey into history ruined **

Unfortunately, Mr. Aczel has lost a golden opportunity to bring out the history of mathematics and mathematicians. His vignettes are enticing but ultimately perfunctory and unsatisfying. He fails to connect the dots in a meaningful way and so the mathematicians he portrays remain both unrelated to each other and mere sketches.

an error: Pythagoras couldn't have possib visited Alexandria ****
Alexandria was founded by Alexander the Great 200 years after Pythagoras's death. But I am enjoing the book any way

an error: Pythagoras couldn't have possib visited Alexandria ****

Alexandria was founded by Alexander the Great 200 years after Pythagoras's death. But I am enjoing the book any way

close but no cigar **
This is a nice book which states without any proof or justification a fair number of conclusions. I bought it expecting something on the order William Dunham's excellent book, Journey Through Genius. In JTG, Dunham gives not only the tenor of the times and the theorems, but also derivations and proofs. Bottom line: if you want to see the whole thing, this doesn't have it. If you want just a cursory overview of who and what was going on at the time, this might be for you.

close but no cigar **

This is a nice book which states without any proof or justification a fair number of conclusions. I bought it expecting something on the order William Dunham's excellent book, Journey Through Genius. In JTG, Dunham gives not only the tenor of the times and the theorems, but also derivations and proofs. Bottom line: if you want to see the whole thing, this doesn't have it. If you want just a cursory overview of who and what was going on at the time, this might be for you.

Misses the target ***
Someone who wants to report events in a complex technical field to laypersons has two choices. First, attempt to explain the content in nontechnical language. Second, concentrate on the personages involved and help us relate to them as human beings. Aczel fails on both counts. He barely even attempts to cover the technical issues involved. Readers will come away from this book knowing virtually nothing about the mathematics entailed in the proof of Fermat's Last Theorem, other than that it builds on topics developed over thousands of years by many contributors. He can hardly be faulted for this, since the math required for understanding the proof is extremely dense and well beyond the capacity of any but graduate-level mathematicians. It is on the personal level that Aczel really fails. His descriptions of most of the mathematicians covered read as if they had been lifted from a poorly-written encyclopedia. He glosses over them and their work so lightly that we are left completely unsatisfied. The question is, "Why?" He could have extended the book beyond its scant 137 pages and given us more detail about the players and explained some of the simpler mathematics. This would have produced a much better book. The reason why this book gets three stars, instead of one, is its coverage of the Taniyama-Shimura-Weil-Serre controversy. This is actually interesting and reasonably well-written. If this had been excerpted and placed in a Sunday supplement, it would have been an admirable effort. The net is that if you want to know anything about the mathematics, or details about the people, look elsewhere. If you only want to know the barest outline of what all the fuss is about, this will suffice.

Misses the target ***

Someone who wants to report events in a complex technical field to laypersons has two choices. First, attempt to explain the content in nontechnical language. Second, concentrate on the personages involved and help us relate to them as human beings. Aczel fails on both counts. He barely even attempts to cover the technical issues involved. Readers will come away from this book knowing virtually nothing about the mathematics entailed in the proof of Fermat's Last Theorem, other than that it builds on topics developed over thousands of years by many contributors. He can hardly be faulted for this, since the math required for understanding the proof is extremely dense and well beyond the capacity of any but graduate-level mathematicians.

It is on the personal level that Aczel really fails. His descriptions of most of the mathematicians covered read as if they had been lifted from a poorly-written encyclopedia. He glosses over them and their work so lightly that we are left completely unsatisfied. The question is, "Why?" He could have extended the book beyond its scant 137 pages and given us more detail about the players and explained some of the simpler mathematics. This would have produced a much better book.

The reason why this book gets three stars, instead of one, is its coverage of the Taniyama-Shimura-Weil-Serre controversy. This is actually interesting and reasonably well-written. If this had been excerpted and placed in a Sunday supplement, it would have been an admirable effort. The net is that if you want to know anything about the mathematics, or details about the people, look elsewhere. If you only want to know the barest outline of what all the fuss is about, this will suffice.

one star for the argument and one for the effort, but... **
For those who read Italian: questo libro e' un'accozzaglia di brevi excursus senza legami fra loro. Quando avrete finito di leggerlo ne saprete come prima, al massimo avra' stimolato la vostra curiosita'. A collection of small notes disconnected from each other. Quite a pity.

one star for the argument and one for the effort, but... **

For those who read Italian: questo libro e' un'accozzaglia di brevi excursus senza legami fra loro. Quando avrete finito di leggerlo ne saprete come prima, al massimo avra' stimolato la vostra curiosita'.
A collection of small notes disconnected from each other. Quite a pity.

By the Numbers ****
This is an exceptional book because the author does a great job in laying out to the layman how the incredibly difficult solution to this simple looking equation was achieved in terms most could understand. The bulk of the book is kind of a history of number theory in which the author gives mention to many great feats in mathematics that had to be achieved before the solution to Fermat's Last Theorem could be devised. It really amplifies the the words of Sir Isaac Newton, "If I have seen further, it is because I have stood on the shoulders of giants".

By the Numbers ****

This is an exceptional book because the author does a great job in laying out to the layman how the incredibly difficult solution to this simple looking equation was achieved in terms most could understand.

The bulk of the book is kind of a history of number theory in which the author gives mention to many great feats in mathematics that had to be achieved before the solution to Fermat's Last Theorem could be devised. It really amplifies the the words of Sir Isaac Newton, "If I have seen further, it is because I have stood on the shoulders of giants".

What, an interesting Math book!? *****
I would have thought the only way to make a Math book interesting would be to have it be a pop up book where the Numbers would start attacking you or something. Let's face it, math blows bit time. This makes Aczel's work even more amazing. This relatively small book reads even quicker than its size. I completed it in one day - a weekday, with a full day of work no less. Akzel's turns the proof of a 300-year-old equation into a great work of literature. He goes through the proof in a unique way, by describing the history of each part of the proof chronologically. He give mathematical history lessons stretching from Babylonian times to the present day in a way that any layman can understand. Even if you have no interest in numbers or equations, this book will fascinate you. It helps me understand why professors devote their whole lives to mathematics. Heck, it even got me a little interested in Math as well (of course I snapped out of once the Simpsons came on). I would highly recommend this book to anyone.

What, an interesting Math book!? *****

I would have thought the only way to make a Math book interesting would be to have it be a pop up book where the Numbers would start attacking you or something. Let's face it, math blows bit time. This makes Aczel's work even more amazing.

This relatively small book reads even quicker than its size. I completed it in one day - a weekday, with a full day of work no less. Akzel's turns the proof of a 300-year-old equation into a great work of literature. He goes through the proof in a unique way, by describing the history of each part of the proof chronologically. He give mathematical history lessons stretching from Babylonian times to the present day in a way that any layman can understand.

Even if you have no interest in numbers or equations, this book will fascinate you. It helps me understand why professors devote their whole lives to mathematics. Heck, it even got me a little interested in Math as well (of course I snapped out of once the Simpsons came on).

I would highly recommend this book to anyone.

On the Right Track but Flawed **
Amir D. Aczel's _Fermat's Last Theorem_ starts with great promise. Aczel begins by describing Andrew Wiles' initial, although flawed, surprise presentation of a proof of Fermat's Last Theorem--one of the "Holy Grails" of mathematics--at a 1993 conference. Here, Aczel writes with gripping suspense. You can't wait to read on and find out all the details--a summary of the solution unfolding like a mystery novel as Wiles spells out the proof on the blackboard, an account of the reaction of Wiles' colleagues, an explanation of the hole in the proof that was soon after discovered, and the tale of how Wiles plugged the hole. But after only a few pages, Aczel takes a sidestep to tell a bit of the history of Pierre de Fermat and the origin of the theorem. This is understandable, since the reader needs some background information on the nature of the problem, its difficulty, and its importance before we get back to the proof. However, the Fermat detour is only the first of many, and the next 100 pages (in a book only 136 pages long) amount to one long alternate route explaining the mathematics that led to Fermat's conjecture and the mathematics that grew out of attempts to prove it. Unfortunately, there are some serious flaws with the approach and the overall conception of the book. _Fermat's Last Theorem_ is written for interested laypersons. That idea in itself is problematic in that the mathematics behind the proof encompasses a huge swath of the entire field, including many complex graduate-level topics. It is still possible to tackle the job, but Aczel, or his publisher, further compounded the problem by limiting the book to 136 relatively scant pages. Aczel's solution is to handle the book as a cursory survey of the personalities and ideas that contribute to the problem and solution. Each personality receives only a few pages, and the ideas are presented in a way that they'll probably further confuse a novice yet frustrate a more serious student or amateur who would like to really _understand_ some of the mathematics--not just know the names of some of the ideas. Worse, Aczel never bothers to really tie the ideas together and relate them all to solving Fermat's Last Theorem--in retrospect many just hang like forgotten laundry. Additionally, Aczel loses his intriguing, suspenseful voice soon after the material on Fermat begins and barely recovers it near the end. The final result is a very shallow history of mathematics where novices will forget 80% of what they read by the next day and serious students and amateurs will feel that they don't know much more than when they began. It would have been wiser to expand the book to at least four times its current size, spend more time on each topic, and present more serious mathematical material in a large number of sidebars, which novices could skip. It would have also been wiser to maintain the Wiles story and lay out a simplified version of the proof step-by-step, delving into background material as necessary. As written, the best we can hope for is that Fermat's Last Theorem might whet your appetite for a more in-depth study. Aczel's writing is not bad, and I'm confident he knows his subject--if he'd only tell us about it. It's a shame that such interesting material is given such a light treatment.

On the Right Track but Flawed **

Amir D. Aczel's _Fermat's Last Theorem_ starts with great promise. Aczel begins by describing Andrew Wiles' initial, although flawed, surprise presentation of a proof of Fermat's Last Theorem--one of the "Holy Grails" of mathematics--at a 1993 conference. Here, Aczel writes with gripping suspense. You can't wait to read on and find out all the details--a summary of the solution unfolding like a mystery novel as Wiles spells out the proof on the blackboard, an account of the reaction of Wiles' colleagues, an explanation of the hole in the proof that was soon after discovered, and the tale of how Wiles plugged the hole.

But after only a few pages, Aczel takes a sidestep to tell a bit of the history of Pierre de Fermat and the origin of the theorem. This is understandable, since the reader needs some background information on the nature of the problem, its difficulty, and its importance before we get back to the proof. However, the Fermat detour is only the first of many, and the next 100 pages (in a book only 136 pages long) amount to one long alternate route explaining the mathematics that led to Fermat's conjecture and the mathematics that grew out of attempts to prove it.

Unfortunately, there are some serious flaws with the approach and the overall conception of the book. _Fermat's Last Theorem_ is written for interested laypersons. That idea in itself is problematic in that the mathematics behind the proof encompasses a huge swath of the entire field, including many complex graduate-level topics. It is still possible to tackle the job, but Aczel, or his publisher, further compounded the problem by limiting the book to 136 relatively scant pages. Aczel's solution is to handle the book as a cursory survey of the personalities and ideas that contribute to the problem and solution. Each personality receives only a few pages, and the ideas are presented in a way that they'll probably further confuse a novice yet frustrate a more serious student or amateur who would like to really _understand_ some of the mathematics--not just know the names of some of the ideas. Worse, Aczel never bothers to really tie the ideas together and relate them all to solving Fermat's Last Theorem--in retrospect many just hang like forgotten laundry. Additionally, Aczel loses his intriguing, suspenseful voice soon after the material on Fermat begins and barely recovers it near the end. The final result is a very shallow history of mathematics where novices will forget 80% of what they read by the next day and serious students and amateurs will feel that they don't know much more than when they began.

It would have been wiser to expand the book to at least four times its current size, spend more time on each topic, and present more serious mathematical material in a large number of sidebars, which novices could skip. It would have also been wiser to maintain the Wiles story and lay out a simplified version of the proof step-by-step, delving into background material as necessary. As written, the best we can hope for is that Fermat's Last Theorem might whet your appetite for a more in-depth study. Aczel's writing is not bad, and I'm confident he knows his subject--if he'd only tell us about it. It's a shame that such interesting material is given such a light treatment.