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A Mathematician's Apology
by
G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and enga
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Paperback, 153 pages
Published
January 31st 1992
by Cambridge University Press
(first published 1940)
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A Serious Business of Taste
The dominant theme of A Mathematician’s Apology, established from the first page, is one of aesthetics. Aesthetics, the study of what is inherently important and valuable, is for Hardy the fundamental power of mathematics, not an incidental result of correct thought. Aesthetics, while not unique to mathematics, is arguably more singlemindedly applied in mathematics than in any other human activity, including art of all kinds.
Hardy, like many poets and artists as well ...more
The dominant theme of A Mathematician’s Apology, established from the first page, is one of aesthetics. Aesthetics, the study of what is inherently important and valuable, is for Hardy the fundamental power of mathematics, not an incidental result of correct thought. Aesthetics, while not unique to mathematics, is arguably more singlemindedly applied in mathematics than in any other human activity, including art of all kinds.
Hardy, like many poets and artists as well ...more
“what are the uses of mathematics?”
This has been a pervasive question that might have occurred to everyone who encounters mathematics in school or elsewhere throughout their lives.
Euclid( a Greek mathematician who lived in 4th century BC) believed in the search of mathematical truth for its own sake. One story tells of a student who questioned him about the use of mathematics. Upon completing the lesson, Euclid turned to his slave and said : ‘ give the boy a penny since he desires to profit fr ...more
This has been a pervasive question that might have occurred to everyone who encounters mathematics in school or elsewhere throughout their lives.
Euclid( a Greek mathematician who lived in 4th century BC) believed in the search of mathematical truth for its own sake. One story tells of a student who questioned him about the use of mathematics. Upon completing the lesson, Euclid turned to his slave and said : ‘ give the boy a penny since he desires to profit fr ...more
I nearly studied maths at university, because of this book.
When I was sixteen, I was scared of the grades and numbers end of academia, and I was determined that whatever I was going to study  and it was going to be something, and a lot of it  I was going to do it for the love of it. I was going to read around my subjects, follow tangents and pick whatever took my fancy. So, a few months into a Maths Alevel, I took this out of Southampton Central Library, and I didn't give it back for nearly a ...more
When I was sixteen, I was scared of the grades and numbers end of academia, and I was determined that whatever I was going to study  and it was going to be something, and a lot of it  I was going to do it for the love of it. I was going to read around my subjects, follow tangents and pick whatever took my fancy. So, a few months into a Maths Alevel, I took this out of Southampton Central Library, and I didn't give it back for nearly a ...more
A pragmatist's review of how math fits into our knowledge, world and psyche.
Q:
The mass of mathematical truth is obvious and imposing; its practical applications, the bridges and steamengines and dynamos, obtrude themselves on the dullest imagination. The public does not need to be convinced that there is something in mathematics. (c)
Q:
I am a lawyer, or a stockbroker, or a professional cricketer, because I have some real talent for that particular job. I am a lawyer because I have a fluent tongu ...more
Q:
The mass of mathematical truth is obvious and imposing; its practical applications, the bridges and steamengines and dynamos, obtrude themselves on the dullest imagination. The public does not need to be convinced that there is something in mathematics. (c)
Q:
I am a lawyer, or a stockbroker, or a professional cricketer, because I have some real talent for that particular job. I am a lawyer because I have a fluent tongu ...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 s ...more
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
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

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
The first thing the reader of this book will notice is that Hardy is an excellent writer. Although he repeatedly insists that his only talent lay in his mathematical ability, it is clear that he is a seasoned wordsmith.
The first mark of a good writer is their seemingly effortless ability to convey their personality through the written word, no matter the subject or format. The reader is immediately presented with Hardy the man, as if he is sitting in front of you giving a lecture.
One of the draw ...more
The first mark of a good writer is their seemingly effortless ability to convey their personality through the written word, no matter the subject or format. The reader is immediately presented with Hardy the man, as if he is sitting in front of you giving a lecture.
One of the draw ...more
I object not to the message, but rather its form. Essentially, GH argues that mathematics is worth the world's time and effortthat it is a beautiful, creative, and noble pursuit. I'm already convinced of this, so maybe I'm not his target audience and should therefore shut up. I've spent a nontrivial amount of around mathematicians. They are almost a different species, and I envy their passion and analytic abilities. While I'm glad GH tried to be their advocatewhich must've been more necessa
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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
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
What a wonderful time I had with this book. GH Hardy, one of last century’s towering mathematical figures now known to a wider audience through the film “The Man Who Knew Infinity”, looks back on his life at a time when, by his own testimony, his mathematical genius was fading.
The opening lines establish a sense of melancholy that I was never quite able to banish when reading his memoir:
It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The ...more
The opening lines establish a sense of melancholy that I was never quite able to banish when reading his memoir:
It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The ...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 applie
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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
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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
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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 "HardyWeinberg'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
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 "HardyWeinberg'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
As Hardy pointed out himself, criticisms are work of secondrate mind. This book is awesome, it sheds so much light on what is going on inside mathematician's mind. I particularly like the part when he argues why mathematics is beautiful, and what constitutes a beautiful mathematical theorem.
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Mr. Hardy explains the difference between pure and applied mathematics. Math history thrown in and some stories about Bertrand Russell and others. There's also a hint of defensiveness as he tries to explain the beauty of spending a life on math that has no real world applications.
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PDF available here: https://www.math.ualberta.ca/mss/misc...
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Since I have recommended this book to some friends, I'd better review it for them. It isn't going to be easy, just like the book wasn't easy to read, so here goes nothing:
1. This is an enlightening book, especially if you are looking to create some form of original work in academics. Are you planning on writing a doctorate thesis at some point? Read this, because it puts forth another academician's ideas about what a good contribution is. It helps that Hardy managed very well for himself.
Even i ...more
1. This is an enlightening book, especially if you are looking to create some form of original work in academics. Are you planning on writing a doctorate thesis at some point? Read this, because it puts forth another academician's ideas about what a good contribution is. It helps that Hardy managed very well for himself.
Even i ...more
How wonderful it is to contact with passionate people! Or, in this case, someone who claims to no longer be passionate, but still transpires passion in his speech. I have always had a penchant for what makes people tick.
How delightful to read about the beauty of mathematical patterns, the harmonious way in which ideas ought to fit together, about the seriousness of a theorem and the significance of the ideas which it connects, about the permanence of mathematical achievement and what makes a goo ...more
How delightful to read about the beauty of mathematical patterns, the harmonious way in which ideas ought to fit together, about the seriousness of a theorem and the significance of the ideas which it connects, about the permanence of mathematical achievement and what makes a goo ...more
Due to the reading assignment from the "Ten Year Reading Plan" I came across this short essay written by the mathematician G.H. Hardy. The introduction to the essay presents briefly his life and work in the domain of pure mathematics and for someone like me who had not known him before was very informative.
The essay itself was written at maturity and Mr. Hardy tries to explain to us and to himself his life choice, which was mathematics. The story is not difficult to read and the mathematical par ...more
The essay itself was written at maturity and Mr. Hardy tries to explain to us and to himself his life choice, which was mathematics. The story is not difficult to read and the mathematical par ...more
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
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I give five stars relative to my expectation  I was totally surprised how much I liked this book. I was taking an afterlunch walk in the library and suddenly the name came to mind, so I pick it up from the shelf. I was expecting some selfimportant manifesto with little information. I was wrong. Though often sounds like he has no interaction with the world outside of mathematics, he's pretty honest. He started off by saying that serious mathematicians do math, don't write stuff about math. I w
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It's always interesting to find out what a math's genius reflects on his own life and work. I found this book rather short, though.
I sort of regret that Hardy didn't dig a bit deeper. I finished the book with the impression that I wanted to find out more about the topics of the book. ...more
I sort of regret that Hardy didn't dig a bit deeper. I finished the book with the impression that I wanted to find out more about the topics of the book. ...more
This is a challenging novel. It is not a thriller, historical book or anything you’ve ever read. This is a book written by a Grand Master Mathematician telling the story about his Apprentice, the young genius Ramanujan, and about the wonderful creativity and the internal urge that, although rare, exist in some people on Earth making them search for the harmony and beauty of the Universe.
Even if you do not know anything about Mathematics you will begin to feel the World of Ideas, although indirec ...more
Even if you do not know anything about Mathematics you will begin to feel the World of Ideas, although indirec ...more
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
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This is something that Englishloving 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
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I got to know prof. Hardy after watching the movie about him and Ramanujan, which inspired me to know more of his personal life and professional work. G.H. Hardy has been famous for his brilliance in mathematics and eccentric character at the same time. This book tries to give a brief insight to mathematicians life in 29 chapters such as defining the usefulness of mathematics, real and applied parts of mathematics, etc. I was fascinated to see a mathematician's attitude towards real life applica
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A short and famous book that's still relevant today. "A man who is always asking 'Is what I do worth while?' and 'Am I the right person to do it?' will always be ineffective himself and a discouragement to others." Indeed, such people are so depressing. In his Apology, G.H. Hardy has gotten to a point in his life at which he feels creatively useless, and only then does he look back on his life and attempt to justify it by assessing pure mathematics as a career. The philosophical aspects are very
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Godfrey Harold Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis.
Nonmathematicians 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
Nonmathematicians 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
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