When Cambridge mathematician Andrew Wiles announced a solution for Fermat's last theorem in 1993, it electrified the world of mathematics. After a flaw was discovered in the proof, Wiles had to work for another year--he had already laboured in solitude for seven years--to establish that he had solved the 350-year-old problem. Simon Singh's book is a lively, comprehensible explanation of Wiles's work and of the colourful history that has build up around Fermat's last theorem over the years. The book contains some problems that offer a taste for the maths, but it also includes limericks to give a feeling for the quirkier side of mathematicians.

Promising...but disappointing in the end, 28 Oct 2008
The book looks like the author is just postponing the end of the story just repeating and repeating the same ideas. The part of the proof and the attempts to correct the proof are quite disappointing because they are too much redundant. Moreover Singh is sliding some e-mails which don't add anything to the story and are quite "impenetrable". I do not like this way of writing. The author pretends not to use math symbology and math concepts beyond very basic ones, and then he lets go concepts like Hecke algebra, Euler system, "quasi-automorphic representations", i.e. without giving any clue about what they mean.
I think it leaves too much maths unexplained (and in a book about a math conundrum you understand it is a big problem!); I would have loved to see the same ingenuity Derbyshire put in his wonderful "Prime Obsession".

Mathematics as you've never seen it before, 21 May 2008
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, 20 May 2008
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 Mks al-Khwrizm+ - 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!, 20 Mar 2008
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, 10 Jan 2008
an interesting book about Mathematics and about mathematicians both the famous and not so famous

Promising...but disappointing in the end, 28 Oct 2008
The book looks like the author is just postponing the end of the story just repeating and repeating the same ideas. The part of the proof and the attempts to correct the proof are quite disappointing because they are too much redundant. Moreover Singh is sliding some e-mails which don't add anything to the story and are quite "impenetrable". I do not like this way of writing. The author pretends not to use math symbology and math concepts beyond very basic ones, and then he lets go concepts like Hecke algebra, Euler system, "quasi-automorphic representations", i.e. without giving any clue about what they mean.
I think it leaves too much maths unexplained (and in a book about a math conundrum you understand it is a big problem!); I would have loved to see the same ingenuity Derbyshire put in his wonderful "Prime Obsession".

Mathematics as you've never seen it before, 21 May 2008
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, 20 May 2008
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 Mks al-Khwrizm+ - 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!, 20 Mar 2008
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, 10 Jan 2008
an interesting book about Mathematics and about mathematicians both the famous and not so famous

Zero and infinity, 07 Aug 2007
Babylonians invented it, Indians worshipped it, Greeks abhorred it. Zero has been a problematic number for a long time. European mathematicians followed Greek footsteps, until they finally realized how important thing zero was for advanced mathematics.

Seife presents us the history of zero and its sister concept infinity, not only in mathematics, but also in physics and quantum mechanics. Zero is an entertaining book, if a bit light. For quick popular science entertainment purposes it's a good choice. (Review based on the Finnish translation.)

one of the best maths books around, 08 Dec 2006
Being an undergraduate philosopher I've had to read a lot of maths books, and this is by far the best. It's true that you don't need much maths background to understand it, but it's also highly enjoyable for those with a lot of maths or physics knowledge - it links up and explains general assumptions in a way which seems never to occur to most teachers of sciences courses. The proof of 0=1 (and, extrapolating, that winston churchill = a carrot) is excellent and well worth committing to memory just to freak out any maths nerds one knows. Also worth a go is the step-by-step guide to making your own wormhole time machine (Step 1: Make a small wormhole, and attach one end to something really heavy). Really excellent, buy everyone you know a copy for christmas.

Mathematics history, 11 Apr 2003
A very readable book. This book covers the life story of the number zero, and it is a facinating story which is being told.

You do not need to have a better than average understanding of maths to be able to appreciate this book.

A good read, highly recommended.

Review for Zero:the Biography of a Dangerous Idea, 30 Jul 2002
This book was absolutely wonderful, it delves into the history of mathematics, as far back as the creation of numbers themselves. It looks at the contribution that the Greeks, Babylonians and Hindus made to mathematics, and how religion had restricted the development of mathematics. The book was written very well, it felt like a story book, rather than a factual book. I recommend this book for everyone with an interest in Maths, you do not need to be a mathematician to enjoy this book.

Highly Recommended, 23 Sep 2001
This is an excellent history of number Zero. Charles Seife takes you from the start, tracing the ideas of zero and inifity through time and how their concepts have been feared and embraced, how they've affected and forced evolution upon religious, philosophical, societal, and scientific ideas. I think this book should be part of any mathematics course. Highly recommend this book!

e: The Story of a Number begins by describing the transition in mathematics brought about by the introduction of the microchip. Until about 1975, logarithms were every scientist's best friend. They were the basis of the slide rule that was the totemic wand of the trade and were listed in the huge books that were consulted in every library. Then handheld calculators arrived, and within a few years slide rules were museum pieces.

But e remains, the centre of the natural logarithmic function and of calculus. Eli Maor's book is the only more or less popular account of the history of this universal constant. Maor gives human faces to fundamental mathematics, as in his fantasia of a meeting between Johann Bernoulli and JS Bach. e: The Story of a Number would be an excellent choice for a any student of trigonometry or calculus. --Mary Ellen Curtin

Promising...but disappointing in the end, 28 Oct 2008
The book looks like the author is just postponing the end of the story just repeating and repeating the same ideas. The part of the proof and the attempts to correct the proof are quite disappointing because they are too much redundant. Moreover Singh is sliding some e-mails which don't add anything to the story and are quite "impenetrable". I do not like this way of writing. The author pretends not to use math symbology and math concepts beyond very basic ones, and then he lets go concepts like Hecke algebra, Euler system, "quasi-automorphic representations", i.e. without giving any clue about what they mean.
I think it leaves too much maths unexplained (and in a book about a math conundrum you understand it is a big problem!); I would have loved to see the same ingenuity Derbyshire put in his wonderful "Prime Obsession".

Mathematics as you've never seen it before, 21 May 2008
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, 20 May 2008
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 Mks al-Khwrizm+ - 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!, 20 Mar 2008
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, 10 Jan 2008
an interesting book about Mathematics and about mathematicians both the famous and not so famous

Zero and infinity, 07 Aug 2007
Babylonians invented it, Indians worshipped it, Greeks abhorred it. Zero has been a problematic number for a long time. European mathematicians followed Greek footsteps, until they finally realized how important thing zero was for advanced mathematics.

Seife presents us the history of zero and its sister concept infinity, not only in mathematics, but also in physics and quantum mechanics. Zero is an entertaining book, if a bit light. For quick popular science entertainment purposes it's a good choice. (Review based on the Finnish translation.)

one of the best maths books around, 08 Dec 2006
Being an undergraduate philosopher I've had to read a lot of maths books, and this is by far the best. It's true that you don't need much maths background to understand it, but it's also highly enjoyable for those with a lot of maths or physics knowledge - it links up and explains general assumptions in a way which seems never to occur to most teachers of sciences courses. The proof of 0=1 (and, extrapolating, that winston churchill = a carrot) is excellent and well worth committing to memory just to freak out any maths nerds one knows. Also worth a go is the step-by-step guide to making your own wormhole time machine (Step 1: Make a small wormhole, and attach one end to something really heavy). Really excellent, buy everyone you know a copy for christmas.

Mathematics history, 11 Apr 2003
A very readable book. This book covers the life story of the number zero, and it is a facinating story which is being told.

You do not need to have a better than average understanding of maths to be able to appreciate this book.

A good read, highly recommended.

Review for Zero:the Biography of a Dangerous Idea, 30 Jul 2002
This book was absolutely wonderful, it delves into the history of mathematics, as far back as the creation of numbers themselves. It looks at the contribution that the Greeks, Babylonians and Hindus made to mathematics, and how religion had restricted the development of mathematics. The book was written very well, it felt like a story book, rather than a factual book. I recommend this book for everyone with an interest in Maths, you do not need to be a mathematician to enjoy this book.

Highly Recommended, 23 Sep 2001
This is an excellent history of number Zero. Charles Seife takes you from the start, tracing the ideas of zero and inifity through time and how their concepts have been feared and embraced, how they've affected and forced evolution upon religious, philosophical, societal, and scientific ideas. I think this book should be part of any mathematics course. Highly recommend this book!

a fascinating book with a brave title, 09 Jul 2001
There aren't many good maths books out there, but this is definitely one of them. It manages to describe the concepts - mentioned below in other reviews - so well that by the end you wish you could meet the author and have a chat about mathematics; the sign of a really good book.

The level is about 18+ and it will be of great benefit to maths students going to or at university. It was recommended to me by my lecturer; not surprisingly, I ignored him, but I found it a few years later. I kicked myself when i finished...I wish i had read it earlier. The title doesn't help either...it turns you off immediately...so he's either brave or stupid to call it that...!

It is true that e is an extremely important number, and really, it is far more interesting than pi in many ways. Unravelling its history leads to an explanation of many interesting areas of mathematics, and calculus is described well. The explanation of logs wasn't all that great, but it tied the book together.

If you're a maths student, it will help give subjects you cover some background and perspective. You may understand them better too, so...go and read it now!

The pleasure of mathematics, 26 Dec 2000
All students who have undertaken a calculus course know that "e" is a very important number and on eof the cornerstones of modern mathematics; but very few students - I am afraid - know its fascinating story. That's why Eli Maor decided to fill this gap and to write his book on the story of "e": he starts with the invention of logarithms by the Scottish nobleman John Napier and guides the reader in a wonderful voyage through the mathematical discoveries of the last four centuries. In this voyage, the interested reader can meet real giants of mathematics such as Newton, Euler and the Bernoullis; he can study curious mathematical curves such as the logarithmic spiral and the catenary; he can understand how calculus was born and how it developed in the minds of the great mathematicians of the 17th Century. The book is noteworthy because of the crystal-clear mathematical accuracy with which Eli Maor explains the facts of his story; therefore a maths background is necessary to enjoy reading this book. Finally, eli Maor makes his book even more interesting by adding some "capsules" on various subjects, such as the importance of hyperbolic functions, the relationship between music and maths, the beauty of the decorative patterns that use the logarithmic spiral. A book that should be in the library of every maths-loving person.

For mystics, philosophers, or even mathematicians!, 16 Jun 2000
This is a truly excellent book. This is not a collection of bound papers, this is an exhaustive study of e and we are guided by the author's own thoughts and opinions throughout. Collections of papers, although useful in saving us the legwork, are a cop-out. The author(s) does not need to make any personal input at all. It is the author's easy and informative style that makes this book so accessible to such a wide audience. Whether you are a mystic, a philosopher, a numerologist or just an ordinary mathematician, you will not be disappointed with this work!

A-level maths standard, but explained in historical context, 12 May 2000
This book quite clearly explains a lot of well-known theorems and their historical context. It is not "high-brow" or obtuse, as some maths history books can be. It is not necessary to read the proofs if you don't want to. It is not just about "e", but explains a little about pi and i also. The only bit that I found confusing at first was the lack of a worked example of Napiers original logarithm table, which is very early in the book. Neither did I think that there was an explanation of the practical logic behind Napier's original sparse log tables (apart from the fact that they take a long time to create by hand). However, there is a worked example near the end of the book.

An interesting little curiousity..., 12 Feb 2000
I thought this was and excellent book, tracing the story of e from Napier logarithms through to the development of calculus and beyond. The author's style is excellent producing an interesting, easily read, non-technical history which fleshes out some of the great characters in the history mathematics. There are also some really diverting asides. If you've any interest in the history of mathematics, I'd recommend this.

Promising...but disappointing in the end, 28 Oct 2008
The book looks like the author is just postponing the end of the story just repeating and repeating the same ideas. The part of the proof and the attempts to correct the proof are quite disappointing because they are too much redundant. Moreover Singh is sliding some e-mails which don't add anything to the story and are quite "impenetrable". I do not like this way of writing. The author pretends not to use math symbology and math concepts beyond very basic ones, and then he lets go concepts like Hecke algebra, Euler system, "quasi-automorphic representations", i.e. without giving any clue about what they mean.
I think it leaves too much maths unexplained (and in a book about a math conundrum you understand it is a big problem!); I would have loved to see the same ingenuity Derbyshire put in his wonderful "Prime Obsession".

Mathematics as you've never seen it before, 21 May 2008
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, 20 May 2008
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 Mks al-Khwrizm+ - 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!, 20 Mar 2008
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, 10 Jan 2008
an interesting book about Mathematics and about mathematicians both the famous and not so famous

Zero and infinity, 07 Aug 2007
Babylonians invented it, Indians worshipped it, Greeks abhorred it. Zero has been a problematic number for a long time. European mathematicians followed Greek footsteps, until they finally realized how important thing zero was for advanced mathematics.

Seife presents us the history of zero and its sister concept infinity, not only in mathematics, but also in physics and quantum mechanics. Zero is an entertaining book, if a bit light. For quick popular science entertainment purposes it's a good choice. (Review based on the Finnish translation.)

one of the best maths books around, 08 Dec 2006
Being an undergraduate philosopher I've had to read a lot of maths books, and this is by far the best. It's true that you don't need much maths background to understand it, but it's also highly enjoyable for those with a lot of maths or physics knowledge - it links up and explains general assumptions in a way which seems never to occur to most teachers of sciences courses. The proof of 0=1 (and, extrapolating, that winston churchill = a carrot) is excellent and well worth committing to memory just to freak out any maths nerds one knows. Also worth a go is the step-by-step guide to making your own wormhole time machine (Step 1: Make a small wormhole, and attach one end to something really heavy). Really excellent, buy everyone you know a copy for christmas.

Mathematics history, 11 Apr 2003
A very readable book. This book covers the life story of the number zero, and it is a facinating story which is being told.

You do not need to have a better than average understanding of maths to be able to appreciate this book.

A good read, highly recommended.

Review for Zero:the Biography of a Dangerous Idea, 30 Jul 2002
This book was absolutely wonderful, it delves into the history of mathematics, as far back as the creation of numbers themselves. It looks at the contribution that the Greeks, Babylonians and Hindus made to mathematics, and how religion had restricted the development of mathematics. The book was written very well, it felt like a story book, rather than a factual book. I recommend this book for everyone with an interest in Maths, you do not need to be a mathematician to enjoy this book.

Highly Recommended, 23 Sep 2001
This is an excellent history of number Zero. Charles Seife takes you from the start, tracing the ideas of zero and inifity through time and how their concepts have been feared and embraced, how they've affected and forced evolution upon religious, philosophical, societal, and scientific ideas. I think this book should be part of any mathematics course. Highly recommend this book!

a fascinating book with a brave title, 09 Jul 2001
There aren't many good maths books out there, but this is definitely one of them. It manages to describe the concepts - mentioned below in other reviews - so well that by the end you wish you could meet the author and have a chat about mathematics; the sign of a really good book.

The level is about 18+ and it will be of great benefit to maths students going to or at university. It was recommended to me by my lecturer; not surprisingly, I ignored him, but I found it a few years later. I kicked myself when i finished...I wish i had read it earlier. The title doesn't help either...it turns you off immediately...so he's either brave or stupid to call it that...!

It is true that e is an extremely important number, and really, it is far more interesting than pi in many ways. Unravelling its history leads to an explanation of many interesting areas of mathematics, and calculus is described well. The explanation of logs wasn't all that great, but it tied the book together.

If you're a maths student, it will help give subjects you cover some background and perspective. You may understand them better too, so...go and read it now!

The pleasure of mathematics, 26 Dec 2000
All students who have undertaken a calculus course know that "e" is a very important number and on eof the cornerstones of modern mathematics; but very few students - I am afraid - know its fascinating story. That's why Eli Maor decided to fill this gap and to write his book on the story of "e": he starts with the invention of logarithms by the Scottish nobleman John Napier and guides the reader in a wonderful voyage through the mathematical discoveries of the last four centuries. In this voyage, the interested reader can meet real giants of mathematics such as Newton, Euler and the Bernoullis; he can study curious mathematical curves such as the logarithmic spiral and the catenary; he can understand how calculus was born and how it developed in the minds of the great mathematicians of the 17th Century. The book is noteworthy because of the crystal-clear mathematical accuracy with which Eli Maor explains the facts of his story; therefore a maths background is necessary to enjoy reading this book. Finally, eli Maor makes his book even more interesting by adding some "capsules" on various subjects, such as the importance of hyperbolic functions, the relationship between music and maths, the beauty of the decorative patterns that use the logarithmic spiral. A book that should be in the library of every maths-loving person.

For mystics, philosophers, or even mathematicians!, 16 Jun 2000
This is a truly excellent book. This is not a collection of bound papers, this is an exhaustive study of e and we are guided by the author's own thoughts and opinions throughout. Collections of papers, although useful in saving us the legwork, are a cop-out. The author(s) does not need to make any personal input at all. It is the author's easy and informative style that makes this book so accessible to such a wide audience. Whether you are a mystic, a philosopher, a numerologist or just an ordinary mathematician, you will not be disappointed with this work!

A-level maths standard, but explained in historical context, 12 May 2000
This book quite clearly explains a lot of well-known theorems and their historical context. It is not "high-brow" or obtuse, as some maths history books can be. It is not necessary to read the proofs if you don't want to. It is not just about "e", but explains a little about pi and i also. The only bit that I found confusing at first was the lack of a worked example of Napiers original logarithm table, which is very early in the book. Neither did I think that there was an explanation of the practical logic behind Napier's original sparse log tables (apart from the fact that they take a long time to create by hand). However, there is a worked example near the end of the book.

An interesting little curiousity..., 12 Feb 2000
I thought this was and excellent book, tracing the story of e from Napier logarithms through to the development of calculus and beyond. The author's style is excellent producing an interesting, easily read, non-technical history which fleshes out some of the great characters in the history mathematics. There are also some really diverting asides. If you've any interest in the history of mathematics, I'd recommend this.

Absolutely brilliant A **, 17 Apr 2006
The first time I've bothered to leave my thoughts on a book. But this one is well worth a recommendation. A must if you wanna recap or bridge knowledge from GCSE level onwards

Gives easily understood explanations, 31 Mar 2006
I've just started studying maths with the Open University and have found this book invaluable. I haven't really thought above maths since leaving school 30 years ago and so needed a refresher in the basics, algebra, fractions, etc. This book has been a great help!

Fantastic book to help bridge the gap, 12 Feb 2003
I was having real difficulty with the maths portion of my Computer Engineering degree having not done A level maths. This book goes over the concepts needed in everyday language and is easy to follow with helpful tips and assessment sections. A must for anyone who is having problems with maths.

Promising...but disappointing in the end, 28 Oct 2008
The book looks like the author is just postponing the end of the story just repeating and repeating the same ideas. The part of the proof and the attempts to correct the proof are quite disappointing because they are too much redundant. Moreover Singh is sliding some e-mails which don't add anything to the story and are quite "impenetrable". I do not like this way of writing. The author pretends not to use math symbology and math concepts beyond very basic ones, and then he lets go concepts like Hecke algebra, Euler system, "quasi-automorphic representations", i.e. without giving any clue about what they mean.
I think it leaves too much maths unexplained (and in a book about a math conundrum you understand it is a big problem!); I would have loved to see the same ingenuity Derbyshire put in his wonderful "Prime Obsession".

Mathematics as you've never seen it before, 21 May 2008
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, 20 May 2008
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 Mks al-Khwrizm+ - 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!, 20 Mar 2008
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, 10 Jan 2008
an interesting book about Mathematics and about mathematicians both the famous and not so famous

Zero and infinity, 07 Aug 2007
Babylonians invented it, Indians worshipped it, Greeks abhorred it. Zero has been a problematic number for a long time. European mathematicians followed Greek footsteps, until they finally realized how important thing zero was for advanced mathematics.

Seife presents us the history of zero and its sister concept infinity, not only in mathematics, but also in physics and quantum mechanics. Zero is an entertaining book, if a bit light. For quick popular science entertainment purposes it's a good choice. (Review based on the Finnish translation.)

one of the best maths books around, 08 Dec 2006
Being an undergraduate philosopher I've had to read a lot of maths books, and this is by far the best. It's true that you don't need much maths background to understand it, but it's also highly enjoyable for those with a lot of maths or physics knowledge - it links up and explains general assumptions in a way which seems never to occur to most teachers of sciences courses. The proof of 0=1 (and, extrapolating, that winston churchill = a carrot) is excellent and well worth committing to memory just to freak out any maths nerds one knows. Also worth a go is the step-by-step guide to making your own wormhole time machine (Step 1: Make a small wormhole, and attach one end to something really heavy). Really excellent, buy everyone you know a copy for christmas.

Mathematics history, 11 Apr 2003
A very readable book. This book covers the life story of the number zero, and it is a facinating story which is being told.

You do not need to have a better than average understanding of maths to be able to appreciate this book.

A good read, highly recommended.

Review for Zero:the Biography of a Dangerous Idea, 30 Jul 2002
This book was absolutely wonderful, it delves into the history of mathematics, as far back as the creation of numbers themselves. It looks at the contribution that the Greeks, Babylonians and Hindus made to mathematics, and how religion had restricted the development of mathematics. The book was written very well, it felt like a story book, rather than a factual book. I recommend this book for everyone with an interest in Maths, you do not need to be a mathematician to enjoy this book.

Highly Recommended, 23 Sep 2001
This is an excellent history of number Zero. Charles Seife takes you from the start, tracing the ideas of zero and inifity through time and how their concepts have been feared and embraced, how they've affected and forced evolution upon religious, philosophical, societal, and scientific ideas. I think this book should be part of any mathematics course. Highly recommend this book!

a fascinating book with a brave title, 09 Jul 2001
There aren't many good maths books out there, but this is definitely one of them. It manages to describe the concepts - mentioned below in other reviews - so well that by the end you wish you could meet the author and have a chat about mathematics; the sign of a really good book.

The level is about 18+ and it will be of great benefit to maths students going to or at university. It was recommended to me by my lecturer; not surprisingly, I ignored him, but I found it a few years later. I kicked myself when i finished...I wish i had read it earlier. The title doesn't help either...it turns you off immediately...so he's either brave or stupid to call it that...!

It is true that e is an extremely important number, and really, it is far more interesting than pi in many ways. Unravelling its history leads to an explanation of many interesting areas of mathematics, and calculus is described well. The explanation of logs wasn't all that great, but it tied the book together.

If you're a maths student, it will help give subjects you cover some background and perspective. You may understand them better too, so...go and read it now!

The pleasure of mathematics, 26 Dec 2000
All students who have undertaken a calculus course know that "e" is a very important number and on eof the cornerstones of modern mathematics; but very few students - I am afraid - know its fascinating story. That's why Eli Maor decided to fill this gap and to write his book on the story of "e": he starts with the invention of logarithms by the Scottish nobleman John Napier and guides the reader in a wonderful voyage through the mathematical discoveries of the last four centuries. In this voyage, the interested reader can meet real giants of mathematics such as Newton, Euler and the Bernoullis; he can study curious mathematical curves such as the logarithmic spiral and the catenary; he can understand how calculus was born and how it developed in the minds of the great mathematicians of the 17th Century. The book is noteworthy because of the crystal-clear mathematical accuracy with which Eli Maor explains the facts of his story; therefore a maths background is necessary to enjoy reading this book. Finally, eli Maor makes his book even more interesting by adding some "capsules" on various subjects, such as the importance of hyperbolic functions, the relationship between music and maths, the beauty of the decorative patterns that use the logarithmic spiral. A book that should be in the library of every maths-loving person.

For mystics, philosophers, or even mathematicians!, 16 Jun 2000
This is a truly excellent book. This is not a collection of bound papers, this is an exhaustive study of e and we are guided by the author's own thoughts and opinions throughout. Collections of papers, although useful in saving us the legwork, are a cop-out. The author(s) does not need to make any personal input at all. It is the author's easy and informative style that makes this book so accessible to such a wide audience. Whether you are a mystic, a philosopher, a numerologist or just an ordinary mathematician, you will not be disappointed with this work!

A-level maths standard, but explained in historical context, 12 May 2000
This book quite clearly explains a lot of well-known theorems and their historical context. It is not "high-brow" or obtuse, as some maths history books can be. It is not necessary to read the proofs if you don't want to. It is not just about "e", but explains a little about pi and i also. The only bit that I found confusing at first was the lack of a worked example of Napiers original logarithm table, which is very early in the book. Neither did I think that there was an explanation of the practical logic behind Napier's original sparse log tables (apart from the fact that they take a long time to create by hand). However, there is a worked example near the end of the book.

An interesting little curiousity..., 12 Feb 2000
I thought this was and excellent book, tracing the story of e from Napier logarithms through to the development of calculus and beyond. The author's style is excellent producing an interesting, easily read, non-technical history which fleshes out some of the great characters in the history mathematics. There are also some really diverting asides. If you've any interest in the history of mathematics, I'd recommend this.

Absolutely brilliant A **, 17 Apr 2006
The first time I've bothered to leave my thoughts on a book. But this one is well worth a recommendation. A must if you wanna recap or bridge knowledge from GCSE level onwards

Gives easily understood explanations, 31 Mar 2006
I've just started studying maths with the Open University and have found this book invaluable. I haven't really thought above maths since leaving school 30 years ago and so needed a refresher in the basics, algebra, fractions, etc. This book has been a great help!

Fantastic book to help bridge the gap, 12 Feb 2003
I was having real difficulty with the maths portion of my Computer Engineering degree having not done A level maths. This book goes over the concepts needed in everyday language and is easy to follow with helpful tips and assessment sections. A must for anyone who is having problems with maths.

A very useful book for anyone thinking of doing Mathematics at university., 31 Oct 2006
I am a first year student at Imperial College (where Professor Liebeck lectures) and I have to say that this book has really helped me. It was on the reading list that the university gave to me, so over the summer I used he book as a study aid.

Liebeck writes clearly and concisely, presenting the mathematics in an easy to understand way. At the same time the material covered is more challenging than at A-Level (which I found to be a bit repetitive) and will stimulate all students, regardless of their ability.

An Excellent Introduction to Pure Mathematics, 17 Sep 2006
I had a privilege of attending a first-year course at Imperial College, based on Prof. Martin Liebeck's book. The book, as well as the course (then taught by Prof. Kevin Buzzard), are superb. They are readily accessible to first-year university students and provide an easy transition from A-level to undergraduate mathematics. Moreover, the language is clear and concise, the examples instructive, and the book is generally fun to read. Liebeck selects some of the most interesting topics in elementary pure mathematics and stimulates the student's interest in the subject. Unfortunately, A-level mathematics is taught as a collection of algorithms, and the student may not be able to appreciate its depth and beauty. Whether you are a first-year mathematics undergraduate, or still at school, I would thoroughly recommend you to read this book so that you know what mathematics is really about.

An excellent introduction to university mathematics, 27 Sep 2004
The gap between high school and university mathematics is
quite noticeable. I found this book to be an excellent book
to prep a smooth landing to university mathematics.
(The best one out of a long list of other similar books
I had a look at)

Starts of really easy and clear but still goes beyond the
"surface" when required.
The chapters are structured very short, which I thought
was a good thing.

It has a lot of worked examples.
However, the book does not have solutions to the
end-of-chapter exercises, which I thought was a long minus
since I was reading the book on my own as a self study..

But all in all, a very enjoyable book to read!

Very useful, 11 Sep 2004
This book is ideal for A-level students who are considering doing a numerate degree, particularly maths. It contains lots of useful methods and tricks, with full proofs of every theorem. It isn't highly technical, nor does it go into much depth, but it is an excellent primer and will make you realise some of the amazing things that can be proved quite simply with the right concepts.

Enjoyable and educational, 05 Sep 2000
A concise Introduction to Pure Mathematics is very legible, it is written so that it is absorbed easily, it intoduces many prime topics including a very extensive and clear section on Integration

Promising...but disappointing in the end, 28 Oct 2008
The book looks like the author is just postponing the end of the story just repeating and repeating the same ideas. The part of the proof and the attempts to correct the proof are quite disappointing because they are too much redundant. Moreover Singh is sliding some e-mails which don't add anything to the story and are quite "impenetrable". I do not like this way of writing. The author pretends not to use math symbology and math concepts beyond very basic ones, and then he lets go concepts like Hecke algebra, Euler system, "quasi-automorphic representations", i.e. without giving any clue about what they mean.
I think it leaves too much maths unexplained (and in a book about a math conundrum you understand it is a big problem!); I would have loved to see the same ingenuity Derbyshire put in his wonderful "Prime Obsession".

Mathematics as you've never seen it before, 21 May 2008
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, 20 May 2008
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 Mks al-Khwrizm+ - 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!, 20 Mar 2008
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, 10 Jan 2008
an interesting book about Mathematics and about mathematicians both the famous and not so famous

Zero and infinity, 07 Aug 2007
Babylonians invented it, Indians worshipped it, Greeks abhorred it. Zero has been a problematic number for a long time. European mathematicians followed Greek footsteps, until they finally realized how important thing zero was for advanced mathematics.

Seife presents us the history of zero and its sister concept infinity, not only in mathematics, but also in physics and quantum mechanics. Zero is an entertaining book, if a bit light. For quick popular science entertainment purposes it's a good choice. (Review based on the Finnish translation.)

one of the best maths books around, 08 Dec 2006
Being an undergraduate philosopher I've had to read a lot of maths books, and this is by far the best. It's true that you don't need much maths background to understand it, but it's also highly enjoyable for those with a lot of maths or physics knowledge - it links up and explains general assumptions in a way which seems never to occur to most teachers of sciences courses. The proof of 0=1 (and, extrapolating, that winston churchill = a carrot) is excellent and well worth committing to memory just to freak out any maths nerds one knows. Also worth a go is the step-by-step guide to making your own wormhole time machine (Step 1: Make a small wormhole, and attach one end to something really heavy). Really excellent, buy everyone you know a copy for christmas.

Mathematics history, 11 Apr 2003
A very readable book. This book covers the life story of the number zero, and it is a facinating story which is being told.

You do not need to have a better than average understanding of maths to be able to appreciate this book.

A good read, highly recommended.

Review for Zero:the Biography of a Dangerous Idea, 30 Jul 2002
This book was absolutely wonderful, it delves into the history of mathematics, as far back as the creation of numbers themselves. It looks at the contribution that the Greeks, Babylonians and Hindus made to mathematics, and how religion had restricted the development of mathematics. The book was written very well, it felt like a story book, rather than a factual book. I recommend this book for everyone with an interest in Maths, you do not need to be a mathematician to enjoy this book.

Highly Recommended, 23 Sep 2001
This is an excellent history of number Zero. Charles Seife takes you from the start, tracing the ideas of zero and inifity through time and how their concepts have been feared and embraced, how they've affected and forced evolution upon religious, philosophical, societal, and scientific ideas. I think this book should be part of any mathematics course. Highly recommend this book!

a fascinating book with a brave title, 09 Jul 2001
There aren't many good maths books out there, but this is definitely one of them. It manages to describe the concepts - mentioned below in other reviews - so well that by the end you wish you could meet the author and have a chat about mathematics; the sign of a really good book.

The level is about 18+ and it will be of great benefit to maths students going to or at university. It was recommended to me by my lecturer; not surprisingly, I ignored him, but I found it a few years later. I kicked myself when i finished...I wish i had read it earlier. The title doesn't help either...it turns you off immediately...so he's either brave or stupid to call it that...!

It is true that e is an extremely important number, and really, it is far more interesting than pi in many ways. Unravelling its history leads to an explanation of many interesting areas of mathematics, and calculus is described well. The explanation of logs wasn't all that great, but it tied the book together.

If you're a maths student, it will help give subjects you cover some background and perspective. You may understand them better too, so...go and read it now!

The pleasure of mathematics, 26 Dec 2000
All students who have undertaken a calculus course know that "e" is a very important number and on eof the cornerstones of modern mathematics; but very few students - I am afraid - know its fascinating story. That's why Eli Maor decided to fill this gap and to write his book on the story of "e": he starts with the invention of logarithms by the Scottish nobleman John Napier and guides the reader in a wonderful voyage through the mathematical discoveries of the last four centuries. In this voyage, the interested reader can meet real giants of mathematics such as Newton, Euler and the Bernoullis; he can study curious mathematical curves such as the logarithmic spiral and the catenary; he can understand how calculus was born and how it developed in the minds of the great mathematicians of the 17th Century. The book is noteworthy because of the crystal-clear mathematical accuracy with which Eli Maor explains the facts of his story; therefore a maths background is necessary to enjoy reading this book. Finally, eli Maor makes his book even more interesting by adding some "capsules" on various subjects, such as the importance of hyperbolic functions, the relationship between music and maths, the beauty of the decorative patterns that use the logarithmic spiral. A book that should be in the library of every maths-loving person.

For mystics, philosophers, or even mathematicians!, 16 Jun 2000
This is a truly excellent book. This is not a collection of bound papers, this is an exhaustive study of e and we are guided by the author's own thoughts and opinions throughout. Collections of papers, although useful in saving us the legwork, are a cop-out. The author(s) does not need to make any personal input at all. It is the author's easy and informative style that makes this book so accessible to such a wide audience. Whether you are a mystic, a philosopher, a numerologist or just an ordinary mathematician, you will not be disappointed with this work!

A-level maths standard, but explained in historical context, 12 May 2000
This book quite clearly explains a lot of well-known theorems and their historical context. It is not "high-brow" or obtuse, as some maths history books can be. It is not necessary to read the proofs if you don't want to. It is not just about "e", but explains a little about pi and i also. The only bit that I found confusing at first was the lack of a worked example of Napiers original logarithm table, which is very early in the book. Neither did I think that there was an explanation of the practical logic behind Napier's original sparse log tables (apart from the fact that they take a long time to create by hand). However, there is a worked example near the end of the book.

An interesting little curiousity..., 12 Feb 2000
I thought this was and excellent book, tracing the story of e from Napier logarithms through to the development of calculus and beyond. The author's style is excellent producing an interesting, easily read, non-technical history which fleshes out some of the great characters in the history mathematics. There are also some really diverting asides. If you've any interest in the history of mathematics, I'd recommend this.

Absolutely brilliant A **, 17 Apr 2006
The first time I've bothered to leave my thoughts on a book. But this one is well worth a recommendation. A must if you wanna recap or bridge knowledge from GCSE level onwards

Gives easily understood explanations, 31 Mar 2006
I've just started studying maths with the Open University and have found this book invaluable. I haven't really thought above maths since leaving school 30 years ago and so needed a refresher in the basics, algebra, fractions, etc. This book has been a great help!

Fantastic book to help bridge the gap, 12 Feb 2003
I was having real difficulty with the maths portion of my Computer Engineering degree having not done A level maths. This book goes over the concepts needed in everyday language and is easy to follow with helpful tips and assessment sections. A must for anyone who is having problems with maths.

A very useful book for anyone thinking of doing Mathematics at university., 31 Oct 2006
I am a first year student at Imperial College (where Professor Liebeck lectures) and I have to say that this book has really helped me. It was on the reading list that the university gave to me, so over the summer I used he book as a study aid.

Liebeck writes clearly and concisely, presenting the mathematics in an easy to understand way. At the same time the material covered is more challenging than at A-Level (which I found to be a bit repetitive) and will stimulate all students, regardless of their ability.

An Excellent Introduction to Pure Mathematics, 17 Sep 2006
I had a privilege of attending a first-year course at Imperial College, based on Prof. Martin Liebeck's book. The book, as well as the course (then taught by Prof. Kevin Buzzard), are superb. They are readily accessible to first-year university students and provide an easy transition from A-level to undergraduate mathematics. Moreover, the language is clear and concise, the examples instructive, and the book is generally fun to read. Liebeck selects some of the most interesting topics in elementary pure mathematics and stimulates the student's interest in the subject. Unfortunately, A-level mathematics is taught as a collection of algorithms, and the student may not be able to appreciate its depth and beauty. Whether you are a first-year mathematics undergraduate, or still at school, I would thoroughly recommend you to read this book so that you know what mathematics is really about.

An excellent introduction to university mathematics, 27 Sep 2004
The gap between high school and university mathematics is
quite noticeable. I found this book to be an excellent book
to prep a smooth landing to university mathematics.
(The best one out of a long list of other similar books
I had a look at)

Starts of really easy and clear but still goes beyond the
"surface" when required.
The chapters are structured very short, which I thought
was a good thing.

It has a lot of worked examples.
However, the book does not have solutions to the
end-of-chapter exercises, which I thought was a long minus
since I was reading the book on my own as a self study..

But all in all, a very enjoyable book to read!

Very useful, 11 Sep 2004
This book is ideal for A-level students who are considering doing a numerate degree, particularly maths. It contains lots of useful methods and tricks, with full proofs of every theorem. It isn't highly technical, nor does it go into much depth, but it is an excellent primer and will make you realise some of the amazing things that can be proved quite simply with the right concepts.

Enjoyable and educational, 05 Sep 2000
A concise Introduction to Pure Mathematics is very legible, it is written so that it is absorbed easily, it intoduces many prime topics including a very extensive and clear section on Integration

This book is the one ...., 05 Mar 2008
I would recommend for everybody who has an interest in mathematics and the development of his mind, whatever his age or education. I've got a lot of mathematical books but this one is a very special one, because it is the only one that could hook me from page one till the end.
It is not a book for readers but a book for people who want to be actively involved with thinking and mathematics. And when I say mathematics I do not mean those high school mathematics books that are designed to torture every student. When you are going to study science at university i would recommend reading this book, because it develops your brain-solving capabilities.


Life changing, 09 Jul 2005
In my experience there are no books that could be termed "life changing". Except this one :)

My view of mathematics was as a dry, complete subject until I met the work of John Mason during my mathematics degree with the OU. This book completed what he started there - and changed me into a passionate mathematician, as opposed to someone who could simply do maths.

'Thinking Mathematically' helps teach you how to literally think like a mathematician, something that a lot of schools fail at. It uses a series of problems that are genuinely interesting and guides you through the process of solving them. For example; "How many squares are on a chessboard?" (It's not 64!).

The books only drawback is that time is not just spent on reading, but also really working on the problems, many of which do not have solutions, and thus I have never manged to finish it!

A wonderful book. Buy now!

A wonderful book for teachers and students alike, 05 Apr 2004
"Thinking Mathematically" is a wonderful book that I warmly recommend to anyone teaching mathematics, at any level, from primary school to university lecturer. I was recently involved in designing an undergraduate course incorporating mathematical writing and thinking, and problem solving. I have only subsequently discovered this book - and John Mason's "Learning and Doing Mathematics" - when I come to write the lectures for the course, these two books will be my main references. There are many excellent open-ended problems for investigation, and the thought processes involved in thinking mathematically are beautifully explained. The problems are at a sufficiently low level that they are likely to be useful for teachers at all levels. I shall encourage our library to buy copies of these books and will strongly recommend them to our students.

A unique and immensley practical book., 25 Apr 2002
This book requires no specialist maths knowledge (hardly any required) but almost from the first page will immerse you in the techniques and strategies which underly mathematical thinking.
I've used this book for many years and still keep coming back to it.
It is the only book I've ever seen which addresses the true emotional states a problem solver must go through AND shows you how to deal with them. Best of all, it will teach you to ask your own questions and find your own answers by the time you reach the end.
I'd suggest one takes one time to really absorb the tips presented in the book - well worth it.

Promising...but disappointing in the end, 28 Oct 2008
The book looks like the author is just postponing the end of the story just repeating and repeating the same ideas. The part of the proof and the attempts to correct the proof are quite disappointing because they are too much redundant. Moreover Singh is sliding some e-mails which don't add anything to the story and are quite "impenetrable". I do not like this way of writing. The author pretends not to use math symbology and math concepts beyond very basic ones, and then he lets go concepts like Hecke algebra, Euler system, "quasi-automorphic representations", i.e. without giving any clue about what they mean.
I think it leaves too much maths unexplained (and in a book about a math conundrum you understand it is a big problem!); I would have loved to see the same ingenuity Derbyshire put in his wonderful "Prime Obsession".

Mathematics as you've never seen it before, 21 May 2008
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, 20 May 2008
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 Mks al-Khwrizm+ - 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!, 20 Mar 2008
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, 10 Jan 2008
an interesting book about Mathematics and about mathematicians both the famous and not so famous

Zero and infinity, 07 Aug 2007
Babylonians invented it, Indians worshipped it, Greeks abhorred it. Zero has been a problematic number for a long time. European mathematicians followed Greek footsteps, until they finally realized how important thing zero was for advanced mathematics.

Seife presents us the history of zero and its sister concept infinity, not only in mathematics, but also in physics and quantum mechanics. Zero is an entertaining book, if a bit light. For quick popular science entertainment purposes it's a good choice. (Review based on the Finnish translation.)

one of the best maths books around, 08 Dec 2006
Being an undergraduate philosopher I've had to read a lot of maths books, and this is by far the best. It's true that you don't need much maths background to understand it, but it's also highly enjoyable for those with a lot of maths or physics knowledge - it links up and explains general assumptions in a way which seems never to occur to most teachers of sciences courses. The proof of 0=1 (and, extrapolating, that winston churchill = a carrot) is excellent and well worth committing to memory just to freak out any maths nerds one knows. Also worth a go is the step-by-step guide to making your own wormhole time machine (Step 1: Make a small wormhole, and attach one end to something really heavy). Really excellent, buy everyone you know a copy for christmas.

Mathematics history, 11 Apr 2003
A very readable book. This book covers the life story of the number zero, and it is a facinating story which is being told.

You do not need to have a better than average understanding of maths to be able to appreciate this book.

A good read, highly recommended.

Review for Zero:the Biography of a Dangerous Idea, 30 Jul 2002
This book was absolutely wonderful, it delves into the history of mathematics, as far back as the creation of numbers themselves. It looks at the contribution that the Greeks, Babylonians and Hindus made to mathematics, and how religion had restricted the development of mathematics. The book was written very well, it felt like a story book, rather than a factual book. I recommend this book for everyone with an interest in Maths, you do not need to be a mathematician to enjoy this book.

Highly Recommended, 23 Sep 2001
This is an excellent history of number Zero. Charles Seife takes you from the start, tracing the ideas of zero and inifity through time and how their concepts have been feared and embraced, how they've affected and forced evolution upon religious, philosophical, societal, and scientific ideas. I think this book should be part of any mathematics course. Highly recommend this book!

a fascinating book with a brave title, 09 Jul 2001
There aren't many good maths books out there, but this is definitely one of them. It manages to describe the concepts - mentioned below in other reviews - so well that by the end you wish you could meet the author and have a chat about mathematics; the sign of a really good book.

The level is about 18+ and it will be of great benefit to maths students going to or at university. It was recommended to me by my lecturer; not surprisingly, I ignored him, but I found it a few years later. I kicked myself when i finished...I wish i had read it earlier. The title doesn't help either...it turns you off immediately...so he's either brave or stupid to call it that...!

It is true that e is an extremely important number, and really, it is far more interesting than pi in many ways. Unravelling its history leads to an explanation of many interesting areas of mathematics, and calculus is described well. The explanation of logs wasn't all that great, but it tied the book together.

If you're a maths student, it will help give subjects you cover some background and perspective. You may understand them better too, so...go and read it now!

The pleasure of mathematics, 26 Dec 2000
All students who have undertaken a calculus course know that "e" is a very important number and on eof the cornerstones of modern mathematics; but very few students - I am afraid - know its fascinating story. That's why Eli Maor decided to fill this gap and to write his book on the story of "e": he starts with the invention of logarithms by the Scottish nobleman John Napier and guides the reader in a wonderful voyage through the mathematical discoveries of the last four centuries. In this voyage, the interested reader can meet real giants of mathematics such as Newton, Euler and the Bernoullis; he can study curious mathematical curves such as the logarithmic spiral and the catenary; he can understand how calculus was born and how it developed in the minds of the great mathematicians of the 17th Century. The book is noteworthy because of the crystal-clear mathematical accuracy with which Eli Maor explains the facts of his story; therefore a maths background is necessary to enjoy reading this book. Finally, eli Maor makes his book even more interesting by adding some "capsules" on various subjects, such as the importance of hyperbolic functions, the relationship between music and maths, the beauty of the decorative patterns that use the logarithmic spiral. A book that should be in the library of every maths-loving person.

For mystics, philosophers, or even mathematicians!, 16 Jun 2000
This is a truly excellent book. This is not a collection of bound papers, this is an exhaustive study of e and we are guided by the author's own thoughts and opinions throughout. Collections of papers, although useful in saving us the legwork, are a cop-out. The author(s) does not need to make any personal input at all. It is the author's easy and informative style that makes this book so accessible to such a wide audience. Whether you are a mystic, a philosopher, a numerologist or just an ordinary mathematician, you will not be disappointed with this work!

A-level maths standard, but explained in historical context, 12 May 2000
This book quite clearly explains a lot of well-known theorems and their historical context. It is not "high-brow" or obtuse, as some maths history books can be. It is not necessary to read the proofs if you don't want to. It is not just about "e", but explains a little about pi and i also. The only bit that I found confusing at first was the lack of a worked example of Napiers original logarithm table, which is very early in the book. Neither did I think that there was an explanation of the practical logic behind Napier's original sparse log tables (apart from the fact that they take a long time to create by hand). However, there is a worked example near the end of the book.

An interesting little curiousity..., 12 Feb 2000
I thought this was and excellent book, tracing the story of e from Napier logarithms through to the development of calculus and beyond. The author's style is excellent producing an interesting, easily read, non-technical history which fleshes out some of the great characters in the history mathematics. There are also some really diverting asides. If you've any interest in the history of mathematics, I'd recommend this.

Absolutely brilliant A **, 17 Apr 2006
The first time I've bothered to leave my thoughts on a book. But this one is well worth a recommendation. A must if you wanna recap or bridge knowledge from GCSE level onwards

Gives easily understood explanations, 31 Mar 2006
I've just started studying maths with the Open University and have found this book invaluable. I haven't really thought above maths since leaving school 30 years ago and so needed a refresher in the basics, algebra, fractions, etc. This book has been a great help!

Fantastic book to help bridge the gap, 12 Feb 2003
I was having real difficulty with the maths portion of my Computer Engineering degree having not done A level maths. This book goes over the concepts needed in everyday language and is easy to follow with helpful tips and assessment sections. A must for anyone who is having problems with maths.

A very useful book for anyone thinking of doing Mathematics at university., 31 Oct 2006
I am a first year student at Imperial College (where Professor Liebeck lectures) and I have to say that this book has really helped me. It was on the reading list that the university gave to me, so over the summer I used he book as a study aid.

Liebeck writes clearly and concisely, presenting the mathematics in an easy to understand way. At the same time the material covered is more challenging than at A-Level (which I found to be a bit repetitive) and will stimulate all students, regardless of their ability.

An Excellent Introduction to Pure Mathematics, 17 Sep 2006
I had a privilege of attending a first-year course at Imperial College, based on Prof. Martin Liebeck's book. The book, as well as the course (then taught by Prof. Kevin Buzzard), are superb. They are readily accessible to first-year university students and provide an easy transition from A-level to undergraduate mathematics. Moreover, the language is clear and concise, the examples instructive, and the book is generally fun to read. Liebeck selects some of the most interesting topics in elementary pure mathematics and stimulates the student's interest in the subject. Unfortunately, A-level mathematics is taught as a collection of algorithms, and the student may not be able to appreciate its depth and beauty. Whether you are a first-year mathematics undergraduate, or still at school, I would thoroughly recommend you to read this book so that you know what mathematics is really about.

An excellent introduction to university mathematics, 27 Sep 2004
The gap between high school and university mathematics is
quite noticeable. I found this book to be an excellent book
to prep a smooth landing to university mathematics.
(The best one out of a long list of other similar books
I had a look at)

Starts of really easy and clear but still goes beyond the
"surface" when required.
The chapters are structured very short, which I thought
was a good thing.

It has a lot of worked examples.
However, the book does not have solutions to the
end-of-chapter exercises, which I thought was a long minus
since I was reading the book on my own as a self study..

But all in all, a very enjoyable book to read!

Very useful, 11 Sep 2004