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Simon Singh

Fermat's Enigma

Note:This book also has the title Fermat's last theorem in the UK.

Andrew Wiles heard about Fermat's last theorem when he was 10 years old, and decided that he was going to prove it. He finally succeeded 30 years later. Fermat's Enigma by Simon Singh tells the story of this proof. Singh tells of how Fermat claimed to have a proof, and of how in the following centuries many people also thought that they had proved the theorem, only for a fault to be found in their work. The attempts did lead to a lot of interesting mathematics though. Thus Fermat's conjecture became more and more famous, and several prizes were offered for its proof.

Although quite a bit of the book deals with the history of mathematics, it isn't one of those books where the author tries to relate as much material as possible to one topic - Singh's book seemed to keep pretty much to the point. Thus there is a chapter on the Taniyama-Shimura conjecture, and quite a bit of the book describes Wiles and how he set about proving the theorem, as well as how he corrected it when a fault was found. The book doesn't really get into the mathematics. There is a bit of maths in the appendices, but even that is fairly simple. Singh has thus written a very readable book which can be enjoyed by a wide readership.

Amazon.com info

Paperback 336 pages
ISBN: 0385493622
Salesrank: 11751
Weight:0.5 lbs

Published: 1998 Anchor

Amazon price $11.16

Marketplace:New from $6.75:Used from $1.98

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Amazon.co.uk info

Paperback 368 pages
ISBN: 1841157910
Salesrank: 4950
Weight:0.66 lbs

Published: 2002 Fourth Estate Ltd

Amazon price £5.99

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Amazon.ca info

Paperback 336 pages
ISBN: 0140268693
Salesrank: 20473

Published: 1998 Penguin Canada (APB)

Amazon price CDN$ 15.33

Marketplace:New from CDN$ 15.33:Used from CDN$ 11.99

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Product Description
xn + yn = zn, where n represents 3, 4, 5, ...no solution "I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain." With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

Product Description

xn + yn = zn, where n represents 3, 4, 5, ...no solution

"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."

With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

Really good read! *****
I am not a avid reader and I read for an hour 2 or 3 times a week i.e if the book is good and after I started reading this book I just couldn't drop it. In fact I used to look up every evening to the time when I can start reading it from where I left off the previous night. Its a great book if you are interested in history of math/science, the great minds, their lives, their hardships and frustrations back then and current trends. You don't need know a whole lot of math to understand this. If you understand the Pythagoras theorem you are good to go:)

Really good read! *****

I am not a avid reader and I read for an hour 2 or 3 times a week i.e if the book is good and after I started reading this book I just couldn't drop it. In fact I used to look up every evening to the time when I can start reading it from where I left off the previous night.
Its a great book if you are interested in history of math/science, the great minds, their lives, their hardships and frustrations back then and current trends. You don't need know a whole lot of math to understand this. If you understand the Pythagoras theorem you are good to go:)

A decent read ***
While this book does make for an enjoyable read, it seems that the whole premise of the book is based on a false pretense. The magic of the quest to solve Fermat's Last Theorem is a direct result of him having written that he has discovered a proof for it. If he had written that he was unsure of a proof it is unlikely that it would have garnered much interest. While what Andrew Wiles has done is a remarkable piece of mathematics, it is most definitely not what Fermat had in mind when he scribbled on the margin of his Arithmetica. [Therefore it is difficult to understand why it should have made any difference to Wiles whether the attempted proof of Fermat by Yoichi Miyaoka in March 1988 was successful or not (as detailed in Chapter 6), as what Wiles was really working on proving was the Taniyama - Shimura Conjecture, and this was not touched upon by Miyaoka.] We are forced to assume that Fermat had erred in writing that he had a proof, which in turn removes the essential ingredient of the drama of this saga, namely figuring out what Fermat had discovered that eluded generations of mathematicians. Singh himself alludes to this in the end of his book, but I believe that this undermines the point of the book as a whole. As to the book itself, the most interesting part for me were the brief presentations of landmark developments in number theory and mathematics of the course of the century. However, any with a strong background in math will already know much of what is covered in the first half, and anyone without a strong background in math will be lost by what is covered in the second half. Obviously, trying to condense the basic ideas of a one hundred page proof that only the top mathematicians in the world can understand into a chapter or two comprehensible to the average reader is an impossible task. This is what Singh attempts to do and fails, although not any worse than any other author would. Bottom line, if you have a healthy interest in math and/or number theory you will enjoy parts of this book, and if you have a degree in math and/or number theory you will enjoy the other parts.

A decent read ***

While this book does make for an enjoyable read, it seems that the whole premise of the book is based on a false pretense. The magic of the quest to solve Fermat's Last Theorem is a direct result of him having written that he has discovered a proof for it. If he had written that he was unsure of a proof it is unlikely that it would have garnered much interest. While what Andrew Wiles has done is a remarkable piece of mathematics, it is most definitely not what Fermat had in mind when he scribbled on the margin of his Arithmetica. [Therefore it is difficult to understand why it should have made any difference to Wiles whether the attempted proof of Fermat by Yoichi Miyaoka in March 1988 was successful or not (as detailed in Chapter 6), as what Wiles was really working on proving was the Taniyama - Shimura Conjecture, and this was not touched upon by Miyaoka.] We are forced to assume that Fermat had erred in writing that he had a proof, which in turn removes the essential ingredient of the drama of this saga, namely figuring out what Fermat had discovered that eluded generations of mathematicians. Singh himself alludes to this in the end of his book, but I believe that this undermines the point of the book as a whole.
As to the book itself, the most interesting part for me were the brief presentations of landmark developments in number theory and mathematics of the course of the century. However, any with a strong background in math will already know much of what is covered in the first half, and anyone without a strong background in math will be lost by what is covered in the second half. Obviously, trying to condense the basic ideas of a one hundred page proof that only the top mathematicians in the world can understand into a chapter or two comprehensible to the average reader is an impossible task. This is what Singh attempts to do and fails, although not any worse than any other author would.
Bottom line, if you have a healthy interest in math and/or number theory you will enjoy parts of this book, and if you have a degree in math and/or number theory you will enjoy the other parts.

Infectiously enthusiastic *****
Who could have thought maths could be so much fun ! Told with infectious enthusiasm, this is the story of pure maths as well as the quest to solve one of its most challenging riddles of all time. Full of fascinating info, this is a true gem.

Infectiously enthusiastic *****

Who could have thought maths could be so much fun ! Told with infectious enthusiasm, this is the story of pure maths as well as the quest to solve one of its most challenging riddles of all time. Full of fascinating info, this is a true gem.

This is how math SHOULD have been taught in school ****
Alongside books like "Fantasia Mathematica", "Flatline" and "E=MC2", Fermat's Enigma does a fantastic job of showing both the human drama of mathematics, as well as the beauty of the science itself. Better than I've ever seen it put before, Singh captures how math is different from every other science - (my summary from pages 18-22) "Math is the pursuit for ultimate truth. Once a mathematical theorom is proven, it is true till the end of time. Scientific proofs, on the other hand, are merely considered highly likely based on the evidence available." And, math is aptly described as a language, a way of talking about everything in the world around us with absolute truth. There is purity. As stated by Pythagoras when describing the shape of rivers, the sound of a musical instrument, the shape of the earth..."Everything is Number". If only we were given that inspiring vision, that clarity of importance, in middle school math...

This is how math SHOULD have been taught in school ****

Alongside books like "Fantasia Mathematica", "Flatline" and "E=MC2", Fermat's Enigma does a fantastic job of showing both the human drama of mathematics, as well as the beauty of the science itself.

Better than I've ever seen it put before, Singh captures how math is different from every other science -

(my summary from pages 18-22)
"Math is the pursuit for ultimate truth. Once a mathematical theorom is proven, it is true till the end of time. Scientific proofs, on the other hand, are merely considered highly likely based on the evidence available."

And, math is aptly described as a language, a way of talking about everything in the world around us with absolute truth. There is purity. As stated by Pythagoras when describing the shape of rivers, the sound of a musical instrument, the shape of the earth..."Everything is Number".

If only we were given that inspiring vision, that clarity of importance, in middle school math...

Excellent reading - how to solve unsolvable *****
You will discover how one day dream can come true. From Pythagoras and Fermat and to Andrew Wiles - Simon Singh will help you to make more than 350 years way to solution of mystery in few hours (or in couple of days). This is really enjoyable historic reading - highly recommended.

Excellent reading - how to solve unsolvable *****

You will discover how one day dream can come true. From Pythagoras and Fermat and to Andrew Wiles - Simon Singh will help you to make more than 350 years way to solution of mystery in few hours (or in couple of days). This is really enjoyable historic reading - highly recommended.

Mathematics as you've never seen it before *****
I was never a fan of maths at school. It did not come easily to me and I failed to see the relevance of trigonometry to my everyday life. I say this so you realise I am not some sort of science geek who was best friends with a calculator. That's because I found this book absolutely fascinating. It made me laugh 3 times in the first 20 pages alone! What Simon Singh does is through Fermat's puzzle describe the history of mathematics from Pythagoras right up to the 1990's. To the layman names like Euclid put in the mind very dull old guys, but they are brought to life with fascinating anecdotes. For example there's the tortured young French mathematician Galois who is dead by 20, his final mathematical theories frantically scribbled down before a dual. Then there's the story that Pythagoras himself drowned a man when he discovered a certain type of number he objected to! All of this is carefully woven into the story of Andrew Wiles' life long obsession to prove Fermat's last theorem a puzzle that had foxed the whole world for over 350 years! Everything is explained in a way that it can be digested by someone who has only a passing interest in maths and as a whole is a remarkable book.

Mathematics as you've never seen it before *****

I was never a fan of maths at school. It did not come easily to me and I failed to see the relevance of trigonometry to my everyday life.

I say this so you realise I am not some sort of science geek who was best friends with a calculator. That's because I found this book absolutely fascinating. It made me laugh 3 times in the first 20 pages alone!

What Simon Singh does is through Fermat's puzzle describe the history of mathematics from Pythagoras right up to the 1990's. To the layman names like Euclid put in the mind very dull old guys, but they are brought to life with fascinating anecdotes. For example there's the tortured young French mathematician Galois who is dead by 20, his final mathematical theories frantically scribbled down before a dual. Then there's the story that Pythagoras himself drowned a man when he discovered a certain type of number he objected to!

All of this is carefully woven into the story of Andrew Wiles' life long obsession to prove Fermat's last theorem a puzzle that had foxed the whole world for over 350 years!

Everything is explained in a way that it can be digested by someone who has only a passing interest in maths and as a whole is a remarkable book.

Interesting, exciting, challenging; great read ****
What I loved the most about this book was it's timeline-structure. Dating back to the Pythagorean ages to the present; I thought this was a brilliant idea. The book is full of interesting stories of what the most famous mathematicians in the world had experienced during their profession. The book reaches out to people on many levels: Women: The story told about Sophie Germain (born in 1776), the daughter of a merchant whom outside of her work shared a great passion for Mathematics. However during this age, female mathematicians were frowned upon, and so to study at the Ecole, she took the identity of a former student at the Academy named August Le Blanc. The academy was unaware that he had left Paris and continued to print lecture notes and problems for him. Germain had been submitting the answers to these problems under his name. As her work progressed she had made a remarkable breakthrough in revealing the proof to Fermat's Last Theorem; and with the help of Gauss, one of the most famous mathematicians. They would keep in regular contact regarding mathematical problems until the day where she had submitted this breakthrough to him, she had also revealed that she in fact, is a woman; and received an astonishing response from Gauss's overwhelming reaction (In the best way possible) - Germain had become an icon for female mathematicians. Mathematicians/People who love maths: Appendixes located in the back of the book where readers with a higher level of mathematical knowledge can read further into the problem with more examples. Musicians: mathematical properties of plucking a string to achieve different tones. Etc. I remember particularly being shocked about Pythagoras's shame. Where one of his students had discovered the concept of irrational numbers, and as Pythagoras failed to understand this concept, he had sent for the student to be drowned, and claimed irrational numbers as the devil's work; absolutely shameful of such a famous and respected mathematician. Again, this could possibly reach the interest of historians. There are so many aspects of the book to talk about but I need to keep this short and sweet. Overall the book was a huge success and covered enough of mathematical history to engage the reader in the problem and allow them to enjoy it at the same time. However I did notice that a lot of other significant people in mathematics were not mentioned, like Muhammad bin Mūsā al-Khwārizmī - who discovered Algebra mathematics. I also feel that towards the end of the book where the story of Andrew Wiles's steps to solving the theorem was slightly lengthy, and to be completely honest, started to bore me (Hence my 4 star rating). I highly recommend this book to anyone interested in mathematics, history, or simply like mysteries and puzzles.

Interesting, exciting, challenging; great read ****

What I loved the most about this book was it's timeline-structure. Dating back to the Pythagorean ages to the present; I thought this was a brilliant idea. The book is full of interesting stories of what the most famous mathematicians in the world had experienced during their profession.

The book reaches out to people on many levels:
Women:
The story told about Sophie Germain (born in 1776), the daughter of a merchant whom outside of her work shared a great passion for Mathematics. However during this age, female mathematicians were frowned upon, and so to study at the Ecole, she took the identity of a former student at the Academy named August Le Blanc. The academy was unaware that he had left Paris and continued to print lecture notes and problems for him. Germain had been submitting the answers to these problems under his name. As her work progressed she had made a remarkable breakthrough in revealing the proof to Fermat's Last Theorem; and with the help of Gauss, one of the most famous mathematicians. They would keep in regular contact regarding mathematical problems until the day where she had submitted this breakthrough to him, she had also revealed that she in fact, is a woman; and received an astonishing response from Gauss's overwhelming reaction (In the best way possible) - Germain had become an icon for female mathematicians.

Mathematicians/People who love maths:
Appendixes located in the back of the book where readers with a higher level of mathematical knowledge can read further into the problem with more examples.

Musicians:
mathematical properties of plucking a string to achieve different tones.

Etc.

I remember particularly being shocked about Pythagoras's shame. Where one of his students had discovered the concept of irrational numbers, and as Pythagoras failed to understand this concept, he had sent for the student to be drowned, and claimed irrational numbers as the devil's work; absolutely shameful of such a famous and respected mathematician. Again, this could possibly reach the interest of historians.

There are so many aspects of the book to talk about but I need to keep this short and sweet. Overall the book was a huge success and covered enough of mathematical history to engage the reader in the problem and allow them to enjoy it at the same time. However I did notice that a lot of other significant people in mathematics were not mentioned, like Muhammad bin Mūsā al-Khwārizmī - who discovered Algebra mathematics. I also feel that towards the end of the book where the story of Andrew Wiles's steps to solving the theorem was slightly lengthy, and to be completely honest, started to bore me (Hence my 4 star rating).

I highly recommend this book to anyone interested in mathematics, history, or simply like mysteries and puzzles.

Better than the Da Vinci Code! *****
This is a very well-written book: high-level mathematics made accessible to all. It is a true adventure story - and if you are also interested in finding out what exactly it is about mathematics that motivates mathematicians - then this is the book to read. Highly recommended.

Better than the Da Vinci Code! *****

This is a very well-written book: high-level mathematics made accessible to all. It is a true adventure story - and if you are also interested in finding out what exactly it is about mathematics that motivates mathematicians - then this is the book to read. Highly recommended.

Fermat's Last Theorem ****
an interesting book about Mathematics and about mathematicians both the famous and not so famous

Fermat's Last Theorem ****

an interesting book about Mathematics and about mathematicians both the famous and not so famous

Dreams come and go, but mathematics is there forever ****
One of my dreams is to understand the proof of this theorem. (Another is to prove the Riemann conjecture, but that's a different history book.) Reading this one didn't get me anywhere nearer this, but on the other hand, neither did the book I got which purports to explain it in some mathematical detail. What this book does give you is an insight into the mathematicians themselves. And on that count it pays in spades. When I read this at the end of the 90's I was considering whether to return to studying maths again after a break of some 15 years or so. After having finished it, I reckoned, yes I would. It's that good. Singh is an excellent writer and conveys the drama of the story impeccably. Unfortunately, as with all books of this nature, it is not possible to go into the mathematical nitty-gritty behind the sweeping curves that make this theorem a thing of beauty - because it's too abstruse a subject. Even as a practising (amateur) mathematician myself, I can't get my head round the aspects of this particular topic. That can be kind of frustrating - but it won't stop me trying. This book is as much about the mathematicians as the mathematics itself. They're an entertaining bunch - there's no such thing as a boring mathematician. Mathematics is next year's new rock and roll.

Dreams come and go, but mathematics is there forever ****

One of my dreams is to understand the proof of this theorem. (Another is to prove the Riemann conjecture, but that's a different history book.) Reading this one didn't get me anywhere nearer this, but on the other hand, neither did the book I got which purports to explain it in some mathematical detail.

What this book *does* give you is an insight into the mathematicians themselves. And on that count it pays in spades. When I read this at the end of the 90's I was considering whether to return to studying maths again after a break of some 15 years or so. After having finished it, I reckoned, yes I would. It's that good.

Singh is an excellent writer and conveys the drama of the story impeccably. Unfortunately, as with all books of this nature, it is not possible to go into the mathematical nitty-gritty behind the sweeping curves that make this theorem a thing of beauty - because it's too abstruse a subject. Even as a practising (amateur) mathematician myself, I can't get my head round the aspects of this particular topic. That can be kind of frustrating - but it won't stop me trying.

This book is as much about the mathematicians as the mathematics itself. They're an entertaining bunch - there's no such thing as a boring mathematician.

Mathematics is next year's new rock and roll.

Never Fails... *****
Simon Singh never fails. This is a great book like all of his others. You really can't go wrong.

Never Fails... *****

Simon Singh never fails. This is a great book like all of his others. You really can't go wrong.

Absolutely absorbing and engaging! *****
Singh writes with great skill of suspense, with minimal of math equations to help readers navigate the path to solving the ultimate math riddle of all time by a lone genius..Profoundly absorbing and engaging! Readers will no doubt also find the appendices helpful and intriguing.

Absolutely absorbing and engaging! *****

Singh writes with great skill of suspense, with minimal of math equations to help readers navigate the path to solving the ultimate math riddle of all time by a lone genius..Profoundly absorbing and engaging! Readers will no doubt also find the appendices helpful and intriguing.

One of the best books I have Read *****
Never thought I would use the words "Romance" "Suspense" "Thriller" and the History of Mathematics in the same sentence. Great book and worth reading. It is a gripping account of the events leading to the solving of one of the greatest puzzles in Mathematics.

One of the best books I have Read *****

Never thought I would use the words "Romance" "Suspense" "Thriller" and the History of Mathematics in the same sentence. Great book and worth reading. It is a gripping account of the events leading to the solving of one of the greatest puzzles in Mathematics.

Amazing Mathematical Saga ****
Singh and Lynch have successfully presented one of the most abstract subjects in a simple to understand language. For those who put down a Maths book by looking at the complex equations: Fear Not, this one does not go too deep into equations and relies more on plain English to convey the point. I think that Appendixes could have been a bit more descriptive. Overall it was a fun read. I highly recommend this one for Mathematics appetite of Not-So-Mathematical.

Amazing Mathematical Saga ****

Singh and Lynch have successfully presented one of the most abstract subjects in a simple to understand language. For those who put down a Maths book by looking at the complex equations: Fear Not, this one does not go too deep into equations and relies more on plain English to convey the point. I think that Appendixes could have been a bit more descriptive. Overall it was a fun read. I highly recommend this one for Mathematics appetite of Not-So-Mathematical.

An Enigma still Not Understood **
I read Singh's FERMAT'S ENIGMA after reading Singh's CODE BOOK. Unfortunately, the latter is by far the better book. Although the CODE BOOK manages to cover both the personal and the quantitative side of the recent revolutions in cryptography, FERMAT'S ENIGMA does not attempt to break into the actual mathematical proofs at all. The result feels like one of those NBC human interest stories that take up airtime from the Olympic Games. The essence is in the math, but we hear instead about the innovators' daily lives.

An Enigma still Not Understood **

I read Singh's FERMAT'S ENIGMA after reading Singh's CODE BOOK. Unfortunately, the latter is by far the better book. Although the CODE BOOK manages to cover both the personal and the quantitative side of the recent revolutions in cryptography, FERMAT'S ENIGMA does not attempt to break into the actual mathematical proofs at all. The result feels like one of those NBC human interest stories that take up airtime from the Olympic Games. The essence is in the math, but we hear instead about the innovators' daily lives.