Tufte is God, 08 Nov 2005
I think I made Tufte very rich. If I didn't it was not my fault. I was a Displays Manager with IBM and used his book to illustrate how colour & pixels could enhance information. I developed a presentation that used his work to exploit data and its visualisation. As a result I sold one hell of a lot of screens (IBM 3279 colour screens - the first ever colour screens - and at £3,000 a crack I sold 6,000 in the first year alone). I also sold a lot of Tufte's books. The quite brilliant example of Minard's graph of Napoleon's campaign in Russia (contained within the book) would keep an audience occupied for 2 hours - and not a yawn - so if ever the Good Professor decides to make a Will, he should remember me and I hope he predececeases me by a goodly margin so I can drink to his memory in style.

I think Professor Tufte's product is quite safe and unlikely to cause injury or death (Amazon Product Compliance Statement).

Professor Tufte writes simply excellent books., 17 Jan 2002
These books appeal on so many levels. They are informative, interesting and entertaining. Beautifully produced and very well written. One hardly notices one is being educated.

Read it, before you make a really bad mistake., 08 Dec 2001
This book should be a compulsory read for all graphic designers dealing with data visualisation.

The clearly focused chapters, all with superb illustrations, take the reader through some of the best and worst graphics and charts ever printed, with Tufte providing crystalline insights and techniques that will stick in your mind and make your own work better.

Whilst this book deals only with printed graphics, I think that the lessons learned are even more valuable as a foundation for interactive media designers. With the added dimensions of time and user involvement comes the potential to commit far worse design-crimes than many of the examples laid bare in this book!

Like I said: Read it before you make a really bad mistake!

invaluable, every scientist, hell every american should read, 23 Jul 1999
the examples are incredible. this book is one of the most beautiful books I have ever read both for its content and execution. The advice Tufte gives with regard to the presentation of information will only become more important in the future. Whether reading the newspaper or writing a technical report, the proper display of quantitative information is an invaluable skill. this book helps you to think clearly and concisely. one of the best books of all time.

If you have to design anything, read this series, 15 Jul 1999
Whether it is presentation slides or internet sites, the concepts provided in Tufte's books will give you insight and skill that will improve your output 1000%.

There is some overlap between the books, but just looking at the pictures and his explanations and concepts will make you say "AHA!" and improve your next design.

Tufte is God, 08 Nov 2005
I think I made Tufte very rich. If I didn't it was not my fault. I was a Displays Manager with IBM and used his book to illustrate how colour & pixels could enhance information. I developed a presentation that used his work to exploit data and its visualisation. As a result I sold one hell of a lot of screens (IBM 3279 colour screens - the first ever colour screens - and at £3,000 a crack I sold 6,000 in the first year alone). I also sold a lot of Tufte's books. The quite brilliant example of Minard's graph of Napoleon's campaign in Russia (contained within the book) would keep an audience occupied for 2 hours - and not a yawn - so if ever the Good Professor decides to make a Will, he should remember me and I hope he predececeases me by a goodly margin so I can drink to his memory in style.

I think Professor Tufte's product is quite safe and unlikely to cause injury or death (Amazon Product Compliance Statement).

Professor Tufte writes simply excellent books., 17 Jan 2002
These books appeal on so many levels. They are informative, interesting and entertaining. Beautifully produced and very well written. One hardly notices one is being educated.

Read it, before you make a really bad mistake., 08 Dec 2001
This book should be a compulsory read for all graphic designers dealing with data visualisation.

The clearly focused chapters, all with superb illustrations, take the reader through some of the best and worst graphics and charts ever printed, with Tufte providing crystalline insights and techniques that will stick in your mind and make your own work better.

Whilst this book deals only with printed graphics, I think that the lessons learned are even more valuable as a foundation for interactive media designers. With the added dimensions of time and user involvement comes the potential to commit far worse design-crimes than many of the examples laid bare in this book!

Like I said: Read it before you make a really bad mistake!

invaluable, every scientist, hell every american should read, 23 Jul 1999
the examples are incredible. this book is one of the most beautiful books I have ever read both for its content and execution. The advice Tufte gives with regard to the presentation of information will only become more important in the future. Whether reading the newspaper or writing a technical report, the proper display of quantitative information is an invaluable skill. this book helps you to think clearly and concisely. one of the best books of all time.

If you have to design anything, read this series, 15 Jul 1999
Whether it is presentation slides or internet sites, the concepts provided in Tufte's books will give you insight and skill that will improve your output 1000%.

There is some overlap between the books, but just looking at the pictures and his explanations and concepts will make you say "AHA!" and improve your next design.

Great For A2 Physics, 15 Sep 2006
I have just started A2 Physics at my school. I didn't do maths to AS (just GCSE). I am the only one in my class without an AS in Maths. My teacher told me that I needed to know about Differentiation and Integration in order to progress my A grade in AS physics to an A in A2.

I always had the idea that Calculus was simply a very complicated area of Mathematics developed by Newton. I didn't know anything else (remember I only had a Maths GCSE).

I thought I'd buy this book to see if it could help me. The fantastic thing is that it explains every single concept in an extremely simple way (starting with the very basics). I believe that I am now up to the high standard of the mathematicians in my class and am able to understand the important mathematical concepts in physics that use calculus as a basis for their explanation. In particular, OCR's Advancing Physics A2 - Creating Models section.

You really don't need to be a math genius to understand this book fully!


Shock, horror, calculus is easy (well sort of!), 06 Nov 2003
If you`ve ever looked at a polynomial equation and thought that learning Martian would be easier, or even that knowing what a polynomial was would make a lot more sense, then this is the book for you. Granted, the book does assume that you have some prior knowledge of algebra and trig but I have only the most basic grasp of them and still managed to follow the book. The chapters are well set out and explain painful looking equations for differentiation and integration in simple,easy to follow terms. Calculus for Dummies acts like a kindly mentor; easing you through the hard bits, holding your hands when the numbers start to look like gibberish and celebrating with you at the end of the chapter that maths no longer seems like a strange and alien concept!

Tufte is God, 08 Nov 2005
I think I made Tufte very rich. If I didn't it was not my fault. I was a Displays Manager with IBM and used his book to illustrate how colour & pixels could enhance information. I developed a presentation that used his work to exploit data and its visualisation. As a result I sold one hell of a lot of screens (IBM 3279 colour screens - the first ever colour screens - and at £3,000 a crack I sold 6,000 in the first year alone). I also sold a lot of Tufte's books. The quite brilliant example of Minard's graph of Napoleon's campaign in Russia (contained within the book) would keep an audience occupied for 2 hours - and not a yawn - so if ever the Good Professor decides to make a Will, he should remember me and I hope he predececeases me by a goodly margin so I can drink to his memory in style.

I think Professor Tufte's product is quite safe and unlikely to cause injury or death (Amazon Product Compliance Statement).

Professor Tufte writes simply excellent books., 17 Jan 2002
These books appeal on so many levels. They are informative, interesting and entertaining. Beautifully produced and very well written. One hardly notices one is being educated.

Read it, before you make a really bad mistake., 08 Dec 2001
This book should be a compulsory read for all graphic designers dealing with data visualisation.

The clearly focused chapters, all with superb illustrations, take the reader through some of the best and worst graphics and charts ever printed, with Tufte providing crystalline insights and techniques that will stick in your mind and make your own work better.

Whilst this book deals only with printed graphics, I think that the lessons learned are even more valuable as a foundation for interactive media designers. With the added dimensions of time and user involvement comes the potential to commit far worse design-crimes than many of the examples laid bare in this book!

Like I said: Read it before you make a really bad mistake!

invaluable, every scientist, hell every american should read, 23 Jul 1999
the examples are incredible. this book is one of the most beautiful books I have ever read both for its content and execution. The advice Tufte gives with regard to the presentation of information will only become more important in the future. Whether reading the newspaper or writing a technical report, the proper display of quantitative information is an invaluable skill. this book helps you to think clearly and concisely. one of the best books of all time.

If you have to design anything, read this series, 15 Jul 1999
Whether it is presentation slides or internet sites, the concepts provided in Tufte's books will give you insight and skill that will improve your output 1000%.

There is some overlap between the books, but just looking at the pictures and his explanations and concepts will make you say "AHA!" and improve your next design.

Great For A2 Physics, 15 Sep 2006
I have just started A2 Physics at my school. I didn't do maths to AS (just GCSE). I am the only one in my class without an AS in Maths. My teacher told me that I needed to know about Differentiation and Integration in order to progress my A grade in AS physics to an A in A2.

I always had the idea that Calculus was simply a very complicated area of Mathematics developed by Newton. I didn't know anything else (remember I only had a Maths GCSE).

I thought I'd buy this book to see if it could help me. The fantastic thing is that it explains every single concept in an extremely simple way (starting with the very basics). I believe that I am now up to the high standard of the mathematicians in my class and am able to understand the important mathematical concepts in physics that use calculus as a basis for their explanation. In particular, OCR's Advancing Physics A2 - Creating Models section.

You really don't need to be a math genius to understand this book fully!


Shock, horror, calculus is easy (well sort of!), 06 Nov 2003
If you`ve ever looked at a polynomial equation and thought that learning Martian would be easier, or even that knowing what a polynomial was would make a lot more sense, then this is the book for you. Granted, the book does assume that you have some prior knowledge of algebra and trig but I have only the most basic grasp of them and still managed to follow the book. The chapters are well set out and explain painful looking equations for differentiation and integration in simple,easy to follow terms. Calculus for Dummies acts like a kindly mentor; easing you through the hard bits, holding your hands when the numbers start to look like gibberish and celebrating with you at the end of the chapter that maths no longer seems like a strange and alien concept!

No need to apologize for this, 27 Nov 2008
"Exposition, criticism, appreciation, is work for second-rate minds." Already, in the first paragraph, G. H. Hardy is deploring the task of writing about mathematics in his characteristically forthright fashion. It's just as well that by the time we begin the Apology we have been softened up by C. P. Snow's excellent introduction and potted biography. Clearly, this first-rate book has attracted an altogether better class of reviewer, the self-effacing type not given to hissy fits on being reminded of their place in the intellectual pantheon.

"I had of course found at school, as every future mathematician does, that I could often do things much better than my teachers". Hardy's later achievements and his matter-of-fact style ensure that this is neither preening vanity nor a pompous boast. A professional mathematician might also agree that the "function of a mathematician is to do something" and not to talk about it. Mathematics as an active pursuit, being cleverer than your maths teacher - these count as revelations to ordinary mortals, even those of us who weren't too bad at maths. Then, and before any unsuspecting non-mathematician can run for cover, Hardy sets about proving "two of the famous theorems of Greek mathematics". There is really nothing to be scared of, even for the most equation-phobic humanities graduate. It's the ideas and the arguments that link them that matter, and they are not difficult to follow. In tracing the steps of Euclid and Pythagoras we are tracing patterns of thought that have lasted two thousand years, and we too can directly appreciate their beauty, and see for ourselves in a small way that a "mathematician, like a painter or a poet, is a maker of patterns."

Hardy does not take kindly to the commonplace idea "that an academic career is one sought mainly by cautious and unambitious persons who care primarily for comfort and security." While he is, unsurprisingly, motivated by "intellectual curiosity" and a "desire to know the truth", he also admits to "professional pride", "ambition" and a "desire for reputation". A lesser mind might have been tempted to feign guilt over such worldly traits, but Hardy has only a good word for ambition, the "noble passion". And his own noblest ambition? That "of leaving behind... something of permanent value". No dreams of heavenly bliss for this atheist.

Just when you might be thinking that all this talk of reputation and ambition must arise from an insufferable self-centredness, he declares that much of his best work was done in collaboration with two other mathematicians, Littlewood and Ramanujan, from very different backgrounds. Hardy's recognition of the unknown Indian was not inevitable: two other eminent Englishmen had returned the manuscripts without comment, on the assumption that Ramanujan was a crank. That too was Hardy's first impression, but he soon changed his mind and saw in Ramanujan a brilliant if untutored mathematical mind. It is a remarkable story by any standards, and has been recently staged as "A Disappearing Number" - a brilliant production in which a rather battered copy of this very edition gets a turn in the limelight.

What was a "melancholy experience" for Hardy (writing about mathematics) provides a rewarding experience for us. Graham Greene considered this the best account of what it is like to be a creative artist. I don't know if Greene is right, or if Hardy is right in his belief "that mathematical reality lies outside us," waiting to be discovered. I defer to their judgements but can better appreciate their conclusions after reading this book. C. P. Snow describes Hardy's "mocking horror of pretentiousness, self-righteous indignation, and the whole stately pantechnicon of the hypocritical virtues." More intriguing, given Hardy's hatred of God and all the pious nonsense carried out in God's name, and given that the spiritual side of human nature has been unthinkingly yoked to religious mumbo jumbo for far too long, is Snow's description of Hardy "as spiritually delicate" and "spiritually candid as few men are".

The dominant sense of "apology" implies a fault for which contrition is being expressed. Hardy's Apology is no craven exercise in self-abasement but a serious and vigorous justification of the intellectual and creative life, whether led by a mathematician or anyone else.


How maths used to be, 24 Nov 2008
Reading this book is like opening a time capsule - which is fun, up to a point. The academic world Hardy inhabited was largely swept away by the first world war, and this book is full of the feeling of that threatened world - one of Hardy's main aims is to show that a. "proper" mathematics is of no practical use, and that b. this is good news, partly because this makes it "purer" and hence better (in some unexplained way) partly because then it can't be blamed for killing people.

The idea that mathematicians should justify their incomes through the value of their work (either through actual income generation or through explaining how the universe works) seems not to occur to Hardy; it's hard to imagine any mathematician today making the uselessness of their subject the major theme of a book.

Unfortunately for Hardy, the very areas he singles out as being especially satisfyingly useless are key to modern code-breaking and secure financial transactions - in fact it's hard to think of any substantial area of mathematics that is "useless" in Hardy's sense.

Hardy's style is also very antiquated, involving a great deal of preparatory throat-clearing, unsupported value-judgments, meandering around the subject, and lengthy vagueness. To a modern reader it all seems a bit smug and fake.

On the other hand, the actual points that Hardy makes about the way mathematicians develop ideas, and the examples of explanations of the amazing way mathematical proof works, are good ones. And, as a look back at a vanished period of academic history, it's great. But as an introduction to how mathematicians work now, or the role of mathematical research, it has become a very weak book.



Hardy's Apology, 23 Jul 2008
I bought Hardy's biography almost 50 years ago, just before going up to university to read Maths. The gentle almost humourous tone of the book convinced me that the life of a mathematician was a potential source of pleasure. In fact I later moved to read Philosophy, for my interests grew to centre on Logic and Mathematical Foundations, but my current work on Infinity still finds me using Hardy's "Pure Mathematics", and I still occasionally read his "Apology" for the pure pleasure that this outstanding book provides.

Disappointing, 26 Mar 2008
I'm not sure I read the same book as the other reviewers. I'm fascinated by mathematics and have, for a long time, been meaning to read this book. Finally I have, and I have to say I was somewhat disappointed. C.P. Snow's foreword was an interesting potted biography of one of Britain's greatest 20th century mathematicians; but, the "apology" itself is overshadowed by its own introduction.

The first nine chapters are a clear indication - if any was needed - that intellectual brilliance is no talisman against small-mindedness. Maybe I'm being unfair but in those nine short chapters Hardy manages to denigrate most of humanity - "most people can do nothing at all well" - by which he means, nothing that he personally considers worthy. I'm not convinced we should readily accept the social opinions of a man who was born to privilege and spent his entire life in rarefied cloisters shielded from what the "most" in question would consider reality. A man who thought we should not go to war with Germany because of the caliber of its mathematicians and scientists. (?) There are many reasons why we shouldn't be at war with Iraq, for example, but that the region is the cradle of civilisation is not one of them.

From chapter ten onwards the book makes a change of direction and deals with the actual subject of mathematics and being a mathematician. This latter section of the book is a much more interesting (less infuriating) read but I still felt he dealt rather ineptly with the attempt to differentiate between "common and garden" mathematics and the truly profound and beautiful creative mathematics that he so clearly loves.

When you compare this book to say Marcus du Sautoy's "Music of the Primes" or Simon Singh's "Fermat's Last Theorem", both books which truly promote the essential character of mathematics, "A Mathematician's Apology" seems very pale.

Read it. Seriously., 04 Feb 2008
This book is a facinating insight into the mind of one of the century's greatest mathematians. However, Hardy's ideas go far beyond this into the purpose of human endevour in general.
The best part of this book is the foreword by C.P Snow. This amounts to a lucid, if brief, biography of Hardy from a man who is brilliant in his own right.
If you have any kind of interest in the realities of mathematics, or the workings of genius, then this book is the place to start.

Tufte is God, 08 Nov 2005
I think I made Tufte very rich. If I didn't it was not my fault. I was a Displays Manager with IBM and used his book to illustrate how colour & pixels could enhance information. I developed a presentation that used his work to exploit data and its visualisation. As a result I sold one hell of a lot of screens (IBM 3279 colour screens - the first ever colour screens - and at £3,000 a crack I sold 6,000 in the first year alone). I also sold a lot of Tufte's books. The quite brilliant example of Minard's graph of Napoleon's campaign in Russia (contained within the book) would keep an audience occupied for 2 hours - and not a yawn - so if ever the Good Professor decides to make a Will, he should remember me and I hope he predececeases me by a goodly margin so I can drink to his memory in style.

I think Professor Tufte's product is quite safe and unlikely to cause injury or death (Amazon Product Compliance Statement).

Professor Tufte writes simply excellent books., 17 Jan 2002
These books appeal on so many levels. They are informative, interesting and entertaining. Beautifully produced and very well written. One hardly notices one is being educated.

Read it, before you make a really bad mistake., 08 Dec 2001
This book should be a compulsory read for all graphic designers dealing with data visualisation.

The clearly focused chapters, all with superb illustrations, take the reader through some of the best and worst graphics and charts ever printed, with Tufte providing crystalline insights and techniques that will stick in your mind and make your own work better.

Whilst this book deals only with printed graphics, I think that the lessons learned are even more valuable as a foundation for interactive media designers. With the added dimensions of time and user involvement comes the potential to commit far worse design-crimes than many of the examples laid bare in this book!

Like I said: Read it before you make a really bad mistake!

invaluable, every scientist, hell every american should read, 23 Jul 1999
the examples are incredible. this book is one of the most beautiful books I have ever read both for its content and execution. The advice Tufte gives with regard to the presentation of information will only become more important in the future. Whether reading the newspaper or writing a technical report, the proper display of quantitative information is an invaluable skill. this book helps you to think clearly and concisely. one of the best books of all time.

If you have to design anything, read this series, 15 Jul 1999
Whether it is presentation slides or internet sites, the concepts provided in Tufte's books will give you insight and skill that will improve your output 1000%.

There is some overlap between the books, but just looking at the pictures and his explanations and concepts will make you say "AHA!" and improve your next design.

Great For A2 Physics, 15 Sep 2006
I have just started A2 Physics at my school. I didn't do maths to AS (just GCSE). I am the only one in my class without an AS in Maths. My teacher told me that I needed to know about Differentiation and Integration in order to progress my A grade in AS physics to an A in A2.

I always had the idea that Calculus was simply a very complicated area of Mathematics developed by Newton. I didn't know anything else (remember I only had a Maths GCSE).

I thought I'd buy this book to see if it could help me. The fantastic thing is that it explains every single concept in an extremely simple way (starting with the very basics). I believe that I am now up to the high standard of the mathematicians in my class and am able to understand the important mathematical concepts in physics that use calculus as a basis for their explanation. In particular, OCR's Advancing Physics A2 - Creating Models section.

You really don't need to be a math genius to understand this book fully!


Shock, horror, calculus is easy (well sort of!), 06 Nov 2003
If you`ve ever looked at a polynomial equation and thought that learning Martian would be easier, or even that knowing what a polynomial was would make a lot more sense, then this is the book for you. Granted, the book does assume that you have some prior knowledge of algebra and trig but I have only the most basic grasp of them and still managed to follow the book. The chapters are well set out and explain painful looking equations for differentiation and integration in simple,easy to follow terms. Calculus for Dummies acts like a kindly mentor; easing you through the hard bits, holding your hands when the numbers start to look like gibberish and celebrating with you at the end of the chapter that maths no longer seems like a strange and alien concept!

No need to apologize for this, 27 Nov 2008
"Exposition, criticism, appreciation, is work for second-rate minds." Already, in the first paragraph, G. H. Hardy is deploring the task of writing about mathematics in his characteristically forthright fashion. It's just as well that by the time we begin the Apology we have been softened up by C. P. Snow's excellent introduction and potted biography. Clearly, this first-rate book has attracted an altogether better class of reviewer, the self-effacing type not given to hissy fits on being reminded of their place in the intellectual pantheon.

"I had of course found at school, as every future mathematician does, that I could often do things much better than my teachers". Hardy's later achievements and his matter-of-fact style ensure that this is neither preening vanity nor a pompous boast. A professional mathematician might also agree that the "function of a mathematician is to do something" and not to talk about it. Mathematics as an active pursuit, being cleverer than your maths teacher - these count as revelations to ordinary mortals, even those of us who weren't too bad at maths. Then, and before any unsuspecting non-mathematician can run for cover, Hardy sets about proving "two of the famous theorems of Greek mathematics". There is really nothing to be scared of, even for the most equation-phobic humanities graduate. It's the ideas and the arguments that link them that matter, and they are not difficult to follow. In tracing the steps of Euclid and Pythagoras we are tracing patterns of thought that have lasted two thousand years, and we too can directly appreciate their beauty, and see for ourselves in a small way that a "mathematician, like a painter or a poet, is a maker of patterns."

Hardy does not take kindly to the commonplace idea "that an academic career is one sought mainly by cautious and unambitious persons who care primarily for comfort and security." While he is, unsurprisingly, motivated by "intellectual curiosity" and a "desire to know the truth", he also admits to "professional pride", "ambition" and a "desire for reputation". A lesser mind might have been tempted to feign guilt over such worldly traits, but Hardy has only a good word for ambition, the "noble passion". And his own noblest ambition? That "of leaving behind... something of permanent value". No dreams of heavenly bliss for this atheist.

Just when you might be thinking that all this talk of reputation and ambition must arise from an insufferable self-centredness, he declares that much of his best work was done in collaboration with two other mathematicians, Littlewood and Ramanujan, from very different backgrounds. Hardy's recognition of the unknown Indian was not inevitable: two other eminent Englishmen had returned the manuscripts without comment, on the assumption that Ramanujan was a crank. That too was Hardy's first impression, but he soon changed his mind and saw in Ramanujan a brilliant if untutored mathematical mind. It is a remarkable story by any standards, and has been recently staged as "A Disappearing Number" - a brilliant production in which a rather battered copy of this very edition gets a turn in the limelight.

What was a "melancholy experience" for Hardy (writing about mathematics) provides a rewarding experience for us. Graham Greene considered this the best account of what it is like to be a creative artist. I don't know if Greene is right, or if Hardy is right in his belief "that mathematical reality lies outside us," waiting to be discovered. I defer to their judgements but can better appreciate their conclusions after reading this book. C. P. Snow describes Hardy's "mocking horror of pretentiousness, self-righteous indignation, and the whole stately pantechnicon of the hypocritical virtues." More intriguing, given Hardy's hatred of God and all the pious nonsense carried out in God's name, and given that the spiritual side of human nature has been unthinkingly yoked to religious mumbo jumbo for far too long, is Snow's description of Hardy "as spiritually delicate" and "spiritually candid as few men are".

The dominant sense of "apology" implies a fault for which contrition is being expressed. Hardy's Apology is no craven exercise in self-abasement but a serious and vigorous justification of the intellectual and creative life, whether led by a mathematician or anyone else.


How maths used to be, 24 Nov 2008
Reading this book is like opening a time capsule - which is fun, up to a point. The academic world Hardy inhabited was largely swept away by the first world war, and this book is full of the feeling of that threatened world - one of Hardy's main aims is to show that a. "proper" mathematics is of no practical use, and that b. this is good news, partly because this makes it "purer" and hence better (in some unexplained way) partly because then it can't be blamed for killing people.

The idea that mathematicians should justify their incomes through the value of their work (either through actual income generation or through explaining how the universe works) seems not to occur to Hardy; it's hard to imagine any mathematician today making the uselessness of their subject the major theme of a book.

Unfortunately for Hardy, the very areas he singles out as being especially satisfyingly useless are key to modern code-breaking and secure financial transactions - in fact it's hard to think of any substantial area of mathematics that is "useless" in Hardy's sense.

Hardy's style is also very antiquated, involving a great deal of preparatory throat-clearing, unsupported value-judgments, meandering around the subject, and lengthy vagueness. To a modern reader it all seems a bit smug and fake.

On the other hand, the actual points that Hardy makes about the way mathematicians develop ideas, and the examples of explanations of the amazing way mathematical proof works, are good ones. And, as a look back at a vanished period of academic history, it's great. But as an introduction to how mathematicians work now, or the role of mathematical research, it has become a very weak book.



Hardy's Apology, 23 Jul 2008
I bought Hardy's biography almost 50 years ago, just before going up to university to read Maths. The gentle almost humourous tone of the book convinced me that the life of a mathematician was a potential source of pleasure. In fact I later moved to read Philosophy, for my interests grew to centre on Logic and Mathematical Foundations, but my current work on Infinity still finds me using Hardy's "Pure Mathematics", and I still occasionally read his "Apology" for the pure pleasure that this outstanding book provides.

Disappointing, 26 Mar 2008
I'm not sure I read the same book as the other reviewers. I'm fascinated by mathematics and have, for a long time, been meaning to read this book. Finally I have, and I have to say I was somewhat disappointed. C.P. Snow's foreword was an interesting potted biography of one of Britain's greatest 20th century mathematicians; but, the "apology" itself is overshadowed by its own introduction.

The first nine chapters are a clear indication - if any was needed - that intellectual brilliance is no talisman against small-mindedness. Maybe I'm being unfair but in those nine short chapters Hardy manages to denigrate most of humanity - "most people can do nothing at all well" - by which he means, nothing that he personally considers worthy. I'm not convinced we should readily accept the social opinions of a man who was born to privilege and spent his entire life in rarefied cloisters shielded from what the "most" in question would consider reality. A man who thought we should not go to war with Germany because of the caliber of its mathematicians and scientists. (?) There are many reasons why we shouldn't be at war with Iraq, for example, but that the region is the cradle of civilisation is not one of them.

From chapter ten onwards the book makes a change of direction and deals with the actual subject of mathematics and being a mathematician. This latter section of the book is a much more interesting (less infuriating) read but I still felt he dealt rather ineptly with the attempt to differentiate between "common and garden" mathematics and the truly profound and beautiful creative mathematics that he so clearly loves.

When you compare this book to say Marcus du Sautoy's "Music of the Primes" or Simon Singh's "Fermat's Last Theorem", both books which truly promote the essential character of mathematics, "A Mathematician's Apology" seems very pale.

Read it. Seriously., 04 Feb 2008
This book is a facinating insight into the mind of one of the century's greatest mathematians. However, Hardy's ideas go far beyond this into the purpose of human endevour in general.
The best part of this book is the foreword by C.P Snow. This amounts to a lucid, if brief, biography of Hardy from a man who is brilliant in his own right.
If you have any kind of interest in the realities of mathematics, or the workings of genius, then this book is the place to start.

Compact knowledge, 15 Apr 2008
I found this book is very interesting. I used this book when doing my research. For me, it is a compact knowledge inside one book. I do not need to search for other book for reference.

This book provide easy to understand structure. A lot of example and proof make this book is very nice.

I agree that this book is good for undergraduate, but it is also good for high level education.

Complete and effective, 10 Jul 2004
This is a very effective book for the student :
- the knowledge is neatly summed up, and proofs are given just afterwards and don't interfere with the concepts, so that reading and understanding the lessons is easy,
- hundreds of corrected exercises, very gradual,
- very complete for undergrads (and enough for most grads who won't do Physics for example).

This book and the S. Lipschutz one on linear algebra are among those I've kept for further use.

Ce livre est hautement recommandable pour le premier cycle scientifique. Clair, complet et graduel.

A good reference, 02 Jan 2002
Thi sbook is not for everyone. It is pitched somewhere at the undergraduate level or to the high school student who would like to go beyond the syllabus. The book presents the axioms and assumptions clearly and concisely before moving quickly on to analysis and examples. Explanations may be too brief for some but all the information necessary to understand and to handle the exercises are there. This approach may not be suitable for readers who want a quick fix but for those whose passion is mathematics, this is a great primer.

Moves too fast. Does not spend enough time on each topic., 02 Sep 1999
My Advanced Calculus class covered only the first two chapters. While we were spending time on detailed analysis of different types of infinities, this book did not cover it at all. This book was almost no help. Make sure the style of the teacher matches the way this book is written, otherwise it may be a waste. My class would have been a lot easier and less satisfying if it had been conducted the way this is written.

Tufte is God, 08 Nov 2005
I think I made Tufte very rich. If I didn't it was not my fault. I was a Displays Manager with IBM and used his book to illustrate how colour & pixels could enhance information. I developed a presentation that used his work to exploit data and its visualisation. As a result I sold one hell of a lot of screens (IBM 3279 colour screens - the first ever colour screens - and at £3,000 a crack I sold 6,000 in the first year alone). I also sold a lot of Tufte's books. The quite brilliant example of Minard's graph of Napoleon's campaign in Russia (contained within the book) would keep an audience occupied for 2 hours - and not a yawn - so if ever the Good Professor decides to make a Will, he should remember me and I hope he predececeases me by a goodly margin so I can drink to his memory in style.

I think Professor Tufte's product is quite safe and unlikely to cause injury or death (Amazon Product Compliance Statement).

Professor Tufte writes simply excellent books., 17 Jan 2002
These books appeal on so many levels. They are informative, interesting and entertaining. Beautifully produced and very well written. One hardly notices one is being educated.

Read it, before you make a really bad mistake., 08 Dec 2001
This book should be a compulsory read for all graphic designers dealing with data visualisation.

The clearly focused chapters, all with superb illustrations, take the reader through some of the best and worst graphics and charts ever printed, with Tufte providing crystalline insights and techniques that will stick in your mind and make your own work better.

Whilst this book deals only with printed graphics, I think that the lessons learned are even more valuable as a foundation for interactive media designers. With the added dimensions of time and user involvement comes the potential to commit far worse design-crimes than many of the examples laid bare in this book!

Like I said: Read it before you make a really bad mistake!

invaluable, every scientist, hell every american should read, 23 Jul 1999
the examples are incredible. this book is one of the most beautiful books I have ever read both for its content and execution. The advice Tufte gives with regard to the presentation of information will only become more important in the future. Whether reading the newspaper or writing a technical report, the proper display of quantitative information is an invaluable skill. this book helps you to think clearly and concisely. one of the best books of all time.

If you have to design anything, read this series, 15 Jul 1999
Whether it is presentation slides or internet sites, the concepts provided in Tufte's books will give you insight and skill that will improve your output 1000%.

There is some overlap between the books, but just looking at the pictures and his explanations and concepts will make you say "AHA!" and improve your next design.

Great For A2 Physics, 15 Sep 2006
I have just started A2 Physics at my school. I didn't do maths to AS (just GCSE). I am the only one in my class without an AS in Maths. My teacher told me that I needed to know about Differentiation and Integration in order to progress my A grade in AS physics to an A in A2.

I always had the idea that Calculus was simply a very complicated area of Mathematics developed by Newton. I didn't know anything else (remember I only had a Maths GCSE).

I thought I'd buy this book to see if it could help me. The fantastic thing is that it explains every single concept in an extremely simple way (starting with the very basics). I believe that I am now up to the high standard of the mathematicians in my class and am able to understand the important mathematical concepts in physics that use calculus as a basis for their explanation. In particular, OCR's Advancing Physics A2 - Creating Models section.

You really don't need to be a math genius to understand this book fully!


Shock, horror, calculus is easy (well sort of!), 06 Nov 2003
If you`ve ever looked at a polynomial equation and thought that learning Martian would be easier, or even that knowing what a polynomial was would make a lot more sense, then this is the book for you. Granted, the book does assume that you have some prior knowledge of algebra and trig but I have only the most basic grasp of them and still managed to follow the book. The chapters are well set out and explain painful looking equations for differentiation and integration in simple,easy to follow terms. Calculus for Dummies acts like a kindly mentor; easing you through the hard bits, holding your hands when the numbers start to look like gibberish and celebrating with you at the end of the chapter that maths no longer seems like a strange and alien concept!

No need to apologize for this, 27 Nov 2008
"Exposition, criticism, appreciation, is work for second-rate minds." Already, in the first paragraph, G. H. Hardy is deploring the task of writing about mathematics in his characteristically forthright fashion. It's just as well that by the time we begin the Apology we have been softened up by C. P. Snow's excellent introduction and potted biography. Clearly, this first-rate book has attracted an altogether better class of reviewer, the self-effacing type not given to hissy fits on being reminded of their place in the intellectual pantheon.

"I had of course found at school, as every future mathematician does, that I could often do things much better than my teachers". Hardy's later achievements and his matter-of-fact style ensure that this is neither preening vanity nor a pompous boast. A professional mathematician might also agree that the "function of a mathematician is to do something" and not to talk about it. Mathematics as an active pursuit, being cleverer than your maths teacher - these count as revelations to ordinary mortals, even those of us who weren't too bad at maths. Then, and before any unsuspecting non-mathematician can run for cover, Hardy sets about proving "two of the famous theorems of Greek mathematics". There is really nothing to be scared of, even for the most equation-phobic humanities graduate. It's the ideas and the arguments that link them that matter, and they are not difficult to follow. In tracing the steps of Euclid and Pythagoras we are tracing patterns of thought that have lasted two thousand years, and we too can directly appreciate their beauty, and see for ourselves in a small way that a "mathematician, like a painter or a poet, is a maker of patterns."

Hardy does not take kindly to the commonplace idea "that an academic career is one sought mainly by cautious and unambitious persons who care primarily for comfort and security." While he is, unsurprisingly, motivated by "intellectual curiosity" and a "desire to know the truth", he also admits to "professional pride", "ambition" and a "desire for reputation". A lesser mind might have been tempted to feign guilt over such worldly traits, but Hardy has only a good word for ambition, the "noble passion". And his own noblest ambition? That "of leaving behind... something of permanent value". No dreams of heavenly bliss for this atheist.

Just when you might be thinking that all this talk of reputation and ambition must arise from an insufferable self-centredness, he declares that much of his best work was done in collaboration with two other mathematicians, Littlewood and Ramanujan, from very different backgrounds. Hardy's recognition of the unknown Indian was not inevitable: two other eminent Englishmen had returned the manuscripts without comment, on the assumption that Ramanujan was a crank. That too was Hardy's first impression, but he soon changed his mind and saw in Ramanujan a brilliant if untutored mathematical mind. It is a remarkable story by any standards, and has been recently staged as "A Disappearing Number" - a brilliant production in which a rather battered copy of this very edition gets a turn in the limelight.

What was a "melancholy experience" for Hardy (writing about mathematics) provides a rewarding experience for us. Graham Greene considered this the best account of what it is like to be a creative artist. I don't know if Greene is right, or if Hardy is right in his belief "that mathematical reality lies outside us," waiting to be discovered. I defer to their judgements but can better appreciate their conclusions after reading this book. C. P. Snow describes Hardy's "mocking horror of pretentiousness, self-righteous indignation, and the whole stately pantechnicon of the hypocritical virtues." More intriguing, given Hardy's hatred of God and all the pious nonsense carried out in God's name, and given that the spiritual side of human nature has been unthinkingly yoked to religious mumbo jumbo for far too long, is Snow's description of Hardy "as spiritually delicate" and "spiritually candid as few men are".

The dominant sense of "apology" implies a fault for which contrition is being expressed. Hardy's Apology is no craven exercise in self-abasement but a serious and vigorous justification of the intellectual and creative life, whether led by a mathematician or anyone else.


How maths used to be, 24 Nov 2008
Reading this book is like opening a time capsule - which is fun, up to a point. The academic world Hardy inhabited was largely swept away by the first world war, and this book is full of the feeling of that threatened world - one of Hardy's main aims is to show that a. "proper" mathematics is of no practical use, and that b. this is good news, partly because this makes it "purer" and hence better (in some unexplained way) partly because then it can't be blamed for killing people.

The idea that mathematicians should justify their incomes through the value of their work (either through actual income generation or through explaining how the universe works) seems not to occur to Hardy; it's hard to imagine any mathematician today making the uselessness of their subject the major theme of a book.

Unfortunately for Hardy, the very areas he singles out as being especially satisfyingly useless are key to modern code-breaking and secure financial transactions - in fact it's hard to think of any substantial area of mathematics that is "useless" in Hardy's sense.

Hardy's style is also very antiquated, involving a great deal of preparatory throat-clearing, unsupported value-judgments, meandering around the subject, and lengthy vagueness. To a modern reader it all seems a bit smug and fake.

On the other hand, the actual points that Hardy makes about the way mathematicians develop ideas, and the examples of explanations of the amazing way mathematical proof works, are good ones. And, as a look back at a vanished period of academic history, it's great. But as an introduction to how mathematicians work now, or the role of mathematical research, it has become a very weak book.



Hardy's Apology, 23 Jul 2008
I bought Hardy's biography almost 50 years ago, just before going up to university to read Maths. The gentle almost humourous tone of the book convinced me that the life of a mathematician was a potential source of pleasure. In fact I later moved to read Philosophy, for my interests grew to centre on Logic and Mathematical Foundations, but my current work on Infinity still finds me using Hardy's "Pure Mathematics", and I still occasionally read his "Apology" for the pure pleasure that this outstanding book provides.

Disappointing, 26 Mar 2008
I'm not sure I read the same book as the other reviewers. I'm fascinated by mathematics and have, for a long time, been meaning to read this book. Finally I have, and I have to say I was somewhat disappointed. C.P. Snow's foreword was an interesting potted biography of one of Britain's greatest 20th century mathematicians; but, the "apology" itself is overshadowed by its own introduction.

The first nine chapters are a clear indication - if any was needed - that intellectual brilliance is no talisman against small-mindedness. Maybe I'm being unfair but in those nine short chapters Hardy manages to denigrate most of humanity - "most people can do nothing at all well" - by which he means, nothing that he personally considers worthy. I'm not convinced we should readily accept the social opinions of a man who was born to privilege and spent his entire life in rarefied cloisters shielded from what the "most" in question would consider reality. A man who thought we should not go to war with Germany because of the caliber of its mathematicians and scientists. (?) There are many reasons why we shouldn't be at war with Iraq, for example, but that the region is the cradle of civilisation is not one of them.

From chapter ten onwards the book makes a change of direction and deals with the actual subject of mathematics and being a mathematician. This latter section of the book is a much more interesting (less infuriating) read but I still felt he dealt rather ineptly with the attempt to differentiate between "common and garden" mathematics and the truly profound and beautiful creative mathematics that he so clearly loves.

When you compare this book to say Marcus du Sautoy's "Music of the Primes" or Simon Singh's "Fermat's Last Theorem", both books which truly promote the essential character of mathematics, "A Mathematician's Apology" seems very pale.

Read it. Seriously., 04 Feb 2008
This book is a facinating insight into the mind of one of the century's greatest mathematians. However, Hardy's ideas go far beyond this into the purpose of human endevour in general.
The best part of this book is the foreword by C.P Snow. This amounts to a lucid, if brief, biography of Hardy from a man who is brilliant in his own right.
If you have any kind of interest in the realities of mathematics, or the workings of genius, then this book is the place to start.

Compact knowledge, 15 Apr 2008
I found this book is very interesting. I used this book when doing my research. For me, it is a compact knowledge inside one book. I do not need to search for other book for reference.

This book provide easy to understand structure. A lot of example and proof make this book is very nice.

I agree that this book is good for undergraduate, but it is also good for high level education.

Complete and effective, 10 Jul 2004
This is a very effective book for the student :
- the knowledge is neatly summed up, and proofs are given just afterwards and don't interfere with the concepts, so that reading and understanding the lessons is easy,
- hundreds of corrected exercises, very gradual,
- very complete for undergrads (and enough for most grads who won't do Physics for example).

This book and the S. Lipschutz one on linear algebra are among those I've kept for further use.

Ce livre est hautement recommandable pour le premier cycle scientifique. Clair, complet et graduel.

A good reference, 02 Jan 2002
Thi sbook is not for everyone. It is pitched somewhere at the undergraduate level or to the high school student who would like to go beyond the syllabus. The book presents the axioms and assumptions clearly and concisely before moving quickly on to analysis and examples. Explanations may be too brief for some but all the information necessary to understand and to handle the exercises are there. This approach may not be suitable for readers who want a quick fix but for those whose passion is mathematics, this is a great primer.

Moves too fast. Does not spend enough time on each topic., 02 Sep 1999
My Advanced Calculus class covered only the first two chapters. While we were spending time on detailed analysis of different types of infinities, this book did not cover it at all. This book was almost no help. Make sure the style of the teacher matches the way this book is written, otherwise it may be a waste. My class would have been a lot easier and less satisfying if it had been conducted the way this is written.

Good not great, 29 Nov 2007
This book is collection of 15 years work and is widely used and highly respected in scientific computing. It seems churlish to criticize it.
However, Numerical Recipes is not without its faults. In my experience (optimisation, MCMC sampling) the algorithms given do not adequately represent the ones available in the field. There is only one global optimiser (simulated annealing), no non-linear contrained optimisers and no mention of slice sampling for instance. This incompleteness would be helped by including a wide ranging bibliography for each group of algorithms. However, I found the references quite limited.
The book describes itself as a cookbook for cooks. Although this is a worthy aim, it cannot compare to reading the original papers or reviews of algorithms available in journals. In essence, this further reading is what someone needs to do in order to alter an algorithm for their own needs.
The shortcomings could be forgiven if the book provided a way of getting something , relatively simple, working quite quickly. However, you have to type the code in yourself or pay extra to get it in electronic form. Using either of these methods, the licencing terms are restrictive and are for personal use only. This made the book an expensive disappointment for me, especially since free alternatives like the GNU scientific library exist.
On the plus side the descriptions of the available algorithms are excellent given the limited space available to describe them. The authors also include tips based on their experience and mention why a particular algorithm may be more popular despite being no better than some of the others. To my knowledge, Numerical Recipes has no decent competition when it comes to the description of algorithms.

Tufte is God, 08 Nov 2005
I think I made Tufte very rich. If I didn't it was not my fault. I was a Displays Manager with IBM and used his book to illustrate how colour & pixels could enhance information. I developed a presentation that used his work to exploit data and its visualisation. As a result I sold one hell of a lot of screens (IBM 3279 colour screens - the first ever colour screens - and at £3,000 a crack I sold 6,000 in the first year alone). I also sold a lot of Tufte's books. The quite brilliant example of Minard's graph of Napoleon's campaign in Russia (contained within the book) would keep an audience occupied for 2 hours - and not a yawn - so if ever the Good Professor decides to make a Will, he should remember me and I hope he predececeases me by a goodly margin so I can drink to his memory in style.

I think Professor Tufte's product is quite safe and unlikely to cause injury or death (Amazon Product Compliance Statement).

Professor Tufte writes simply excellent books., 17 Jan 2002
These books appeal on so many levels. They are informative, interesting and entertaining. Beautifully produced and very well written. One hardly notices one is being educated.

Read it, before you make a really bad mistake., 08 Dec 2001
This book should be a compulsory read for all graphic designers dealing with data visualisation.

The clearly focused chapters, all with superb illustrations, take the reader through some of the best and worst graphics and charts ever printed, with Tufte providing crystalline insights and techniques that will stick in your mind and make your own work better.

Whilst this book deals only with printed graphics, I think that the lessons learned are even more valuable as a foundation for interactive media designers. With the added dimensions of time and user involvement comes the potential to commit far worse design-crimes than many of the examples laid bare in this book!

Like I said: Read it before you make a really bad mistake!

invaluable, every scientist, hell every american should read, 23 Jul 1999
the examples are incredible. this book is one of the most beautiful books I have ever read both for its content and execution. The advice Tufte gives with regard to the presentation of information will only become more important in the future. Whether reading the newspaper or writing a technical report, the proper display of quantitative information is an invaluable skill. this book helps you to think clearly and concisely. one of the best books of all time.

If you have to design anything, read this series, 15 Jul 1999
Whether it is presentation slides or internet sites, the concepts provided in Tufte's books will give you insight and skill that will improve your output 1000%.

There is some overlap between the books, but just looking at the pictures and his explanations and concepts will make you say "AHA!" and improve your next design.

Great For A2 Physics, 15 Sep 2006
I have just started A2 Physics at my school. I didn't do maths to AS (just GCSE). I am the only one in my class without an AS in Maths. My teacher told me that I needed to know about Differentiation and Integration in order to progress my A grade in AS physics to an A in A2.

I always had the idea that Calculus was simply a very complicated area of Mathematics developed by Newton. I didn't know anything else (remember I only had a Maths GCSE).

I thought I'd buy this book to see if it could help me. The fantastic thing is that it explains every single concept in an extremely simple way (starting with the very basics). I believe that I am now up to the high standard of the mathematicians in my class and am able to understand the important mathematical concepts in physics that use calculus as a basis for their explanation. In particular, OCR's Advancing Physics A2 - Creating Models section.

You really don't need to be a math genius to understand this book fully!


Shock, horror, calculus is easy (well sort of!), 06 Nov 2003
If you`ve ever looked at a polynomial equation and thought that learning Martian would be easier, or even that knowing what a polynomial was would make a lot more sense, then this is the book for you. Granted, the book does assume that you have some prior knowledge of algebra and trig but I have only the most basic grasp of them and still managed to follow the book. The chapters are well set out and explain painful looking equations for differentiation and integration in simple,easy to follow terms. Calculus for Dummies acts like a kindly mentor; easing you through the hard bits, holding your hands when the numbers start to look like gibberish and celebrating with you at the end of the chapter that maths no longer seems like a strange and alien concept!

No need to apologize for this, 27 Nov 2008
"Exposition, criticism, appreciation, is work for second-rate minds." Already, in the first paragraph, G. H. Hardy is deploring the task of writing about mathematics in his characteristically forthright fashion. It's just as well that by the time we begin the Apology we have been softened up by C. P. Snow's excellent introduction and potted biography. Clearly, this first-rate book has attracted an altogether better class of reviewer, the self-effacing type not given to hissy fits on being reminded of their place in the intellectual pantheon.

"I had of course found at school, as every future mathematician does, that I could often do things much better than my teachers". Hardy's later achievements and his matter-of-fact style ensure that this is neither preening vanity nor a pompous boast. A professional mathematician might also agree that the "function of a mathematician is to do something" and not to talk about it. Mathematics as an active pursuit, being cleverer than your maths teacher - these count as revelations to ordinary mortals, even those of us who weren't too bad at maths. Then, and before any unsuspecting non-mathematician can run for cover, Hardy sets about proving "two of the famous theorems of Greek mathematics". There is really nothing to be scared of, even for the most equation-phobic humanities graduate. It's the ideas and the arguments that link them that matter, and they are not difficult to follow. In tracing the steps of Euclid and Pythagoras we are tracing patterns of thought that have lasted two thousand years, and we too can directly appreciate their beauty, and see for ourselves in a small way that a "mathematician, like a painter or a poet, is a maker of patterns."

Hardy does not take kindly to the commonplace idea "that an academic career is one sought mainly by cautious and unambitious persons who care primarily for comfort and security." While he is, unsurprisingly, motivated by "intellectual curiosity" and a "desire to know the truth", he also admits to "professional pride", "ambition" and a "desire for reputation". A lesser mind might have been tempted to feign guilt over such worldly traits, but Hardy has only a good word for ambition, the "noble passion". And his own noblest ambition? That "of leaving behind... something of permanent value". No dreams of heavenly bliss for this atheist.

Just when you might be thinking that all this talk of reputation and ambition must arise from an insufferable self-centredness, he declares that much of his best work was done in collaboration with two other mathematicians, Littlewood and Ramanujan, from very different backgrounds. Hardy's recognition of the unknown Indian was not inevitable: two other eminent Englishmen had returned the manuscripts without comment, on the assumption that Ramanujan was a crank. That too was Hardy's first impression, but he soon changed his mind and saw in Ramanujan a brilliant if untutored mathematical mind. It is a remarkable story by any standards, and has been recently staged as "A Disappearing Number" - a brilliant production in which a rather battered copy of this very edition gets a turn in the limelight.

What was a "melancholy experience" for Hardy (writing about mathematics) provides a rewarding experience for us. Graham Greene considered this the best account of what it is like to be a creative artist. I don't know if Greene is right, or if Hardy is right in his belief "that mathematical reality lies outside us," waiting to be discovered. I defer to their judgements but can better appreciate their conclusions after reading this book. C. P. Snow describes Hardy's "mocking horror of pretentiousness, self-righteous indignation, and the whole stately pantechnicon of the hypocritical virtues." More intriguing, given Hardy's hatred of God and all the pious nonsense carried out in God's name, and given that the spiritual side of human nature has been unthinkingly yoked to religious mumbo jumbo for far too long, is Snow's description of Hardy "as spiritually delicate" and "spiritually candid as few men are".

The dominant sense of "apology" implies a fault for which contrition is being expressed. Hardy's Apology is no craven exercise in self-abasement but a serious and vigorous justification of the intellectual and creative life, whether led by a mathematician or anyone else.


How maths used to be, 24 Nov 2008
Reading this book is like opening a time capsule - which is fun, up to a point. The academic world Hardy inhabited was largely swept away by the first world war, and this book is full of the feeling of that threatened world - one of Hardy's main aims is to show that a. "proper" mathematics is of no practical use, and that b. this is good news, partly because this makes it "purer" and hence better (in some unexplained way) partly because then it can't be blamed for killing people.

The idea that mathematicians should justify their incomes through the value of their work (either through actual income generation or through explaining how the universe works) seems not to occur to Hardy; it's hard to imagine any mathematician today making the uselessness of their subject the major theme of a book.

Unfortunately for Hardy, the very areas he singles out as being especially satisfyingly useless are key to modern code-breaking and secure financial transactions - in fact it's hard to think of any substantial area of mathematics that is "useless" in Hardy's sense.

Hardy's style is also very antiquated, involving a great deal of preparatory throat-clearing, unsupported value-judgments, meandering around the subject, and lengthy vagueness. To a modern reader it all seems a bit smug and fake.

On the other hand, the actual points that Hardy makes about the way mathematicians develop ideas, and the examples of explanations of the amazing way mathematical proof works, are good ones. And, as a look back at a vanished period of academic history, it's great. But as an introduction to how mathematicians work now, or the role of mathematical research, it has become a very weak book.



Hardy's Apology, 23 Jul 2008
I bought Hardy's biography almost 50 years ago, just before going up to university to read Maths. The gentle almost humourous tone of the book convinced me that the life of a mathematician was a potential source of pleasure. In fact I later moved to read Philosophy, for my interests grew to centre on Logic and Mathematical Foundations, but my current work on Infinity still finds me using Hardy's "Pure Mathematics", and I still occasionally read his "Apology" for the pure pleasure that this outstanding book provides.

Disappointing, 26 Mar 2008
I'm not sure I read the same book as the other reviewers. I'm fascinated by mathematics and have, for a long time, been meaning to read this book. Finally I have, and I have to say I was somewhat disappointed. C.P. Snow's foreword was an interesting potted biography of one of Britain's greatest 20th century mathematicians; but, the "apology" itself is overshadowed by its own introduction.

The first nine chapters are a clear indication - if any was needed - that intellectual brilliance is no talisman against small-mindedness. Maybe I'm being unfair but in those nine short chapters Hardy manages to denigrate most of humanity - "most people can do nothing at all well" - by which he means, nothing that he personally considers worthy. I'm not convinced we should readily accept the social opinions of a man who was born to privilege and spent his entire life in rarefied cloisters shielded from what the "most" in question would consider reality. A man who thought we should not go to war with Germany because of the caliber of its mathematicians and scientists. (?) There are many reasons why we shouldn't be at war with Iraq, for example, but that the region is the cradle of civilisation is not one of them.

From chapter ten onwards the book makes a change of direction and deals with the actual subject of mathematics and being a mathematician. This latter section of the book is a much more interesting (less infuriating) read but I still felt he dealt rather ineptly with the attempt to differentiate between "common and garden" mathematics and the truly profound and beautiful creative mathematics that he so clearly loves.

When you compare this book to say Marcus du Sautoy's "Music of the Primes" or Simon Singh's "Fermat's Last Theorem", both books which truly promote the essential character of mathematics, "A Mathematician's Apology" seems very pale.

Read it. Seriously., 04 Feb 2008
This book is a facinating insight into the mind of one of the century's greatest mathematians. However, Hardy's ideas go far beyond this into the purpose of human endevour in general.
The best part of this book is the foreword by C.P Snow. This amounts to a lucid, if brief, biography of Hardy from a man who is brilliant in his own right.
If you have any kind of interest in the realities of mathematics, or the workings of genius, then this book is the place to start.

Compact knowledge, 15 Apr 2008
I found this book is very interesting. I used this book when doing my research. For me, it is a compact knowledge inside one book. I do not need to search for other book for reference.

This book provide easy to understand structure. A lot of example and proof make this book is very nice.

I agree that this book is good for undergraduate, but it is also good for high level education.

Complete and effective, 10 Jul 2004
This is a very effective book for the student :
- the knowledge is neatly summed up, and proofs are given just afterwards and don't interfere with the concepts, so that reading and understanding the lessons is easy,
- hundreds of corrected exercises, very gradual,
- very complete for undergrads (and enough for most grads who won't do Physics for example).

This book and the S. Lipschutz one on linear algebra are among those I've kept for further use.

Ce livre est hautement recommandable pour le premier cycle scientifique. Clair, complet et graduel.

A good reference, 02 Jan 2002
Thi sbook is not for everyone. It is pitched somewhere at the undergraduate level or to the high school student who would like to go beyond the syllabus. The book presents the axioms and assumptions clearly and concisely before moving quickly on to analysis and examples. Explanations may be too brief for some but all the information necessary to understand and to handle the exercises are there. This approach may not be suitable for readers who want a quick fix but for those whose passion is mathematics, this is a great primer.

Moves too fast. Does not spend enough time on each topic., 02 Sep 1999
My Advanced Calculus class covered only the first two chapters. While we were spending time on detailed analysis of different types of infinities, this book did not cover it at all. This book was almost no help. Make sure the style of the teacher matches the way this book is written, otherwise it may be a waste. My class would have been a lot easier and less satisfying if it had been conducted the way this is written.

Good not great, 29 Nov 2007
This book is collection of 15 years work and is widely used and highly respected in scientific computing. It seems churlish to criticize it.
However, Numerical Recipes is not without its faults. In my experience (optimisation, MCMC sampling) the algorithms given do not adequately represent the ones available in the field. There is only one global optimiser (simulated annealing), no non-linear contrained optimisers and no mention of slice sampling for instance. This incompleteness would be helped by including a wide ranging bibliography for each group of algorithms. However, I found the references quite limited.
The book describes itself as a cookbook for cooks. Although this is a worthy aim, it cannot compare to reading the original papers or reviews of algorithms available in journals. In essence, this further reading is what someone needs to do in order to alter an algorithm for their own needs.
The shortcomings could be forgiven if the book provided a way of getting something , relatively simple, working quite quickly. However, you have to type the code in yourself or pay extra to get it in electronic form. Using either of these methods, the licencing terms are restrictive and are for personal use only. This made the book an expensive disappointment for me, especially since free alternatives like the GNU scientific library exist.
On the plus side the descriptions of the available algorithms are excellent given the limited space available to describe them. The authors also include tips based on their experience and mention why a particular algorithm may be more popular despite being no better than some of the others. To my knowledge, Numerical Recipes has no decent competition when it comes to the description of algorithms.

Good, but you have to work at reading it, 08 Feb 2008
If I had never read any of Eli Maor's excellent books I would have scored this book as 5 stars. It is a very good book that guides you through a series of difficult mathematical concepts without being a textbook. It is very readable, but it is peppered with 'roadblocks' where you suddenly have to pay a lot more attention, and possibly re-read sections, before you can proceed. It also, despite being a new 'bugs removed' edition, has at least one grammatical error which makes a paragraph hard to follow.

Having said all that, it really is a very good book. It is just that I have been spoiled by Eli Maor's books, which cover similar ground (trigonometry, e) in a similar way (history, characters, mathematical ideas, related concepts), but manage to make it an effortless joy for the reader. This book somehow never became a joy to read.

Disappointing presentation of the material, 14 Oct 2002
I read this book on the back of having just finished Eli Maor's excellent "To infinity and beyond". Unlike Maor's book, "An imaginary tale" is poorly written and presented. While Maor has a fluid and engrossing writing style, Nahin is much less convincing. The material is all there, but it's the presentation with which I have a problem. It's not all bad -- the chapter on the geometry of i is well done, for example, but that's the exception rather than the rule. Another problem is the poor quality of the diagrams. Cubic curves are hastily drawn freehand. Right angled triangles don't always have right angles, and so on. On the whole, I came away with an impression of a book with lots of potential, but most of it left unrealised.

Eulogy, 23 Aug 1999
I rate this book as one of the three best general mathematical books that I have ever bought. Its style is clear and light and the scope of the mathematics is breathtaking; I learnt a great deal from it and saw explained some hard ideas in a very readable way. Not every question is answered but as the author says it isn't a text book. If you want to get into complex analysis and learn about its development and the geniuses who have been involved in it I can think of no better path to take-but you will need to work at some bits! The author avoids actually defining complex numbers in a rigorous way and I would have liked to have seen them defined somewhere as ordered pairs of reals with a reasonable definition of addition and a funny definition of multiplication, with i simply a change of notation. Not easy to fit into the historical development but worth an appendix.

Buy the book. If you don't like it I reckon the problem's with you!

Fantastic! Thorough, scholarly, interesting!, 05 Mar 1999
This is an excellent, beautiful book! Just the section on Kepler's laws is worth the price of the book (hardcover to boot!)

If you like math, if you are willing to spend a bit of time understanding the wonderful results -- get it! Some calculus background needed -- nothing beyond high school.

The book goes well beyond providing a narrative on the history of "square root of -1". It actually shows in complete detail how to use "i" to do wonderful things. Along the way the author provides the important historical events and plenty of notes and references for anyone interested in getting some more. It is clear the author took his time to research and study the subject. He has presented it well, thouroghly, and in an interesting way -- without sacrificing detail!

Tufte is God, 08 Nov 2005
I think I made Tufte very rich. If I didn't it was not my fault. I was a Displays Manager with IBM and used his book to illustrate how colour & pixels could enhance information. I developed a presentation that used his work to exploit data and its visualisation. As a result I sold one hell of a lot of screens (IBM 3279 colour screens - the first ever colour screens - and at £3,000 a crack I sold 6,000 in the first year alone). I also sold a lot of Tufte's books. The quite brilliant example of Minard's graph of Napoleon's campaign in Russia (contained within the book) would keep an audience occupied for 2 hours - and not a yawn - so if ever the Good Professor decides to make a Will, he should remember me and I hope he predececeases me by a goodly margin so I can drink to his memory in style.

I think Professor Tufte's product is quite safe and unlikely to cause injury or death (Amazon Product Compliance Statement).

Professor Tufte writes simply excellent books., 17 Jan 2002
These books appeal on so many levels. They are informative, interesting and entertaining. Beautifully produced and very well written. One hardly notices one is being educated.

Read it, before you make a really bad mistake., 08 Dec 2001
This book should be a compulsory read for all graphic designers dealing with data visualisation.

The clearly focused chapters, all with superb illustrations, take the reader through some of the best and worst graphics and charts ever printed, with Tufte providing crystalline insights and techniques that will stick in your mind and make your own work better.

Whilst this book deals only with printed graphics, I think that the lessons learned are even more valuable as a foundation for interactive media designers. With the added dimensions of time and user involvement comes the potential to commit far worse design-crimes than many of the examples laid bare in this book!

Like I said: Read it before you make a really bad mistake!

invaluable, every scientist, hell every american should read, 23 Jul 1999
the examples are incredible. this book is one of the most beautiful books I have ever read both for its content and execution. The advice Tufte gives with regard to the presentation of information will only become more important in the future. Whether reading the newspaper or writing a technical report, the proper display of quantitative information is an invaluable skill. this book helps you to think clearly and concisely. one of the best books of all time.

If you have to design anything, read this series, 15 Jul 1999
Whether it is presentation slides or internet sites, the concepts provided in Tufte's books will give you insight and skill that will improve your output 1000%.

There is some overlap between the books, but just looking at the pictures and his explanations and concepts will make you say "AHA!" and improve your next design.

Great For A2 Physics, 15 Sep 2006
I have just started A2 Physics at my school. I didn't do maths to AS (just GCSE). I am the only one in my class without an AS in Maths. My teacher told me that I needed to know about Differentiation and Integration in order to progress my A grade in AS physics to an A in A2.

I always had the idea that Calculus was simply a very complicated area of Mathematics developed by Newton. I didn't know anything else (remember I only had a Maths GCSE).

I thought I'd buy this book to see if it could help me. The fantastic thing is that it explains every single concept in an extremely simple way (starting with the very basics). I believe that I am now up to the high standard of the mathematicians in my class and am able to understand the important mathematical concepts in physics that use calculus as a basis for their explanation. In particular, OCR's Advancing Physics A2 - Creating Models section.

You really don't need to be a math genius to understand this book fully!


Shock, horror, calculus is easy (well sort of!), 06 Nov 2003
If you`ve ever looked at a polynomial equation and thought that learning Martian would be easier, or even that knowing what a polynomial was would make a lot more sense, then this is the book for you. Granted, the book does assume that you have some prior knowledge of algebra and trig but I have only the most basic grasp of them and still managed to follow the book. The chapters are well set out and explain painful looking equations for differentiation and integration in simple,easy to follow terms. Calculus for Dummies acts like a kindly mentor; easing you through the hard bits, holding your hands when the numbers start to look like gibberish and celebrating with you at the end of the chapter that maths no longer seems like a strange and alien concept!

No need to apologize for this, 27 Nov 2008
"Exposition, criticism, appreciation, is work for second-rate minds." Already, in the first paragraph, G. H. Hardy is deploring the task of writing about mathematics in his characteristically forthright fashion. It's just as well that by the time we begin the Apology we have been softened up by C. P. Snow's excellent introduction and potted biography. Clearly, this first-rate book has attracted an altogether better class of reviewer, the self-effacing type not given to hissy fits on being reminded of their place in the intellectual pantheon.

"I had of course found at school, as every future mathematician does, that I could often do things much better than my teachers". Hardy's later achievements and his matter-of-fact style ensure that this is neither preening vanity nor a pompous boast. A professional mathematician might also agree that the "function of a mathematician is to do something" and not to talk about it. Mathematics as an active pursuit, being cleverer than your maths teacher - these count as revelations to ordinary mortals, even those of us who weren't too bad at maths. Then, and before any unsuspecting non-mathematician can run for cover, Hardy sets about proving "two of the famous theorems of Greek mathematics". There is really nothing to be scared of, even for the most equation-phobic humanities graduate. It's the ideas and the arguments that link them that matter, and they are not difficult to follow. In tracing the steps of Euclid and Pythagoras we are tracing patterns of thought that have lasted two thousand years, and we too can directly appreciate their beauty, and see for ourselves in a small way that a "mathematician, like a painter or a poet, is a maker of patterns."

Hardy does not take kindly to the commonplace idea "that an academic career is one sought mainly by cautious and unambitious persons who care primarily for comfort and security." While he is, unsurprisingly, motivated by "intellectual curiosity" and a "desire to know the truth", he also admits to "professional pride", "ambition" and a "desire for reputation". A lesser mind might have been tempted to feign guilt over such worldly traits, but Hardy has only a good word for ambition, the "noble passion". And his own noblest ambition? That "of leaving behind... something of permanent value". No dreams of heavenly bliss for this atheist.

Just when you might be thinking that all this talk of reputation and ambition must arise from an insufferable self-centredness, he declares that much of his best work was done in collaboration with two other mathematicians, Littlewood and Ramanujan, from very different backgrounds. Hardy's recognition of the unknown Indian was not inevitable: two other eminent Englishmen had returned the manuscripts without comment, on the assumption that Ramanujan was a crank. That too was Hardy's first impression, but he soon changed his mind and saw in Ramanujan a brilliant if untutored mathematical mind. It is a remarkable story by any standards, and has been recently staged as "A Disappearing Number" - a brilliant production in which a rather battered copy of this very edition gets a turn in the limelight.

What was a "melancholy experience" for Hardy (writing about mathematics) provides a rewarding experience for us. Graham Greene considered this the best account of what it is like to be a creative artist. I don't know if Greene is right, or if Hardy is right in his belief "that mathematical reality lies outside us," waiting to be discovered. I defer to their judgements but can better appreciate their conclusions after reading this book. C. P. Snow describes Hardy's "mocking horror of pretentiousness, self-righteous indignation, and the whole stately pantechnicon of the hypocritical virtues." More intriguing, given Hardy's hatred of God and all the pious nonsense carried out in God's name, and given that the spiritual side of human nature has been unthinkingly yoked to religious mumbo jumbo for far too long, is Snow's description of Hardy "as spiritually delicate" and "spiritually candid as few men are".

The dominant sense of "apology" implies a fault for which contrition is being expressed. Hardy's Apology is no craven exercise in self-abasement but a serious and vigorous justification of the intellectual and creative life, whether led by a mathematician or anyone else.


How maths used to be, 24 Nov 2008
Reading this book is like opening a time capsule - which is fun, up to a point. The academic world Hardy inhabited was largely swept away by the first world war, and this book is full of the feeling of that threatened world - one of Hardy's main aims is to show that a. "proper" mathematics is of no practical use, and that b. this is good news, partly because this makes it "purer" and hence better (in some unexplained way) partly because then it can't be blamed for killing people.

The idea that mathematicians should justify their incomes through the value of their work (either through actual income generation or through explaining how the universe works) seems not to occur to Hardy; it's hard to imagine any mathematician today making the uselessness of their subject the major theme of a book.

Unfortunately for Hardy, the very areas he singles out as being especially satisfyingly useless are key to modern code-breaking and secure financial transactions - in fact it's hard to think of any substantial area of mathematics that is "useless" in Hardy's sense.

Hardy's style is also very antiquated, involving a great deal of preparatory throat-clearing, unsupported value-judgments, meandering around the subject, and lengthy vagueness. To a modern reader it all seems a bit smug and fake.

On the other hand, the actual points that Hardy makes about the way mathematicians develop ideas, and the examples of explanations of the amazing way mathematical proof works, are good ones. And, as a look back at a vanished period of academic history, it's great. But as an introduction to how mathematicians work now, or the role of mathematical research, it has become a very weak book.



Hardy's Apology, 23 Jul 2008
I bought Hardy's biography almost 50 years ago, just before going up to university to read Maths. The gentle almost humourous tone of the book convinced me that the life of a mathematician was a potential source of pleasure. In fact I later moved to read Philosophy, for my interests grew to centre on Logic and Mathematical Foundations, but my current work on Infinity still finds me using Hardy's "Pure Mathematics", and I still occasionally read his "Apology" for the pure pleasure that this outstanding book provides.

Disappointing, 26 Mar 2008
I'm not sure I read the same book as the other reviewers. I'm fascinated by mathematics and have, for a long time, been meaning to read this book. Finally I have, and I h