Turns life inside out, 28 Oct 2008
The author writes about living things as if the gene is the animal and the animal is simply a seed for the gene. He basically turns life inside out. It's a powerful mind tool to get a different perspective on life but don't get too carried away with the idea. The whole theory of evolution is valuable in understanding the world but like a lot of science it starts to become too difficult to use. So in conclusion I don't believe that the author has discovered the secret of life, he just has another way of looking at things that you may find useful. It should be one of the books you have read.

jean genie, 05 Oct 2008
Dawkins is excellent while he sticks to biology
however he may have lost the plot in the last chapter
as he has in thinking promoting science involves attacking
religion
If an evangalist is someone who does not leave people to work
it out for themselves but pushes his point of view Dawkins is one
Nutty Baptists and Dawkins looked similar on channel 4 for example
ie they both spin world events too far to promote a point of view

Imaginative guessing, 13 Sep 2008
I have attempted to read Dawkins's books on a few occasions but seldom get beyond the first 100 pages. I simply find his style of writing boring and his theories pure imaginative guesswork; I cannot take this author's ideas onboard yet biology fascinates me and especially that of epigenetics which seems to disprove all that this author advocates. I suspect that there is a snobbery value to those who support him. Irrespective of his academic standing I cannot avoid regarding the author as an imposter as I constantly want to wage war with his views. Admittedly, he comes across publicly as a very plausible academic but, that does not sway me.

Blind theorizing, 27 Jun 2008
Dawkins writes that "the argument of this book is that we, and all other animals, are machines created by our genes" (p.xxi) and that "We are survival machines - robot vehicles blindly programmed to preserve the selfish molecules known as genes" (p.xxi). Yet, according to him, this book "is not science fiction; it is science" (p.xxi)!

Dawkins contrives to overlook the twin discoveries that:
1. the observable traits of organisms are mostly conditioned by the interactions of many genes;
2. most genes have multiple effects on many of these traits.

Dawkins transfers characteristics with which he is familiar from human behaviour on the macro-level to the inanimate components, "genes", of which we are physically constructed. He then proceeds to argue that these impersonal entities, which he imagines to possess characteristically human traits, infallibly generate the same unpleasant traits in human behaviour on the macro-level. So he writes: "The gene is the basic unit of selfishness" (p.36).

The absurdity is evident in that genes or other nonconscious entities cannot be either selfish or unselfish. They cannot "compete" against anything or "choose" anything.

If Dawkins were right, what would be the point of declaring, as he does: "Let us try to *teach* generosity and altruism, because we are born selfish" (p.3)? For if we really were machines, as he believes, even these very concepts would be meaningless to us. And certainly his oratory could have no effect whatever on our actual behaviour.

In fact genes do not force us to behave in any particular way. Neither can they possess the ability to direct or to comprehend all that is required to adopt a course of either heartless selfishness or heartfelt, sacrificial compassion.

The arguments in this review have been challenged by the claim that Dawkins himself answers these charges. His claim is, in effect, that that "the evolution of behavioural reactions or patterns via natural selection" and "control by nonconscious mechanisms" are two vastly different ideas. Also it is said that Dawkins does not deny a freedom of choice as the very last lines in this book itself "celebrate the human ability to make choices that transcend genetic control and instinctive reactions." So it is said that Dawkins "repeatedly draws clear distinctions" to prevent his readers from jumping to the conclusions expressed above.

However, there is a vast difference between asserting that such distinctions exist and actually laying a solid theoretical foundation for such distinctions. To lay the kinds of foundations which Dawkins does and then to go on to insist that these foundations do not lead to their logical conclusion is nothing less than an act of faith on Dawkins' part. It certainly does not bestow any validity upon Dawkins alleged distinctions. The bottom line is that Dawkins' presuppositions simply do not lead logically to the sort of distinction which he asserts.

Essentially this debate is an argument not about data, but about underlying assumptions. Here is a example of what I mean:

ASSUMPTION: 1. "evolution is true";
DATUM: 2. "human beings have consciousness";
ASSUMPTION: 3. "therefore evolution is capable of generating consciousness".

Once again, it is a case of "garbage in, garbage out" (as Dawkins himself would say).



Scientifically sound but philosophically flawed, 29 May 2008
Darwin's theory of evolution is no doubt a successful scientific hypothesis, and Prof. Dawkins brings across this very clearly. However, I do have some doubts regarding his philosophical assertions.

Essentially Prof. Dawkins believes that:

1) Selfishness and competition is at the root of all biological phenomena - nature as "red in tooth and claw"
2) There is no basic "dis-continuity" between humanity and other animals - humans are not qualitatively different from other animals
3) There is however no ethical dilemma between this basic fact and the human desire for goodness - since descriptive and normative realities are intrinsically separate (what is and what should be are independent of each other)

Yet the basis for point 3) - the inherent seperation of "what is" and "what ought to be" is just a philosophical assertion. Prof. Dawkins is very correct in stating that the belief in God and all other religious assertions should be treated and critically analysed as scientific hypotheses. However, strictly speaking this should go beyond the subject of religion to include every other field of human intellectual activity, including of course philosophy itself. If we treat the assertion "'what is' is fundamentally separate from 'what ought to be'" as a strict scientific hypothesis in the same sense that "God exists" is treated as such a hypothesis, then it has to be said that it is no more than just a blank assertion without any kind of empirical justification.

In other words, Prof. Dawkins is mistaken in assuming that his particular view of evolution and Darwinism does not leave us with an ethical dilemma, because it evidently does. The only argument Prof. Dawkins has offered against this is the mere assertion that "what ought to be" must be seperate from "what is", yet this assertion, just like religious assertions regarding God, cannot be scientifically or empirically proven.

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.

Turns life inside out, 28 Oct 2008
The author writes about living things as if the gene is the animal and the animal is simply a seed for the gene. He basically turns life inside out. It's a powerful mind tool to get a different perspective on life but don't get too carried away with the idea. The whole theory of evolution is valuable in understanding the world but like a lot of science it starts to become too difficult to use. So in conclusion I don't believe that the author has discovered the secret of life, he just has another way of looking at things that you may find useful. It should be one of the books you have read.

jean genie, 05 Oct 2008
Dawkins is excellent while he sticks to biology
however he may have lost the plot in the last chapter
as he has in thinking promoting science involves attacking
religion
If an evangalist is someone who does not leave people to work
it out for themselves but pushes his point of view Dawkins is one
Nutty Baptists and Dawkins looked similar on channel 4 for example
ie they both spin world events too far to promote a point of view

Imaginative guessing, 13 Sep 2008
I have attempted to read Dawkins's books on a few occasions but seldom get beyond the first 100 pages. I simply find his style of writing boring and his theories pure imaginative guesswork; I cannot take this author's ideas onboard yet biology fascinates me and especially that of epigenetics which seems to disprove all that this author advocates. I suspect that there is a snobbery value to those who support him. Irrespective of his academic standing I cannot avoid regarding the author as an imposter as I constantly want to wage war with his views. Admittedly, he comes across publicly as a very plausible academic but, that does not sway me.

Blind theorizing, 27 Jun 2008
Dawkins writes that "the argument of this book is that we, and all other animals, are machines created by our genes" (p.xxi) and that "We are survival machines - robot vehicles blindly programmed to preserve the selfish molecules known as genes" (p.xxi). Yet, according to him, this book "is not science fiction; it is science" (p.xxi)!

Dawkins contrives to overlook the twin discoveries that:
1. the observable traits of organisms are mostly conditioned by the interactions of many genes;
2. most genes have multiple effects on many of these traits.

Dawkins transfers characteristics with which he is familiar from human behaviour on the macro-level to the inanimate components, "genes", of which we are physically constructed. He then proceeds to argue that these impersonal entities, which he imagines to possess characteristically human traits, infallibly generate the same unpleasant traits in human behaviour on the macro-level. So he writes: "The gene is the basic unit of selfishness" (p.36).

The absurdity is evident in that genes or other nonconscious entities cannot be either selfish or unselfish. They cannot "compete" against anything or "choose" anything.

If Dawkins were right, what would be the point of declaring, as he does: "Let us try to *teach* generosity and altruism, because we are born selfish" (p.3)? For if we really were machines, as he believes, even these very concepts would be meaningless to us. And certainly his oratory could have no effect whatever on our actual behaviour.

In fact genes do not force us to behave in any particular way. Neither can they possess the ability to direct or to comprehend all that is required to adopt a course of either heartless selfishness or heartfelt, sacrificial compassion.

The arguments in this review have been challenged by the claim that Dawkins himself answers these charges. His claim is, in effect, that that "the evolution of behavioural reactions or patterns via natural selection" and "control by nonconscious mechanisms" are two vastly different ideas. Also it is said that Dawkins does not deny a freedom of choice as the very last lines in this book itself "celebrate the human ability to make choices that transcend genetic control and instinctive reactions." So it is said that Dawkins "repeatedly draws clear distinctions" to prevent his readers from jumping to the conclusions expressed above.

However, there is a vast difference between asserting that such distinctions exist and actually laying a solid theoretical foundation for such distinctions. To lay the kinds of foundations which Dawkins does and then to go on to insist that these foundations do not lead to their logical conclusion is nothing less than an act of faith on Dawkins' part. It certainly does not bestow any validity upon Dawkins alleged distinctions. The bottom line is that Dawkins' presuppositions simply do not lead logically to the sort of distinction which he asserts.

Essentially this debate is an argument not about data, but about underlying assumptions. Here is a example of what I mean:

ASSUMPTION: 1. "evolution is true";
DATUM: 2. "human beings have consciousness";
ASSUMPTION: 3. "therefore evolution is capable of generating consciousness".

Once again, it is a case of "garbage in, garbage out" (as Dawkins himself would say).



Scientifically sound but philosophically flawed, 29 May 2008
Darwin's theory of evolution is no doubt a successful scientific hypothesis, and Prof. Dawkins brings across this very clearly. However, I do have some doubts regarding his philosophical assertions.

Essentially Prof. Dawkins believes that:

1) Selfishness and competition is at the root of all biological phenomena - nature as "red in tooth and claw"
2) There is no basic "dis-continuity" between humanity and other animals - humans are not qualitatively different from other animals
3) There is however no ethical dilemma between this basic fact and the human desire for goodness - since descriptive and normative realities are intrinsically separate (what is and what should be are independent of each other)

Yet the basis for point 3) - the inherent seperation of "what is" and "what ought to be" is just a philosophical assertion. Prof. Dawkins is very correct in stating that the belief in God and all other religious assertions should be treated and critically analysed as scientific hypotheses. However, strictly speaking this should go beyond the subject of religion to include every other field of human intellectual activity, including of course philosophy itself. If we treat the assertion "'what is' is fundamentally separate from 'what ought to be'" as a strict scientific hypothesis in the same sense that "God exists" is treated as such a hypothesis, then it has to be said that it is no more than just a blank assertion without any kind of empirical justification.

In other words, Prof. Dawkins is mistaken in assuming that his particular view of evolution and Darwinism does not leave us with an ethical dilemma, because it evidently does. The only argument Prof. Dawkins has offered against this is the mere assertion that "what ought to be" must be seperate from "what is", yet this assertion, just like religious assertions regarding God, cannot be scientifically or empirically proven.

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

Turns life inside out, 28 Oct 2008
The author writes about living things as if the gene is the animal and the animal is simply a seed for the gene. He basically turns life inside out. It's a powerful mind tool to get a different perspective on life but don't get too carried away with the idea. The whole theory of evolution is valuable in understanding the world but like a lot of science it starts to become too difficult to use. So in conclusion I don't believe that the author has discovered the secret of life, he just has another way of looking at things that you may find useful. It should be one of the books you have read.

jean genie, 05 Oct 2008
Dawkins is excellent while he sticks to biology
however he may have lost the plot in the last chapter
as he has in thinking promoting science involves attacking
religion
If an evangalist is someone who does not leave people to work
it out for themselves but pushes his point of view Dawkins is one
Nutty Baptists and Dawkins looked similar on channel 4 for example
ie they both spin world events too far to promote a point of view

Imaginative guessing, 13 Sep 2008
I have attempted to read Dawkins's books on a few occasions but seldom get beyond the first 100 pages. I simply find his style of writing boring and his theories pure imaginative guesswork; I cannot take this author's ideas onboard yet biology fascinates me and especially that of epigenetics which seems to disprove all that this author advocates. I suspect that there is a snobbery value to those who support him. Irrespective of his academic standing I cannot avoid regarding the author as an imposter as I constantly want to wage war with his views. Admittedly, he comes across publicly as a very plausible academic but, that does not sway me.

Blind theorizing, 27 Jun 2008
Dawkins writes that "the argument of this book is that we, and all other animals, are machines created by our genes" (p.xxi) and that "We are survival machines - robot vehicles blindly programmed to preserve the selfish molecules known as genes" (p.xxi). Yet, according to him, this book "is not science fiction; it is science" (p.xxi)!

Dawkins contrives to overlook the twin discoveries that:
1. the observable traits of organisms are mostly conditioned by the interactions of many genes;
2. most genes have multiple effects on many of these traits.

Dawkins transfers characteristics with which he is familiar from human behaviour on the macro-level to the inanimate components, "genes", of which we are physically constructed. He then proceeds to argue that these impersonal entities, which he imagines to possess characteristically human traits, infallibly generate the same unpleasant traits in human behaviour on the macro-level. So he writes: "The gene is the basic unit of selfishness" (p.36).

The absurdity is evident in that genes or other nonconscious entities cannot be either selfish or unselfish. They cannot "compete" against anything or "choose" anything.

If Dawkins were right, what would be the point of declaring, as he does: "Let us try to *teach* generosity and altruism, because we are born selfish" (p.3)? For if we really were machines, as he believes, even these very concepts would be meaningless to us. And certainly his oratory could have no effect whatever on our actual behaviour.

In fact genes do not force us to behave in any particular way. Neither can they possess the ability to direct or to comprehend all that is required to adopt a course of either heartless selfishness or heartfelt, sacrificial compassion.

The arguments in this review have been challenged by the claim that Dawkins himself answers these charges. His claim is, in effect, that that "the evolution of behavioural reactions or patterns via natural selection" and "control by nonconscious mechanisms" are two vastly different ideas. Also it is said that Dawkins does not deny a freedom of choice as the very last lines in this book itself "celebrate the human ability to make choices that transcend genetic control and instinctive reactions." So it is said that Dawkins "repeatedly draws clear distinctions" to prevent his readers from jumping to the conclusions expressed above.

However, there is a vast difference between asserting that such distinctions exist and actually laying a solid theoretical foundation for such distinctions. To lay the kinds of foundations which Dawkins does and then to go on to insist that these foundations do not lead to their logical conclusion is nothing less than an act of faith on Dawkins' part. It certainly does not bestow any validity upon Dawkins alleged distinctions. The bottom line is that Dawkins' presuppositions simply do not lead logically to the sort of distinction which he asserts.

Essentially this debate is an argument not about data, but about underlying assumptions. Here is a example of what I mean:

ASSUMPTION: 1. "evolution is true";
DATUM: 2. "human beings have consciousness";
ASSUMPTION: 3. "therefore evolution is capable of generating consciousness".

Once again, it is a case of "garbage in, garbage out" (as Dawkins himself would say).



Scientifically sound but philosophically flawed, 29 May 2008
Darwin's theory of evolution is no doubt a successful scientific hypothesis, and Prof. Dawkins brings across this very clearly. However, I do have some doubts regarding his philosophical assertions.

Essentially Prof. Dawkins believes that:

1) Selfishness and competition is at the root of all biological phenomena - nature as "red in tooth and claw"
2) There is no basic "dis-continuity" between humanity and other animals - humans are not qualitatively different from other animals
3) There is however no ethical dilemma between this basic fact and the human desire for goodness - since descriptive and normative realities are intrinsically separate (what is and what should be are independent of each other)

Yet the basis for point 3) - the inherent seperation of "what is" and "what ought to be" is just a philosophical assertion. Prof. Dawkins is very correct in stating that the belief in God and all other religious assertions should be treated and critically analysed as scientific hypotheses. However, strictly speaking this should go beyond the subject of religion to include every other field of human intellectual activity, including of course philosophy itself. If we treat the assertion "'what is' is fundamentally separate from 'what ought to be'" as a strict scientific hypothesis in the same sense that "God exists" is treated as such a hypothesis, then it has to be said that it is no more than just a blank assertion without any kind of empirical justification.

In other words, Prof. Dawkins is mistaken in assuming that his particular view of evolution and Darwinism does not leave us with an ethical dilemma, because it evidently does. The only argument Prof. Dawkins has offered against this is the mere assertion that "what ought to be" must be seperate from "what is", yet this assertion, just like religious assertions regarding God, cannot be scientifically or empirically proven.

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

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

Few writers distinguish themselves by their ability to write about complicated, even obscure topics clearly and engagingly. In Chaos, James Gleick, a former science writer for the New York Times, shows that he resides in this exclusive category. Here he takes on the job of depicting the first years of the study of chaos--the seemingly random patterns that characterise many natural phenomena.

This is not a purely technical book. Instead, it focuses as much on the scientists studying chaos as on the chaos itself. In the pages of Gleick's book, the reader meets dozens of extraordinary and eccentric people. For instance, Mitchell Feigenbaum, who constructed and regulated his life by a 26-hour clock and watched his waking hours come in and out of phase with those of his coworkers at Los Alamos National Laboratory.

As for chaos itself, Gleick does an outstanding job of explaining the thought processes and investigative techniques that researchers bring to bear on chaos problems. Rather than attempt to explain Julia sets, Lorenz attractors and the Mandelbrot Set with gigantically complicated equations, Chaos relies on sketches, photographs and Gleick's wonderful descriptive prose. --Christine Buttery

Turns life inside out, 28 Oct 2008
The author writes about living things as if the gene is the animal and the animal is simply a seed for the gene. He basically turns life inside out. It's a powerful mind tool to get a different perspective on life but don't get too carried away with the idea. The whole theory of evolution is valuable in understanding the world but like a lot of science it starts to become too difficult to use. So in conclusion I don't believe that the author has discovered the secret of life, he just has another way of looking at things that you may find useful. It should be one of the books you have read.

jean genie, 05 Oct 2008
Dawkins is excellent while he sticks to biology
however he may have lost the plot in the last chapter
as he has in thinking promoting science involves attacking
religion
If an evangalist is someone who does not leave people to work
it out for themselves but pushes his point of view Dawkins is one
Nutty Baptists and Dawkins looked similar on channel 4 for example
ie they both spin world events too far to promote a point of view

Imaginative guessing, 13 Sep 2008
I have attempted to read Dawkins's books on a few occasions but seldom get beyond the first 100 pages. I simply find his style of writing boring and his theories pure imaginative guesswork; I cannot take this author's ideas onboard yet biology fascinates me and especially that of epigenetics which seems to disprove all that this author advocates. I suspect that there is a snobbery value to those who support him. Irrespective of his academic standing I cannot avoid regarding the author as an imposter as I constantly want to wage war with his views. Admittedly, he comes across publicly as a very plausible academic but, that does not sway me.

Blind theorizing, 27 Jun 2008
Dawkins writes that "the argument of this book is that we, and all other animals, are machines created by our genes" (p.xxi) and that "We are survival machines - robot vehicles blindly programmed to preserve the selfish molecules known as genes" (p.xxi). Yet, according to him, this book "is not science fiction; it is science" (p.xxi)!

Dawkins contrives to overlook the twin discoveries that:
1. the observable traits of organisms are mostly conditioned by the interactions of many genes;
2. most genes have multiple effects on many of these traits.

Dawkins transfers characteristics with which he is familiar from human behaviour on the macro-level to the inanimate components, "genes", of which we are physically constructed. He then proceeds to argue that these impersonal entities, which he imagines to possess characteristically human traits, infallibly generate the same unpleasant traits in human behaviour on the macro-level. So he writes: "The gene is the basic unit of selfishness" (p.36).

The absurdity is evident in that genes or other nonconscious entities cannot be either selfish or unselfish. They cannot "compete" against anything or "choose" anything.

If Dawkins were right, what would be the point of declaring, as he does: "Let us try to *teach* generosity and altruism, because we are born selfish" (p.3)? For if we really were machines, as he believes, even these very concepts would be meaningless to us. And certainly his oratory could have no effect whatever on our actual behaviour.

In fact genes do not force us to behave in any particular way. Neither can they possess the ability to direct or to comprehend all that is required to adopt a course of either heartless selfishness or heartfelt, sacrificial compassion.

The arguments in this review have been challenged by the claim that Dawkins himself answers these charges. His claim is, in effect, that that "the evolution of behavioural reactions or patterns via natural selection" and "control by nonconscious mechanisms" are two vastly different ideas. Also it is said that Dawkins does not deny a freedom of choice as the very last lines in this book itself "celebrate the human ability to make choices that transcend genetic control and instinctive reactions." So it is said that Dawkins "repeatedly draws clear distinctions" to prevent his readers from jumping to the conclusions expressed above.

However, there is a vast difference between asserting that such distinctions exist and actually laying a solid theoretical foundation for such distinctions. To lay the kinds of foundations which Dawkins does and then to go on to insist that these foundations do not lead to their logical conclusion is nothing less than an act of faith on Dawkins' part. It certainly does not bestow any validity upon Dawkins alleged distinctions. The bottom line is that Dawkins' presuppositions simply do not lead logically to the sort of distinction which he asserts.

Essentially this debate is an argument not about data, but about underlying assumptions. Here is a example of what I mean:

ASSUMPTION: 1. "evolution is true";
DATUM: 2. "human beings have consciousness";
ASSUMPTION: 3. "therefore evolution is capable of generating consciousness".

Once again, it is a case of "garbage in, garbage out" (as Dawkins himself would say).



Scientifically sound but philosophically flawed, 29 May 2008
Darwin's theory of evolution is no doubt a successful scientific hypothesis, and Prof. Dawkins brings across this very clearly. However, I do have some doubts regarding his philosophical assertions.

Essentially Prof. Dawkins believes that:

1) Selfishness and competition is at the root of all biological phenomena - nature as "red in tooth and claw"
2) There is no basic "dis-continuity" between humanity and other animals - humans are not qualitatively different from other animals
3) There is however no ethical dilemma between this basic fact and the human desire for goodness - since descriptive and normative realities are intrinsically separate (what is and what should be are independent of each other)

Yet the basis for point 3) - the inherent seperation of "what is" and "what ought to be" is just a philosophical assertion. Prof. Dawkins is very correct in stating that the belief in God and all other religious assertions should be treated and critically analysed as scientific hypotheses. However, strictly speaking this should go beyond the subject of religion to include every other field of human intellectual activity, including of course philosophy itself. If we treat the assertion "'what is' is fundamentally separate from 'what ought to be'" as a strict scientific hypothesis in the same sense that "God exists" is treated as such a hypothesis, then it has to be said that it is no more than just a blank assertion without any kind of empirical justification.

In other words, Prof. Dawkins is mistaken in assuming that his particular view of evolution and Darwinism does not leave us with an ethical dilemma, because it evidently does. The only argument Prof. Dawkins has offered against this is the mere assertion that "what ought to be" must be seperate from "what is", yet this assertion, just like religious assertions regarding God, cannot be scientifically or empirically proven.

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

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

Order from Chaos, 29 Sep 2007
We all know things that are not predictable. These can be everyday occurrences like the weather, or more specialised events (whether the stock market will go up or down). The unpredictable plays a large part in "normal life". Yet for some of these matters, there is a nagging feeling that if sufficient information were known, the unpredictable would indeed be able to be forecast with as much certainty as whether the sun will rise tomorrow. Thus James Gleick introduces the topic of `chaos' - there can be a "sensitive dependence on initial conditions". If we were to know the initial conditions in all their details, predictability would be brought within our grasp. Thus the flapping of the wings of a butterfly in China could result in rainfall in Indianapolis.

At times I was lost in the small detail, but the strength of this book is that it paints a big picture. The mathematics (and physics, and chemistry, and biology, and .....) is sometimes beyond me, but the overall story is that there is `chaos' all around. Some of the chaos is linked into classic Newtonian mechanics, but strangely enough, chaos almost has in itself an order and `predictability' about it.

The three of the most significant scientific theories of the 20th century are reckoned to be Einstein's General Relativity, Quantum Mechanics, and ...... Chaos Theory. Before opening this very historical account of the last mentioned, I knew nothing about the theory of chaos. Now I have an awareness of the subject, and how experimentation can play a part in mathematics. Experimentation and mathematics are not normally uttered in the same sentence.

Look for the big picture, and do not get lost in the people and places, which can be bewildering. If you read this book, please ensure that it has colour photographs within it - the pictures are both staggering, and help to bring home the message. Some areas of chaos have their roots in self similarity, and the pictures from Mendelbrot sets are both staggering and fascinating. Self similarity can be best summed up by the classic (and anonymous) ditty: "Big fleas have on their backs small fleas to bite them, small flees have smaller fleas and so ad infinitum"

Gleick is strong on the history and roots of chaos, and how the ideas were received when initially tabled. There was shock and disbelief that others from external communities could have something to say that would have relevance to (say) population growth models, from totally different scientific disciplines. There was also reluctance initially to publish some of the ground-braking ideas.

Chaos is about non-linear dynamics, fractals, fractal boundary basins and much more. As `chaos' as a concept (and almost as a discipline) spread, rather than bringing order when chaos had existed before (and this could be described as one of the main purposes of `science'), evidence of more chaos emerges.

From study, it could be that there is more evidence of chaos than we thought hitherto. There could be chaos in space, and the onset of cardiac arrhythmias (heart attacks) seems chaotic. Gleick speculates that `evolution' is chaos with feedback. He has made me more aware of randomness. Classic determinism generates randomness. Perhaps, just perhaps, chaos is a way to reconcile free will and determinism. All in all, unlike the pure scientists of old, I now find myself positively looking for chaos.

Perhaps that is a mark of a well presented book.

Peter Morgan (morganp@supanet.com)


New wisdom, 18 May 2007
I love this book because of its association with systems theory and the concept of emergent properties. I also find the story about the struggle to get the ideas accepted by the establishment very reminiscent of the struggle to get new ideas into the world of work.


A Truly Enlightening Introduction to a Whole New World, 29 Dec 2004
I am educated to degree level, however my degree is not in any scientific discipline. I only recently developed an interest in science, and have since read many popular science books to try and fill a few of the gaping holes in my knowledge.

Before reading this book, I had no knowledge of Chaos Theory beyond the analogy that a butterfly flapping its wings in Peking could apparently cause a hurricane in New York. I never really understood this idea so I decided to read the book and find out about it.

Chaos: Making a New Science - unlike many other books in the popular science genre - doesn't talk down to the reader, and makes no apology for the complexity of the subject. Don't let this put you off, Gleick doesn't need to talk down to you, instead he relies on carefully and precisely explaining all of the facts. I have to admit to re-reading some of the more complex areas, however upon re-reading I found everything accessible despite my limited scientific education.

The book primarily tells the history of Chaos Theory and its scientists, which in itself requires a discussion of the theories involved. This means that it explains what the different concepts mean (The Butterfly Effect, non-linear equations, fractals etc.) but doesn't get lost in the very complex mathematics behind them. The theories in this book are often explained very effectively with good use of diagrams. I found these to be priceless, for example the description of a fractal left me a little confused until I saw the diagram of a Koch curve and suddenly understood that it really is possible for a shape to have a finite area and an infinite perimeter.

If you already know a lot about Chaos Theory and want to know more I recommend a text book, otherwise I recommend Chaos: Making a New Science.

Top Book, 30 Jan 2003
This was the first book I ever read on chaos theory. I am not involved in chaos theory at all, but I was interested in finding out more about it as it was big news at the time.

While at times the concept can be difficult to grasp, the author does go to great pains to make things clear. I think this book is aimed at people with some kind of background in maths, science or engineering ho know nothing about chaos theory.

THe story of how chaos theory came to be is enlightening and a real insight into how such ideas evolve over time.

By the end of the book I was quite able to create and run my own (basic) chaos equations. Quite a feat, really.

A delightful read !, 24 Jan 2003
This book is called 'Chaos : Making a new science' - so it should hardly
surprise anyone that it deals with the history of Chaos, bringing forth
the elementary concepts of the field along the way.
This book isn't, nor does it pretend to be, a textbook on chaos theory,
so one shouldn't expect too much maths or technical details. On the other
hand, a little maths is unavoidable for discussing even the most basic
notions of chaos theory, so the reader should be prepared for some
(not very demanding) maths.

The style adopted by Gleick is to interweave the personal lives of the
major players involved in the birth of chaos with a description the
concepts, thus giving the book a feel of an interesting story while
introducing a plethora of dazzling ideas at the same time.

The idea of self-similarity, of patterns composed of infinitely-repeating
tiny replicas of themselves, is astounding, to say the least. And to
learn that nature is full of such patterns is revealing indeed. The
implications to science and technology are far-reaching and often
surprising - researchers in Computer Networking have discovered that
network traffic in large networks such as the internet may actually be
following self-similar patterns !!

Personally, i found this to be a delightful read - Gleick's writing is
racy, the ideas involved are mind-bending, and the vivid imagery will
stay with you for a long,long time. I fell in love with fractals at
first sight and can gaze at a collection of beautiful fractals for hours.

In brief, this is a light, breezy account of the history of Chaos, with
a gentle introduction to the basic ideas of Chaos without much technical
details and only a minimum of maths.

One of the best 'Science for everyone' books i've ever read!

Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to discover one of the greatest problems in mathematics. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem, which was to find proof of the conjecture "all non-trivial zeros of the zeta function have real part one-half".

That statement may be nonsense to anyone but a mathematician but Derbyshire walks the reader through the decades of reasoning that led to the Riemann Hypothesis in a way that makes it perfectly clear. Riemann never proved the statement and it remains unsolved to this day.

Prime Obsession offers alternating chapters of step-by-step maths and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea and allows readers to explore the theory without insisting on page after page of formulae.

In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, GH Hardy, Alan Turing, André Weil and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire and he makes the effort seem very worthwhile. --Therese Littleton, Amazon.com

Turns life inside out, 28 Oct 2008
The author writes about living things as if the gene is the animal and the animal is simply a seed for the gene. He basically turns life inside out. It's a powerful mind tool to get a different perspective on life but don't get too carried away with the idea. The whole theory of evolution is valuable in understanding the world but like a lot of science it starts to become too difficult to use. So in conclusion I don't believe that the author has discovered the secret of life, he just has another way of looking at things that you may find useful. It should be one of the books you have read.

jean genie, 05 Oct 2008
Dawkins is excellent while he sticks to biology
however he may have lost the plot in the last chapter
as he has in thinking promoting science involves attacking
religion
If an evangalist is someone who does not leave people to work
it out for themselves but pushes his point of view Dawkins is one
Nutty Baptists and Dawkins looked similar on channel 4 for example
ie they both spin world events too far to promote a point of view

Imaginative guessing, 13 Sep 2008
I have attempted to read Dawkins's books on a few occasions but seldom get beyond the first 100 pages. I simply find his style of writing boring and his theories pure imaginative guesswork; I cannot take this author's ideas onboard yet biology fascinates me and especially that of epigenetics which seems to disprove all that this author advocates. I suspect that there is a snobbery value to those who support him. Irrespective of his academic standing I cannot avoid regarding the author as an imposter as I constantly want to wage war with his views. Admittedly, he comes across publicly as a very plausible academic but, that does not sway me.

Blind theorizing, 27 Jun 2008
Dawkins writes that "the argument of this book is that we, and all other animals, are machines created by our genes" (p.xxi) and that "We are survival machines - robot vehicles blindly programmed to preserve the selfish molecules known as genes" (p.xxi). Yet, according to him, this book "is not science fiction; it is science" (p.xxi)!

Dawkins contrives to overlook the twin discoveries that:
1. the observable traits of organisms are mostly conditioned by the interactions of many genes;
2. most genes have multiple effects on many of these traits.

Dawkins transfers characteristics with which he is familiar from human behaviour on the macro-level to the inanimate components, "genes", of which we are physically constructed. He then proceeds to argue that these impersonal entities, which he imagines to possess characteristically human traits, infallibly generate the same unpleasant traits in human behaviour on the macro-level. So he writes: "The gene is the basic unit of selfishness" (p.36).

The absurdity is evident in that genes or other nonconscious entities cannot be either selfish or unselfish. They cannot "compete" against anything or "choose" anything.

If Dawkins were right, what would be the point of declaring, as he does: "Let us try to *teach* generosity and altruism, because we are born selfish" (p.3)? For if we really were machines, as he believes, even these very concepts would be meaningless to us. And certainly his oratory could have no effect whatever on our actual behaviour.

In fact genes do not force us to behave in any particular way. Neither can they possess the ability to direct or to comprehend all that is required to adopt a course of either heartless selfishness or heartfelt, sacrificial compassion.

The arguments in this review have been challenged by the claim that Dawkins himself answers these charges. His claim is, in effect, that that "the evolution of behavioural reactions or patterns via natural selection" and "control by nonconscious mechanisms" are two vastly different ideas. Also it is said that Dawkins does not deny a freedom of choice as the very last lines in this book itself "celebrate the human ability to make choices that transcend genetic control and instinctive reactions." So it is said that Dawkins "repeatedly draws clear distinctions" to prevent his readers from jumping to the conclusions expressed above.

However, there is a vast difference between asserting that such distinctions exist and actually laying a solid theoretical foundation for such distinctions. To lay the kinds of foundations which Dawkins does and then to go on to insist that these foundations do not lead to their logical conclusion is nothing less than an act of faith on Dawkins' part. It certainly does not bestow any validity upon Dawkins alleged distinctions. The bottom line is that Dawkins' presuppositions simply do not lead logically to the sort of distinction which he asserts.

Essentially this debate is an argument not about data, but about underlying assumptions. Here is a example of what I mean:

ASSUMPTION: 1. "evolution is true";
DATUM: 2. "human beings have consciousness";
ASSUMPTION: 3. "therefore evolution is capable of generating consciousness".

Once again, it is a case of "garbage in, garbage out" (as Dawkins himself would say).



Scientifically sound but philosophically flawed, 29 May 2008
Darwin's theory of evolution is no doubt a successful scientific hypothesis, and Prof. Dawkins brings across this very clearly. However, I do have some doubts regarding his philosophical assertions.

Essentially Prof. Dawkins believes that:

1) Selfishness and competition is at the root of all biological phenomena - nature as "red in tooth and claw"
2) There is no basic "dis-continuity" between humanity and other animals - humans are not qualitatively different from other animals
3) There is however no ethical dilemma between this basic fact and the human desire for goodness - since descriptive and normative realities are intrinsically separate (what is and what should be are independent of each other)

Yet the basis for point 3) - the inherent seperation of "what is" and "what ought to be" is just a philosophical assertion. Prof. Dawkins is very correct in stating that the belief in God and all other religious assertions should be treated and critically analysed as scientific hypotheses. However, strictly speaking this should go beyond the subject of religion to include every other field of human intellectual activity, including of course philosophy itself. If we treat the assertion "'what is' is fundamentally separate from 'what ought to be'" as a strict scientific hypothesis in the same sense that "God exists" is treated as such a hypothesis, then it has to be said that it is no more than just a blank assertion without any kind of empirical justification.

In other words, Prof. Dawkins is mistaken in assuming that his particular view of evolution and Darwinism does not leave us with an ethical dilemma, because it evidently does. The only argument Prof. Dawkins has offered against this is the mere assertion that "what ought to be" must be seperate from "what is", yet this assertion, just like religious assertions regarding God, cannot be scientifically or empirically proven.

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

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

Order from Chaos, 29 Sep 2007
We all know things that are not predictable. These can be everyday occurrences like the weather, or more specialised events (whether the stock market will go up or down). The unpredictable plays a large part in "normal life". Yet for some of these matters, there is a nagging feeling that if sufficient information were known, the unpredictable would indeed be able to be forecast with as much certainty as whether the sun will rise tomorrow. Thus James Gleick introduces the topic of `chaos' - there can be a "sensitive dependence on initial conditions". If we were to know the initial conditions in all their details, predictability would be brought within our grasp. Thus the flapping of the wings of a butterfly in China could result in rainfall in Indianapolis.

At times I was lost in the small detail, but the strength of this book is that it paints a big picture. The mathematics (and physics, and chemistry, and biology, and .....) is sometimes beyond me, but the overall story is that there is `chaos' all around. Some of the chaos is linked into classic Newtonian mechanics, but strangely enough, chaos almost has in itself an order and `predictability' about it.

The three of the most significant scientific theories of the 20th century are reckoned to be Einstein's General Relativity, Quantum Mechanics, and ...... Chaos Theory. Before opening this very historical account of the last mentioned, I knew nothing about the theory of chaos. Now I have an awareness of the subject, and how experimentation can play a part in mathematics. Experimentation and mathematics are not normally uttered in the same sentence.

Look for the big picture, and do not get lost in the people and places, which can be bewildering. If you read this book, please ensure that it has colour photographs within it - the pictures are both staggering, and help to bring home the message. Some areas of chaos have their roots in self similarity, and the pictures from Mendelbrot sets are both staggering and fascinating. Self similarity can be best summed up by the classic (and anonymous) ditty: "Big fleas have on their backs small fleas to bite them, small flees have smaller fleas and so ad infinitum"

Gleick is strong on the history and roots of chaos, and how the ideas were received when initially tabled. There was shock and disbelief that others from external communities could have something to say that would have relevance to (say) population growth models, from totally different scientific disciplines. There was also reluctance initially to publish some of the ground-braking ideas.

Chaos is about non-linear dynamics, fractals, fractal boundary basins and much more. As `chaos' as a concept (and almost as a discipline) spread, rather than bringing order when chaos had existed before (and this could be described as one of the main purposes of `science'), evidence of more chaos emerges.

From study, it could be that there is more evidence of chaos than we thought hitherto. There could be chaos in space, and the onset of cardiac arrhythmias (heart attacks) seems chaotic. Gleick speculates that `evolution' is chaos with feedback. He has made me more aware of randomness. Classic determinism generates randomness. Perhaps, just perhaps, chaos is a way to reconcile free will and determinism. All in all, unlike the pure scientists of old, I now find myself positively looking for chaos.

Perhaps that is a mark of a well presented book.

Peter Morgan (morganp@supanet.com)


New wisdom, 18 May 2007
I love this book because of its association with systems theory and the concept of emergent properties. I also find the story about the struggle to get the ideas accepted by the establishment very reminiscent of the struggle to get new ideas into the world of work.


A Truly Enlightening Introduction to a Whole New World, 29 Dec 2004
I am educated to degree level, however my degree is not in any scientific discipline. I only recently developed an interest in science, and have since read many popular science books to try and fill a few of the gaping holes in my knowledge.

Before reading this book, I had no knowledge of Chaos Theory beyond the analogy that a butterfly flapping its wings in Peking could apparently cause a hurricane in New York. I never really understood this idea so I decided to read the book and find out about it.

Chaos: Making a New Science - unlike many other books in the popular science genre - doesn't talk down to the reader, and makes no apology for the complexity of the subject. Don't let this put you off, Gleick doesn't need to talk down to you, instead he relies on carefully and precisely explaining all of the facts. I have to admit to re-reading some of the more complex areas, however upon re-reading I found everything accessible despite my limited scientific education.

The book primarily tells the history of Chaos Theory and its scientists, which in itself requires a discussion of the theories involved. This means that it explains what the different concepts mean (The Butterfly Effect, non-linear equations, fractals etc.) but doesn't get lost in the very complex mathematics behind them. The theories in this book are often explained very effectively with good use of diagrams. I found these to be priceless, for example the description of a fractal left me a little confused until I saw the diagram of a Koch curve and suddenly understood that it really is possible for a shape to have a finite area and an infinite perimeter.

If you already know a lot about Chaos Theory and want to know more I recommend a text book, otherwise I recommend Chaos: Making a New Science.

Top Book, 30 Jan 2003
This was the first book I ever read on chaos theory. I am not involved in chaos theory at all, but I was interested in finding out more about it as it was big news at the time.

While at times the concept can be difficult to grasp, the author does go to great pains to make things clear. I think this book is aimed at people with some kind of background in maths, science or engineering ho know nothing about chaos theory.

THe story of how chaos theory came to be is enlightening and a real insight into how such ideas evolve over time.

By the end of the book I was quite able to create and run my own (basic) chaos equations. Quite a feat, really.

A delightful read !, 24 Jan 2003
This book is called 'Chaos : Making a new science' - so it should hardly
surprise anyone that it deals with the history of Chaos, bringing forth
the elementary concepts of the field along the way.
This book isn't, nor does it pretend to be, a textbook on chaos theory,
so one shouldn't expect too much maths or technical details. On the other
hand, a little maths is unavoidable for discussing even the most basic
notions of chaos theory, so the reader should be prepared for some
(not very demanding) maths.

The style adopted by Gleick is to interweave the personal lives of the
major players involved in the birth of chaos with a description the
concepts, thus giving the book a feel of an interesting story while
introducing a plethora of dazzling ideas at the same time.

The idea of self-similarity, of patterns composed of infinitely-repeating
tiny replicas of themselves, is astounding, to say the least. And to
learn that nature is full of such patterns is revealing indeed. The
implications to science and technology are far-reaching and often
surprising - researchers in Computer Networking have discovered that
network traffic in large networks such as the internet may actually be
following self-similar patterns !!

Personally, i found this to be a delightful read - Gleick's writing is
racy, the ideas involved are mind-bending, and the vivid imagery will
stay with you for a long,long time. I fell in love with fractals at
first sight and can gaze at a collection of beautiful fractals for hours.

In brief, this is a light, breezy account of the history of Chaos, with
a gentle introduction to the basic ideas of Chaos without much technical
details and only a minimum of maths.

One of the best 'Science for everyone' books i've ever read!

Challenging, but worth it, 15 Sep 2008
The great German mathematician, David Hilbert was once asked what question would he ask if could come back in 500 years' time. His response was immidiate:

"Has anyone proved the Riemann Hypothesis?"

Reading this book, you'll understand why Hilbert didn't hesitate. This is by far the most 'mathematical' of the popular books on the RH, and if you are a mathematical numpty like me, you might be discouraged at first glance. Don't be!!! Derbyshire actually does a really good job of walking you through it. It's an extremely rewarding read. I particularly like the way he also wove in the politcal and social upheavals that were taking place in Germany and Europe in general at the time that Riemann was formulating his hypothesis.

Interesting, 19 Aug 2008
I enjoyed the first half of the book - which provides a good background of the subject matter. Towards the latter half I grew weary of the author's style of writing and also found all the non-mathematical anecdotes annoying. I think the author's effort to dumb everything down ultimately destroys the point of the book. But this is a good starting point for a layperson who is interested in the Riemann hypothesis. I yearn for a more mathematical book, though.

A popularisation the focuses on the actual mathematics, 05 Jan 2008
Most books of this kind don't bother to try to talk about the actual maths, so they waffle on about the mathematicians, which is something like watching interviews of rock stars when you want to be seeing them performing.

This book is an exception - it does its mightiest to actually explain the innards of the conjecture and goes some way towards achieving its aim.

No quibble - this is the best book on its subject that's available at the moment, unless you're going for something more technical.

Do not buy any others, 12 Apr 2007
I have read this book and one of the other two popularisations about the Riemann hypothesis. Instead of interviewing mathematicians who may be near to solving it or writing around the subject, this book actually works through the mathematics of Riemann's 1859 paper.
It emphasises the centrality of Riemann's other parts of the paper apart from the famous Hypothesis and so helps to explain why some 30 years later that mathematicians were able to prove the Prime Number Theorem, independently of the truth or otherwise of the famous hypothesis: roughly that as numbers get larger the number of primes less than that number tends to about the number divided by its logarithm (base e). The reason is because of the techniques that Riemann invented in his paper.

Riemann's starting point was to generalise Euler's formula which relates the sum of a reciprocals of natural numbers: 1+1/2+1/3+1/4+... to the product of the inverses of the prime numbers. Derbyshire's explanation is far clearer than others and even I was able to understand it.

This book is precise and clear: one really feels that one has some insight into an astonishing piece of creative mathematical work by the time one has read the book. That alone in my opinion should qualify it as one of the greatest pieces of popular science writing of this or any other decade.

This book needs to be more actively marketed: whatever its faults, the author has made a genuine attempt to really explain a great piece of science technically to a non -technical audience, rather than just waffling around the subject and making us all feel these things are so far above our heads we will never understand them in any way. This courage on the author's part needs to be more widely feted.

I cannot do more than endorse the other reviewers' praise for this classic-to-be.

A fabulous read, 19 Jan 2005
Having read Marcus de Sautoy's book on prime numbers my appetite was sufficiently wetted to go out and by Edwards book on the Zeta function. Unfirtunately one look at this told me I wasn't going to be able to get through it. I picked this book up by accident and it was fascinating in that the author goes through the whole of Riemanns 1859 paper and explains the whole theorem, which is quite breathtaking in its brilliance. He loses it a bit at the end, but he can be forgiven for that as it does become very complicated. That combined with the way he weaves the history of prime numbers in alternative chapters makes this a thoroughly enjoyable book. If you like maths go and buy it!

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

Turns life inside out, 28 Oct 2008
The author writes about living things as if the gene is the animal and the animal is simply a seed for the gene. He basically turns life inside out. It's a powerful mind tool to get a different perspective on life but don't get too carried away with the idea. The whole theory of evolution is valuable in understanding the world but like a lot of science it starts to become too difficult to use. So in conclusion I don't believe that the author has discovered the secret of life, he just has another way of looking at things that you may find useful. It should be one of the books you have read.

jean genie, 05 Oct 2008
Dawkins is excellent while he sticks to biology
however he may have lost the plot in the last chapter
as he has in thinking promoting science involves attacking
religion
If an evangalist is someone who does not leave people to work
it out for themselves but pushes his point of view Dawkins is one
Nutty Baptists and Dawkins looked similar on channel 4 for example
ie they both spin world events too far to promote a point of view

Imaginative guessing, 13 Sep 2008
I have attempted to read Dawkins's books on a few occasions but seldom get beyond the first 100 pages. I simply find his style of writing boring and his theories pure imaginative guesswork; I cannot take this author's ideas onboard yet biology fascinates me and especially that of epigenetics which seems to disprove all that this author advocates. I suspect that there is a snobbery value to those who support him. Irrespective of his academic standing I cannot avoid regarding the author as an imposter as I constantly want to wage war with his views. Admittedly, he comes across publicly as a very plausible academic but, that does not sway me.

Blind theorizing, 27 Jun 2008
Dawkins writes that "the argument of this book is that we, and all other animals, are machines created by our genes" (p.xxi) and that "We are survival machines - robot vehicles blindly programmed to preserve the selfish molecules known as genes" (p.xxi). Yet, according to him, this book "is not science fiction; it is science" (p.xxi)!

Dawkins contrives to overlook the twin discoveries that:
1. the observable traits of organisms are mostly conditioned by the interactions of many genes;
2. most genes have multiple effects on many of these traits.

Dawkins transfers characteristics with which he is familiar from human behaviour on the macro-level to the inanimate components, "genes", of which we are physically constructed. He then proceeds to argue that these impersonal entities, which he imagines to possess characteristically human traits, infallibly generate the same unpleasant traits in human behaviour on the macro-level. So he writes: "The gene is the basic unit of selfishness" (p.36).

The absurdity is evident in that genes or other nonconscious entities cannot be either selfish or unselfish. They cannot "compete" against anything or "choose" anything.

If Dawkins were right, what would be the point of declaring, as he does: "Let us try to *teach* generosity and altruism, because we are born selfish" (p.3)? For if we rea