Rate this book

Clear rating

1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars

A Mathematician's Apology

3.89 of 5 stars 3.89 · rating details · 1,229 ratings · 77 reviews

Written in 1940 as his mathematical powers were declining, G.H. Hardy's apology offers an engaging account of the thoughts of a man known for his eccentricities as well as his brilliance in mathematics.

Paperback, 153 pages

Published January 31st 1992 by Cambridge University Press (first published 1940)

more details... edit details

Get a copy:

More…

Friend Reviews

To see what your friends thought of this book, please sign up.

Lists with This Book

Gödel, Escher, Bach by Douglas R. Hofstadter

Journey through Genius by William Dunham

Best Books About Mathematics

15th out of 132 books — 153 voters

Nicolle's Reading List

50th out of 92 books — 26 voters

More lists with this book...

Community Reviews

(showing 1-30 of 2,609)

filter | sort: default (?) | rating details

Feb 05, 2013 Yasiru rated it 5 of 5 stars

Shelves: mathematics, favourites

The text may be found at http://www.math.ualberta.ca/~mss/misc...

I had the good fortune to come across this title just as I was finally beginning to see the glimmers of beauty in mathematics thanks to the efforts of some wonderful instructors on the subject during my later school years. It called upon me for a deeper reflection on my chosen pursuit, which at that point appealed to me for its fundamental importance to the other sciences and for the simple pleasure that can be gleaned of it. I was...more The text may be found at http://www.math.ualberta.ca/~mss/misc...

I had the good fortune to come across this title just as I was finally beginning to see the glimmers of beauty in mathematics thanks to the efforts of some wonderful instructors on the subject during my later school years. It called upon me for a deeper reflection on my chosen pursuit, which at that point appealed to me for its fundamental importance to the other sciences and for the simple pleasure that can be gleaned of it. I was confronted with a fleeting, tricksome nature even in mathematical truth, which had till then been sacrosanct and taken for granted. It became apparent that there was more artistic excitement in mathematics than the safety of empirical sciences and it has been my great love ever since, however modestly ability dresses me.

Hardy's is an essay of paradoxes and duals, with examples littered through the text. These may seem contradictory at a glance, but close scrutiny reveals them to be mutually reliant points that hint to the complexities of Hardy's pursuit. One instance is in his claim that mathematical patterns are more enduring than any artist's or poet's. While this may leave many an artist or poet bristling, this endurance is manifest in the progression of a mathematician's significant ideas, even though these are all in a language of ideas that does not rely on being evocative (so unlike the artist or poet). This is at odds however, with the aesthetic appreciation to be had in nontrivial mathematics that Hardy keeps returning to. The prospect of leaving some mark so enduring is certainly catering to ambition (which Hardy encourages), but this is incompatible with failing to capture beauty, and so it is that one cannot stand without the other. It has been said that this is a tragic account, but here is a thread of hope- that one should remain steadfast in the area of one's talent and atop that cultivate ambitions and seek too what is beautiful. There is a terrible, indubitable rationale here which could strike some as arrogant (though even if it were taken to be so, not something diminishing from the work), but is ultimately a course of efficiency (something Hardy valued in his mathematical aesthetic) devoid of any lingering melancholy.

Another instance is what he has to say about the worthwhile mathematics and trivial. Frequently, Hardy is misrepresented as disdaining applied mathematics upon the haughty perch of the pure. This is unfortunate since special mention is made that mathematicians do not tend to revel in the uselessness of their work. Hardy is no fool to try untangling the mathematics that will come to some use and what stands detached and austere. He draws the crucial distinction instead based on aesthetic value once again, setting aside those abundant trifles of mathematics so often connected with the mundane world of everyday and advocating the deep framework (of rather few significant contributions) of what might be dubbed the 'true mathematics'. Hardy is rather half-hearted about elaborating on his standards of beauty, but there is no real surprise in this for anyone acquainted with higher mathematics, because it really is a difficult thing to define. There is efficiency and sweeping elegance in a great result, but too a contribution to that progression of ideas which makes mathematics so enduring. Whether these criteria capture beauty is contestable and so I make no claims. But this difficulty in explaining a thing like beauty highlights the crucial problem in Hardy's endeavour to explain to the public what a mathematician does and why. He justifies the pursuit of the true mathematics exactly because it is so removed from mundane being and so comes of purer intentions than much else that can be directed to harm as well as good, but it is a difficult thing to impart the joy of actually doing mathematics to the uninitiated, which is perhaps why so many reviews have picked upon the thread of personal tragedy here (partly owing to the foreword I suppose, thought Hardy's circumstances are the least of the work's significance, I thought, both on my first reading and now) instead of the 'apology' itself. There is nowadays a great scuffle to get some manner of emotional fix upon an author one is reading. This sort of thing is seldom the author's intent (else they would simply save themselves the trouble of writing a reasoned and coherent account with objective value and instead send their diaries to a publisher), especially in a work as this where the author is attempting to convey a position and defend it. The arguments do not require lenses coloured with the author's circumstances. I imagine Hardy the pure mathematician would rather have avoided this, as he remarks the following in the present work (something of a spoiler warning is due here)-

"Dr Snow had also made an interesting point about §8. Even if we grant that ‘Archimedes will be remembered when Aeschylus is forgotten’, is not mathematical fame a little too ‘anonymous’ to be wholly satisfying? We could form a fairly coherent picture of the personality of Aeschylus (still more, of course, of Shakespeare or Tolstoi) from their works alone, while Archimedes and Eudoxus would remain mere names. Mr J M Lomas put this point more picturesquely when we were passing the Nelson column in Trafalgar square. If I had a statue on a column in London, would I prefer the columns to be so high that the statue was invisible, or low enough for the features to be recognizable? I would choose the first alternative, Dr Snow, presumably, the second."
(Dr Snow here is C P Snow, who wrote the foreword to this edition. It's worth reading, but perhaps after Hardy's own words, since its biographical tint somewhat along the line I've discussed above may detract from the potent general ideas Hardy is forwarding here.)

Few other works have attempted the exposition of what creative enterprise demands and entails quite so well as this one, and this from a master who has seen ability and passions come and go. I recommend it highly.(less)

like 1 like · see review

May 09, 2013 Jocelyn rated it 4 of 5 stars

Recommended to Jocelyn by: Yasiru

Shelves: needs-review, interesting-stuff

Ok, going to review this in earnest. Review pending.

like 2 likes · see review

May 16, 2013 spoko rated it 2 of 5 stars

I am a bit of a sucker for esoteric works that stand out beyond their field. One of my favorite books is Eric Gill's Essay on Typography, for example. So I had asked for recommendations in an online forum, and this was one of the ones that was suggested. It was the only one that wasn't from the hard sciences, and it wasn't that long, so I figured I'd give it a shot. Honestly, I barely finished it. If it weren't that I am this particular type of sucker, and also that I had a goal of reading a cer...more

like · see review

Apr 28, 2013 the review man rated it 3 of 5 stars

Shelves: math-and-stats, religion-or-lack-thereof

My skill in mathematics pales in comparison to Hardy's, but here goes anyway.

Essentially, pure mathematics is more 'important' (if such a thing can be said) than applied mathematics, because the research conducted in the latter depends on the former. For example, cryptographers would not have a job were it not for the pure mathematicians who discovered the basis of the field in the 1970s. However, Hardy's comments about the utility of mathematics are outdated due to the importance of number theo...more

like 1 like · see review

Jan 06, 2013 Ryan Kasyfil rated it 4 of 5 stars

G.H. Hardy adalah seorang yang jenius di matematika. Ia mengemukakan pendapatnya tentang matematika yang sebenarnya. Ia membagi matematika dalam dua kategori : useless dan useful. Ia menyebut golongan useless sebagai "real mathematician" dan golongan useful sebagai "trivial mathematician". Terdapat kontradiksi dalam istilah yang ia gunakan. "real" untuk useless dan "trivial" untuk useful, namun ia memberikan alasan yang menarik untuk pemakaian istilah ini.

Ia memberikan Judul dari buku ini adalah...more G.H. Hardy adalah seorang yang jenius di matematika. Ia mengemukakan pendapatnya tentang matematika yang sebenarnya. Ia membagi matematika dalam dua kategori : useless dan useful. Ia menyebut golongan useless sebagai "real mathematician" dan golongan useful sebagai "trivial mathematician". Terdapat kontradiksi dalam istilah yang ia gunakan. "real" untuk useless dan "trivial" untuk useful, namun ia memberikan alasan yang menarik untuk pemakaian istilah ini.

Ia memberikan Judul dari buku ini adalah a mathematician's apology : sebuah permintaan maaf seorang matematikawan karena saya merasa Hardy memang meminta maaf kepada golongan Trivial atas deskripsi yang ia berikan. Saya sendiri memang merasa bahwa Hardy "mengejek" para golongan Trivial karena baginya, Real Mathematics adalah suatu hal berat yang tak bisa dikerjakan oleh orang selevel "trivial".

Saya berkuliah dijurusan matematika dan bahkan melanjutkan pendidikan saya ke jenjang yang lebih tinggi. Penelitian saya adalah di bidang modern algebra, yang dikategorikan Hardy ke dalam "real mathematics", maka saya sebenarnya ingin mengatakan bahwa saya adalah seorang "real mathematician". Tapi rasanya buku ini tak mengizinkan saya untuk menyebut diri saya seorang "real". Memang ada bagian dari buku ini yang membuat saya merasa bangga mengambil bidang pure math, tetapi ada sedikit rasa kesal dan iri. At least buku ini memotivasi saya agar saya lebih banyak belajar dan suatu saat nanti saya merasa pantas memanggil diri saya "real mathematician".

Saya ingat kalimat Hardy dalam buku ini : A mathematician, like a painter or poet, is a maker of patterns. A mathematician's patterns, like the painter's or poet's must be beautiful. Beauty is the first test : there is no permanent place in this world for ugly mathematics. Inilah inti dari buku ini, memisahkan matematika yang sebenarnya dengan matematika yang jelek. Hardy menjelaskan pemikirannya dengan cukup ekstrim.

Saya menyarankan bagi siapapun yang mengaku matematikawan untuk membaca buku ini. Hanya 56 lembar, tapi cukup membuat emosi saya sebagai matematikawan teraduk.(less)

like · see review

May 27, 2012 Jason rated it 5 of 5 stars

Shelves: nonfiction, mathematics, memoir

A Mathematician's Apology has been on my mental reading list for a long time and, like many titles on that mental list, I cannot understand how I didn't read it before. The edition contains a 50 page Foreword by C.P. Snow followed by the 90 page book by Hardy (actually, adjusting for different font sizes, the two parts are probably about equal in length). I read the book first so that I could think about it on its own terms and the Foreword afterwords. Both of them are outstanding and I would re...more

like · see review

Apr 02, 2012 Douglas Dalrymple rated it 2 of 5 stars

I wonder how much my enjoyment of this book was hampered by my mathematical incompetence. Not too much, I hope. CP Snow’s introduction is as good as the book, but you can’t fault Hardy with not giving you something to chew on. Rather than try to summarize my feelings about Hardy’s little book, I’m going to take the lazy option here and simply repost from my blog:

-

In A Mathematician’s Apology G.H. Hardy estimates that only five or ten people in a hundred can do something “rather well.” Considerab...more I wonder how much my enjoyment of this book was hampered by my mathematical incompetence. Not too much, I hope. CP Snow’s introduction is as good as the book, but you can’t fault Hardy with not giving you something to chew on. Rather than try to summarize my feelings about Hardy’s little book, I’m going to take the lazy option here and simply repost from my blog:

-

In A Mathematician’s Apology G.H. Hardy estimates that only five or ten people in a hundred can do something “rather well.” Considerably fewer are really gifted. We do not each have a valuable talent waiting for discovery. We may dream of making names for ourselves, but most “talents” are talents only by inflation, and many true talents are never valued. The influence of the cult of achievement extends even beyond its membership. Those who renounce the pursuit of worldly accomplishment often do so with other (more comfortably nebulous) goals in mind: sainthood, perhaps, or self-realization. They’re chasing the same fox by another tail.

Hardy’s calculation is stark, and depressing. I’ve been working on a novel two nights each week for the past four years. I’m well into my third draft and hope to shop it around to agents this summer. Re-reading and re-writing it is a bruising, infuriating, ego-punishing business. What I’ve created is, I think, better than a lot of what gets published today, but that’s saying awfully little when 99% of what gets published is an unjustifiable waste of both writer’s and reader’s time. Almost every book ever written more than deserves its inevitable oblivion.

My book surely will too. Though I’m bold enough to say that it’s “better than many,” I’m not going to fool myself and say “better than 99%.” It may beat fifty or even sixty percent of the schlock printed these days, but I won’t bluff any higher than that. Even if I succeed in getting it published, it’s not something to be too ridiculously proud of. If writing it has taught me anything, it’s that I am no Herman Melville or Henry James. Tonic as it may be to fess up to that inadequacy, my sickness is such that I plod on anyway. I’m even making notes for a second book. Ambition isn’t going to let lack of genius stand in its way.

I may be neglecting avenues for achievement that are better suited to me. Hardy writes that “poetry is more valuable than cricket, but Bradman would be a fool if he sacrificed his cricket in order to write second-rate minor poetry.” I know nothing about cricket or Bradman, but I’ll agree that you don’t give up on a first-rate talent merely because it happens to be for a second-rate activity. I manage to make a living in the business world without much effort. What might I achieve if I focused my ambitions in that direction? But most days it’s a struggle even to fake a tepid enthusiasm.

According to Hardy, first-rate minds care only for creation. If second-rate minds care for it too, so much the worse for them. They would do better, he says, to restrict themselves to the very second-rate tasks of criticism and appreciation. “Appreciation.” The term, as he utters it, drips condescension. But I want to say that Hardy gets it wrong here. He shows his scheme of values to be debased. It may be that I’m too democratic-minded, or just plotting myself an escape from Hardy’s sentence, but I hate the idea that the worthiest of human endeavors is beyond the reach of most people. Surely it’s not only scarce things that can have ultimate value?

Appreciation, in the sense of pure enjoyment, seems to me a better candidate than creative accomplishment for the title of “man’s true work.” It may sound Jeffersonian (“pursuit of happiness”), or Epicurean, or bourgeois of me to say so. I don’t mean that people with leisure are morally superior to those without it. But though it’s not an idea that lends itself to proof by argument, I do believe that, other things being equal, there’s no nobler human aspiration than simply to enjoy and delight in things. To appreciate a particular face, a meal, a tree, a note, a book, a fact, an idea is something available to most of us. To enjoy something to the limit of one’s capacity is better than to create it.
(less)

like 2 likes · see review

May 31, 2011 Nick rated it 4 of 5 stars

Amusing, even if it was as sad as the introduction suggested. Read it in high school, but haven't since. Glad I took another crack at it. It just about made me want to crack open one of my math books! I enjoyed the style of exposition, as well as much of the message, though, admittedly, I probably lost track of an argument here or there.

I think avoided pulling out some of the more quoted passages, though I'm sure these aren't entirely original selections:

68: If a man has any genuine talent, he s...more Amusing, even if it was as sad as the introduction suggested. Read it in high school, but haven't since. Glad I took another crack at it. It just about made me want to crack open one of my math books! I enjoyed the style of exposition, as well as much of the message, though, admittedly, I probably lost track of an argument here or there.

I think avoided pulling out some of the more quoted passages, though I'm sure these aren't entirely original selections:

68: If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.

70: ... it is undeniable that a gift for mathematics is one of the most specialized talents, and that mathematicians as a class are not particularly distinguished for general ability of versatility. If a man is any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that he would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields.

73: It is quite true that most people can do nothing well. <-- Dang, Hardy. How do you really feel?

77: A man's first duty, a young man's at any rate, is to be ambitious. Ambition is a noble passion which may legitimately take many forms...

80: [A mathematician's] subject is the most curious of all -- there is none in which truth plays such odd pranks.

116: Mathematics may, like poetry or music, 'promote and sustain a lofty habit of mind'...

117-8: It is indeed rather astonishing how little practical value scientific knowledge has for ordinary men, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to its reputed utility. <-- ah, school

143: When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one how can easily take refuge where, as Bertrand Russell says, 'one at least of our nobler impulses can best escape from the dreary exile of the actual world.'(less)

like 4 likes · see review

Feb 16, 2011 Basicallyrun rated it 4 of 5 stars · review of another edition

Shelves: non-fiction, science-maths

I read this because I have vague hopes of writing a mathematician character at some point in the future and hoped it would help me understand some of the mindset. And it did. Some of it. I suspect I'm just too un-mathematical to get all of Hardy's points (especially the bits where he says 'This is a beautiful theorem. If you don't find it beautiful, you're clearly not cut out to be a mathematician.' Well, I *know* I'm not, but I'd have liked a little more explanation of what *makes* it beautiful...more

like · see review

Jul 31, 2010 Manussawee rated it 3 of 5 stars

Shelves: recently-read

I heard about this book on NPR so I thought to check it out. The story is written by mathematician Godfrey Hardy, a man who is accredited for many number theory and and other mathematical analysis. The "apology" is actually more like an explanation of his passion for math and why he believes it's more "pure" than any other forms of science.

The mass of mathematical truth is obvious and imposing; its practical applications, the bridges and steam-engines and dynamos, obtrude themselves on the dulle

...more

like · see review

Jan 23, 2010 Fraser Kinnear rated it 4 of 5 stars

Shelves: math

The C.P. Snow introduction, which was nearly as long as the Apology itself, was a fantastic inclusion, as it provided context which I felt really brought me closer to Hardy. Without it, I think, I would have found Hardy to have been a bit too full of himself, as he feels dismissive of perspectives other than his own. Having said that, Hardy is very sensible in explaining the limits of his ability to explain his thoughts, and admits that he is unqualified to approach topics like the aesthetics of...more The C.P. Snow introduction, which was nearly as long as the Apology itself, was a fantastic inclusion, as it provided context which I felt really brought me closer to Hardy. Without it, I think, I would have found Hardy to have been a bit too full of himself, as he feels dismissive of perspectives other than his own. Having said that, Hardy is very sensible in explaining the limits of his ability to explain his thoughts, and admits that he is unqualified to approach topics like the aesthetics of mathematics philosophically.

I've come away really wishing that I had this book as part of a dialog, rather than a soliloquy which. I think that there is a lot of fertile ground here, especially in comparing his Platonism with other schools of thought at the time, which he must have been aware of, like Wittgenstein.

Hardy's main point (I think) is that there are two types of mathematics: Real (academic, pure) and trivial (basic, simple, everyday). Trivial mathematics is applied to our lives and serves its purpose (and so is commonly known as applied mathematics). But real mathematics has almost no connection to our lives (outside of philosophy and some of the high sciences), even if it is describing a reality that Hardy, as a Platonist, believes is greater than the one we observe. Real mathematics, to Hardy, can only "be justified as art if it can be justified at all."

This may be seen as a sad book, certainly. But I see Hardy's opinion of his own mortality (he committed suicide) as starkly inconsistent with his opinion of pure mathematics. Near the close of the book, Hardy admits "It is plain now that my life, for what it is worth, is finished, and that nothing I can do can perceptibly increase or diminish its value." What a shame that he considers his life finished because he can't increase its value. Hasn't he spent an entire book justifying (or at least enjoying) something which he admits to be useless? If Hardy saw his life the way he saw his mathematics, he would have spent the remainder of it enjoying himself, simply for his own sake.(less)

like · see review

Jul 16, 2009 Bill Johnston rated it 3 of 5 stars

Despite how well known it is, and how many say it speaks for mathematics, I am unable to give this book a high rating. I doubt the less-than-stellar 50 page introduction to a 100 page book biased me against the actual A Mathematician's Apology. The Apology is a long-winded, repetitive statement of a few core beliefs of mathematics professors: that pure math is better than applied, that logic is better than reality, and that they can take satisfaction that their actions will neither help nor harm...more

like 1 like · see review

Feb 04, 2013 Hasan rated it 4 of 5 stars

Often at times I have "deluded" myeslf into thinking that I would enjoy doing Mathematics. The delusion lies not in the act in itself but is described by the fact that I admit I do not have the capacity to do Mathematics as Hardy describes it: a creative act.

Some reviewers have claimed that Hardy's tone is one of lamentation (of a Mathematician not able to do Mathematics). One can certainly find evidence of this in his writing though it is not as pronounced as has been made out to be. Snow's fo...more

like · see review

Sep 06, 2009 Teeuhh rated it 3 of 5 stars

I was a bit put off by what I felt was an arrogant attitude in the beginning - but then he began to actually talk about math. It's clear he's much better at that than discourse on what it means to be a poet or painter. By the end, when you could really tell he was trying to make a big sweeping point about the worth of his existence and work, I couldn't help but feel a little sorry for the guy. I mean look at this, “It is indeed rather astonishing how little practical value scientific knowledge h...more

like · see review

Jan 24, 2013 Mary rated it 4 of 5 stars

As anyone who knows me can attest, I am NOT by any means a mathematician. And, full disclosure, i skimmed a lot of the heavier math sections. Nevertheless I enjoyed this short book about the beauty and art of pure mathematics, and especially enjoyed CP Snow's forward, which provides a charming glimpse into the life of an Oxbridge don in the early 20th century and is a lovely tribute to his friend and mentor GH Hardy. For fans of the movie Good Will Hunting, Snow's forward includes interesting de...more

like · see review

Mar 11, 2012 Dan Cohen rated it 2 of 5 stars

I thought it was about time I read this book, having heard of it many years ago. But in truth, it was a huge disappointment. It's a quirky book that makes some interesting arguments, written in a very old-fashioned manner. I was waiting for something more interesting or revealing, but it sticks to it's rather cold logic (hardly surprising, I suppose) and ultimately disappoints. The forward, by C.P. Snow, was rather more interesting - a short biography of Hardy and description of Snow's friendshi...more

like · see review

Feb 24, 2013 Laura Méndez rated it 2 of 5 stars

I read this book because it was quoted in a coursera class about Genetics and Evolution. The quote was: "I have never done anything ‘useful’. No discovery of mine has
made, or is likely to make, directly or indirectly, for good or ill,
the least difference to the amenity of the world." Interestingly, one of Hardy's equation called the "Hardy-Weinberg's equation" is used in genetics, in population allele analysis and in fact it has become very useful for geneticians that ultimately benefit medici...more

like 2 likes · see review

Jan 27, 2012 Jake rated it 3 of 5 stars

Shelves: math

Recently I started teaching myself to program. An article I read recommended Project Euler, which is a set of math exercises intended to be completed with computer code. So for the last few months I've been doing more writing than reading, as I puzzled through these math problems. Research on various problems led to me to other math websites, and often G.H. Hardy's short book "A Mathematician's Apology" was mentioned in various contexts. I picked it up, and found a lot of what Hardy wrote applie...more Recently I started teaching myself to program. An article I read recommended Project Euler, which is a set of math exercises intended to be completed with computer code. So for the last few months I've been doing more writing than reading, as I puzzled through these math problems. Research on various problems led to me to other math websites, and often G.H. Hardy's short book "A Mathematician's Apology" was mentioned in various contexts. I picked it up, and found a lot of what Hardy wrote applied to other fields, including the computer programming I was attempting to learn.

Boiled down to its essence, "A Mathematician's Apology" is a book about beauty. Hardy writes: "the mathematician's patterns, like the painter's or the poet's, must be beautiful... there is no permanent place in the world for ugly mathematics." The nature of this beauty, in all its subtlety, is what Hardy spends most of the book writing about. To him, beautiful math combines simplicity with depth- connecting previously unconnected branches of mathematics and revealing new solutions to unsolvable problems- as well as new problems to be solved. You can apply the same ideas to science, or to art- there is something deeply zen about Hardy's formulation.

This is strange, because Hardy himself is deeply unzen. As C.P. Snow writes in his long introduction, "it is very rare for a writer to realize, with the finality of truth, that he is absolutely finished." While beautiful, the book is very sad, because Hardy was deeply depressed when he wrote it. At the end of his career, with his health failing, he seems to have abandoned all hope. Even writing seems to bring him no satisfaction: "There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds."

For a man who saw so far into such undiscovered philosophical territory, it's sad that Hardy didn't acquire a sense of perspective about himself, or his place in the universe. He hung his entire self-worth on his sense of mathematical accomplishment, and as his powers faded, so did his ability to experience joy. This kind of unzen attitude is found throughout the book- here's just one small taste: "I shall assume that I am writing for readers who are full, or have in the past been full, of a proper spirit of ambition. A man's first duty, a young man's at any rate, is to be ambitious."

Hardy's unhappiness has been explained in a number of ways- dissatisfaction with his work, a horror at the oncoming war (this book was written in 1940), and perhaps problems of the heart (Snow hints that Hardy was gay, but it seems that he lived asexually.) But I think it's really his world-view that ultimately defeated him- this idea that a man is to be judged by what he creates and nothing else. No man who truly believes that could ever be lastingly happy- especially not in old age. (less)

like 2 likes · see review

Apr 11, 2010 Snehal Bhagat rated it 3 of 5 stars

As everybody knows from personal experience, maths is no picnic, unless you're singularly gifted.

And gifted mathematicians tend to be notoriously reclusive; it is rare that one as distinguished as Hardy should have undertaken an exercise such as this: a defense for mathematics. The subject is rather topical; if maths needed defending seventy years ago when the book was first published, it certainly does now, as governments strained for funds seek soft targets in academia. Which is odd, really,...more

like · see review

Jun 28, 2008 Jenni Lunde rated it 5 of 5 stars Recommends it for: People who enjoy reading and despise math

Recommended to Jenni by: Jim Hendrickson, a Calculus professor

This is something that English-loving people who hate math should read. Hardy was, in his terms, a "pure" (not applied or even "useful") mathematician. This means that he saw his world in terms of math (very complicated math), even though he realized that his world of math does not always represent "reality." In fact, in this work, he comes to think of math in terms of art, since it is made up entirely of human ideas and is open to play and interpretation. He also makes the obvious parallel of m...more

like 2 likes · see review

Mar 10, 2008 Douglas rated it 5 of 5 stars

Here's a reason one might want to read this book. In his introduction, C.P. Snow points out that Hardy's capacity for dissimulation "was always minimial." And he goes on to illustrate this with a passage in the Apology where Hardy says, "I do not remember having felt, as a boy, any passion for mathematics, and such notions as I may have had of the career of a mathematician were far from noble. I thought of mathematics in terms of examinations and scholarships; I wanted to beat other boys, and th...more

like 1 like · see review

Mar 07, 2012 Ben rated it 4 of 5 stars

Summary: A mathematician reflects on the value of his life.

Things I liked:

It made me laugh a couple of times.

It made me think.

I taught me a couple of things about maths which is a subject I don't really know much about it.

Things I thought could be improved:

?? Too short I didn't really notice anything I objected to.

Highlight: Comment that the vast majority of people are talentless hacks that will have no real impact on the world. With a start like that, really how could you go wrong.

like · see review

Jan 02, 2013 Bernard rated it 3 of 5 stars

Recommended to Bernard by: David Assaf, IV

This book opens with a lengthy biography of Englishman G. H. Hardy and is followed by a from-the-heart essay by Hardy about mathematics from his perspective as a self-proclaimed "real" mathematician of pure mathematics (as opposed to a mathematician of what he calls trivial mathematics). He wrote the apology in 1940 as he approached the twilight of his life, and past the time of his life when he confesses there is any creativity left in him. Ironically the creation of his essay was as endearing...more

like · see review

Jan 26, 2012 Matt rated it 5 of 5 stars

Fantastic. Hardy knows what he's talking about, and neither he nor you needs me defending him or his knowledge of mathematics.

Higher mathematics is like philosophy: eminently useless by definition. The moment it becomes "useful", mathematics becomes engineering, philosophy becomes science, algorithms become implementation; and the purists lose interest.

Pure mathematics and philosophy are indeed the vanguards of human knowledge; Captain Picard would be proud.

like · see review

Jan 19, 2012 Ashutosh rated it 3 of 5 stars

The author makes very valid points. I love the way he ends the book by recalling a point that Dr. Snow made regarding achievements versus popularity tradeoff. A mathematician in the real sense (not the applied mathematicians) might be tempted to diverge and delve into things which are popular, but then this tradeoff is like a statue on top of a pillar - should be pillar be so high that the statue is invisible or so stoop such that all the features are readily observable ?

like · see review

Apr 19, 2011 Merilee rated it 4 of 5 stars

I'm finally actually getting to it. I just read the wonderful 50+ page intro my C.P. Snow (one of my heros). The intro is almost as long as the actual Hardy part. Apparently Graham Greene, in a review, said that along with Henry James' notebooks, Hardy's book was the best description of what it's like to be a creative artist. Despite much googling, I sadly cannot find a copy of the original Greene review. Perhaps I'll finish the rest this evening, if the wonderful Indian food we're off to eat wi...more

like 3 likes · see review

Jan 05, 2009 Brian rated it 3 of 5 stars

This is G.H. Hardy's memoir of a once-great mathematician. A bit on the wan side -- an essay on faded genius. Amusing stories on the discovery of the Indian mathematician, Ramanujan (who gets a mention in Good Will Hunting). No mathematics to skip here. If you used to be a genius and you are sad that you are no longer, then you will relate. Otherwise you might find it somewhat whimpering like I did (I'm still a genius).

like · see review

Feb 06, 2012 Kemalure rated it 5 of 5 stars

What is motivation for doing science ? Is it for the good of mankind ? Do we study mathematics for making engineers and physician lives easier ? Hardy's answer is NO. Only motivation for studying mathematics comes from one's passion for solving puzzles and nothing more. This book has changed the way I looked at mathematical sciences.

like · see review

Nov 13, 2011 Nicolle rated it 5 of 5 stars

Shelves: mathematics, 1940s, favorites

This memoir from G.H Hardy has truly changed my perception of mathematics and mathematicians. Hardy is a remarkable man, though unusual (he likes cricket!) and with collaborations with Littlewood and Ramanujan he made astonishing breakthroughs in the mathematical field. The one thing which struck me in this novel was Hardy's sorrow caused by old age, he seemed in mourning for the creativity and drive for mathematics that he had once held. Some of his deep emotions are layed bare in this novel, a...more

like 3 likes · see review

Dec 20, 2012 Carolyn rated it 3 of 5 stars

Shelves: nonfiction, math

A loaner from my Dad, who has been doing a lot of "math" reading inspired by Charlie on NUMB3RS (no, I'm not joking about that). An essay on math the way some write on writing; why one does it, what it means, the creative process. Tangible regret on the author's part that he's past his time. Lovely.

like · see review

« previous 1 2 3 4 5 6 7 8 9 … 86 87 next »

new topic
Discuss This Book

There are no discussion topics on this book yet. Be the first to start one »

Recommend it | Stats | Recent status updates

combine
Other Editions (12)

More editions...

Genres

Science > Mathematics

89 users

Non Fiction

51 users

Science

36 users

Philosophy

19 users

Biography

16 users

Autobiography > Memoir

7 users

Biography > Autobiography

6 users

Writing > Essays

5 users

European Literature > British Literature

4 users

Science > Popular Science

3 users

See top shelves...

Readers also enjoyed similar books

About G.H. Hardy

Godfrey Harold Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis.

Non-mathematicians usually know him for A Mathematician's Apology, his essay from 1940 on the aesthetics of mathematics. The apology is often considered one of the best insights into the mind of a working mathematician written for the layman.

His relationship as ment...more

More about G.H. Hardy...

Books by G.H. Hardy

An Introduction to the Theory of Numbers

More…

Share This Book

Facebook Twitter Your website

Trivia About A Mathematician's...

No trivia or quizzes yet. Add some now »

Quotes from A Mathematician's Apology

“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.” — 12 people liked it

“Immortality is often ridiculous or cruel: few of us would have chosen to be Og or Ananias or Gallio. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel’s Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country’s greatest man. But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.” — 4 people liked it

More quotes…

title link	preview: A Mathematician's Apology
avg rating	preview: A Mathematician's Apology Goodreads rating: 3.89 (1229 ratings)
small image	preview: click here [close]
med image	preview: click here [close]
BBCode	[url=https://www.goodreads.com/book/show/154060.A_Mathematician_s_Apology?utm_medium=api&utm_source=blog_book][img]https://d202m5krfqbpi5.cloudfront.net/books/1348629338l/154060.jpg[/img][/url] [url=https://www.goodreads.com/book/show/154060.A_Mathematician_s_Apology?utm_medium=api&utm_source=blog_book]A Mathematician's Apology by G.H. Hardy[/url]

A Mathematician's Apology

Friend Reviews

Community Reviews

Share This Book

Share This Book on Your Website