| View Larger Image | A Mathematician's Apology (Canto) | Paperbackby G. H. Hardy (Author), C. P. Snow (Foreword)
| List Price: | $18.99 | | Price: | $12.91 | | You Save: | $6.08 (32%) | | | Available: | Usually ships in 24 hours |
| | Binding: | Paperback | | Publisher: | Cambridge University Press | | Page Count: | 153 Pages | | Publication Date: | January 31, 1992 | | Sales Rank: | 42,664nd |
|
FEATURES | - ISBN13: 9780521427067
- Condition: NEW
- Notes: Brand New from Publisher. No Remainder Mark.
- Click here to view our Condition Guide and Shipping Prices
|
EDITORIAL REVIEWS |
Product Description
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 engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times. |
Amazon.com Review
A Mathematician's Apology is a profoundly sad book, the memoir of a man who has reached the end of his ambition, who can no longer effectively practice the art that has consumed him since he was a boy. But at the same time, it is a joyful celebration of the subject--and a stern lecture to those who would sully it by dilettantism or attempts to make it merely useful. "The mathematician's patterns," G.H. Hardy declares, "like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." Hardy was, in his own words, "for a short time the fifth best pure mathematician in the world" and knew full well that "no mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." In a long biographical foreword to Apology, C.P. Snow (now best known for The Two Cultures) offers invaluable background and a context for his friend's occasionally brusque tone: "His life remained the life of a brilliant young man until he was old; so did his spirit: his games, his interests, kept the lightness of a young don's. And, like many men who keep a young man's interests into their sixties, his last years were the darker for it." Reading Snow's recollections of Hardy's Cambridge University years only makes Apology more poignant. Hardy was popular, a terrific conversationalist, and a notoriously good cricket player. When summer came, it was taken for granted that we should meet at the cricket ground.... He used to walk round the cinderpath with a long, loping, clumping-footed stride (he was a slight spare man, physically active even in his late fifties, still playing real tennis), head down, hair, tie, sweaters, papers all flowing, a figure that caught everyone's eyes. "There goes a Greek poet, I'll be bound," once said some cheerful farmer as Hardy passed the score-board. G.H. Hardy's elegant 1940 memoir has provided generations of mathematicians with pithy quotes and examples for their office walls, and plenty of inspiration to either be great or find something else to do. He is a worthy mentor, a man who understood deeply and profoundly the rewards and losses of true devotion. --Therese Littleton |
CUSTOMER REVIEWS (Average Customer Rating: 5.0 based on 28 reviews)
|
What is mathematical beauty? by Viktor Blasjo  4 Stars
May 26, 2009
In the most famous phrase of the book, Hardy proclaims that "Beauty is the first test: there is no permanent place in this world for ugly mathematics." Quite so, but wherein does mathematical beauty consist? Here is Hardy's answer:
"What 'purely aesthetic' qualities can we distinguish in such theorems as Euclid's [on the infinity of primes] or Pythagoras's [on the irrationality of the square root of two]? ... In both theorems (and in the theorems, of course, I include the proofs) there is a very high degree of [1] unexpectedness, combined with [2] inevitability and [3] economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions. There are no complications of detail; one line of attack is enough in each case; and this is true too of the proofs of many much more difficult theorems, the full appreciation of which demands quite a high degree of technical proficiency. We do not want many 'variations' in the proof of a mathematical theorem: 'enumeration of cases', indeed, is one of the duller forms of mathematical argument." "The beauty of a mathematical theorem depends a great deal on its [4] seriousness ... The 'seriousness' of a mathematical theorem lies ... in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas."
I say: these four conditions are neither individually necessary nor jointly sufficient. In support of which I offer the following considerations.
Unexpectedness. Counterexample to the necessity of this criterion: Bernoulli's theorems on the logarithmic spiral. Bernoulli discovered numerous remarkable properties of this spiral: that it is "equal to its caustics by reflection and refraction, to its evolute, and to numerous other derived or conjugate curves" (Le Lionnais). Surely the unexpectedness would have worn off as his study went on. But there is no indication that Bernoulli's appreciation for the theorems diminished with it. On the contrary he wrote that "This marvelous spiral gives me such overwhelming pleasure that I can scarcely satisfy my desire to contemplate it" (ibid.).
Inevitability. There are many senses in which there can be ``no escape from the conclusion'' in a proof. A specification is needed for meaningful discussion. It seems to me that the only way to narrow down Hardy's intention is to take his phrase regarding "one line of attack" as his explication of inevitability. This is still very vague, but I think it is precise enough to admit counterexamples. A counterexample, then, would have to be a proof which we admire not for charging at the Achilles heel of the enemy, but rather for winning the battle by masterful deployment of forces and exquisite interplay between cavalry and infantry. I believe there is mathematical beauty of this type, for example Galois theory, and in particular its proof of the insolubility of the quintic. Another example is the theory of Riemann surfaces, which any general enjoys deploying with a deft touch, but which is nevertheless unlikely to win a battle all by itself. These are examples of a more general phenomena: the application of ideas from one field to a seemingly unrelated one (in our cases: group theory in algebra, and topology in complex analysis). Such interconnections are a considerable source of aesthetic pleasure. But this can hardly be said to be due to their enabling a single line of attack to replace a plurality of such lines. On the contrary, such interconnections often, as in our examples, function as simpler and more elegant alternatives to some aspect of a previously perceived "brute force" line of attack. (In fact, such connections are often discovered in precisely this manner; again this is the case in our examples.)
Economy. This, I take it, is what Hardy defines when he writes that "the weapons used seem so childishly simple when compared with the far-reaching results." A counterexample, then, would consist in beautiful use of advanced weapons to prove simple results. But surely there can be no doubt that advanced theories can yield beautiful spin-off proofs of rather basic results. For example, there are a number of beautiful solutions of the ancient isoperimetric problem based on modern theories such as complex analysis, vector analysis, etc. (for which, see my article in the Am. Math. Monthly).
Seriousness. As we see above, seriousness amounts to connectivity. Now, a theorem with no connectivity with the rest of mathematics is not likely to count as mathematics at all. However, it seems to me that there are enough beautiful theorems whose seriousness is so unexceptional (e.g., Bernoulli's theorems on the logarithmic spiral, the theorem that there are five regular polyhedra) that a criterion weak enough to include them would be too weak to have any teeth. Another source of examples of beautiful theorems with very limited connectivity is classical number theory, of which Euler wrote that "I must confess that I derive nearly as much pleasure from investigations of this kind as from the deepest speculations of higher mathematics".
All criteria at once. The theorem on integration by parts (which is surely not beautiful) scores highly on all four counts, thus proving that they are not jointly sufficient.
| |
What is the cause for which we live humbly? by Adesh K. Seuraj (Trinidad, WI)  5 Stars
May 25, 2009
For Hardy, it was Mathematical Creativity. His last great work, "A Mathematician's Apology" represents one man's dissolution and subsequent crystallization of lament, despair, and acceptance: the same that will inevitably veil us all, perhaps not though, to the same extent. I believe Hardy's trepidations surrounding death had less to do with corporeal existence than acknowledging the slow demise of his postcard universe of a bygone Cambridge - that Ivory Tower teeming with the greatest minds of his generation, all players in the graceful game of numbers.
Credit must also be given to C.P Snow. His foreword to the Author, forestalls any bias we may have before Hardy makes his personal introduction, and Snow is careful not to daub exaggerations or hypocritical praises, balancing sixteen years of acquaintanceship quite comprehensively in his short introduction. His part, though asymmetric in comparision with Hardy's, is nonetheless equally important.
| |
a great mathematician presents his view of what constitutes math and what constitutes a mathematician by Patrick Regan (Northampton, MA USA) 5 Stars
November 10, 2008
First off, A Mathematician's Apology is not very apologetic and G. H. Hardy did not need to be apologetic! The author believed that great mathematics cannot be done by older mathematicians and, so, one thing he apologizes for is being too old to produce math. As the creation of mathematics is the sole purpose of a mathematician, he felt that being too old to create it made him useless. But need I remind you that, during that time, he created this book! Another thing that G. H. Hardy apologizes for is for doing mathematics for mathematics sake. Hardy did not consider applied math to be real mathematics. He felt only pure mathematics mattered. It is perhaps ironic that the very mathematics he considered pure, his, became useful for the study of encryption later in the 20th century. In any case, one of the great things that G. H. Hardy did was liberate England from the chains of a single minded approach to applied mathematics. He also mentored the great genius Ramanujan. Hardy considered his time with Ramanujan and Littlewood, another great mathematician, to be the most productive time in his life. This book, which includes a mini biography of Hardy by C. P. Snow can give the reader a glimpse of what it is like to be a great mathematician if not what it is like to do great mathematics. I suppose no book can do the latter.
| |
Brief but valuable, a book for everyone by Luis Mansilla Miranda (Viña del Mar, Chile) 5 Stars
April 08, 2008
I learned about this book while reading another book, "Prime Obsession" and it awoke my curiosity mainly for two reasons: because it was a interesting subject, an apology for being a mathematician, trying to explain the purpose and usufulness of mathematics, and because I wanted to know more about Hardy's life, since I knew a few things about the nice story of this mathematician and Ramanujan. This is a brief book, there is a foreword that serve as a brief biography before enjoying Hardy thoughts, which by the way really grab your attention, even you learn a few lessons of simple mathematics proofs that try to show the beauty of it. I consider this book valuable for everyone.
| |
This is a book which should be read by all college students by Charles Saunders (Tallahassee, FL United States) 5 Stars
November 08, 2007
Hardy was a giant among early 20th century mathematicians. It is difficult to overstate his importance. He was one of the first to show that mathematics is as much art as science without having to have interpretation (such as Dunham's "Journey Through Genius...").
This is what makes this book so poignant. Hardy realizes that he no longer is Hardy. In today's mathematics world that may not have been the case given the immediate communications possible between humans which may have kept him going. However, it may have been that he was suffering from the onset of dementia or Alzheimer's - it is difficult to tell given his admissions of not being up to the task - regardless, this book is overwhelmingly sad.
Anyone who cares about math should read this and thank Hardy for his contributions - plus they should have a copy of "A Course in Pure Mathematics".
| |
SIMILAR PRODUCTS |
| The Man Who Knew Infinity: A Life of the Genius Ramanujan
by Robert Kanigel (Author)
A biography of the Ramanujan describes how the natural genius of an unschooled Indian clerk came to the attention of a preeminent mathematician and the world. Reprint.
| 
| A Course Of Pure Mathematics
by G. H. Hardy (Author)
Designed For The Scholarship Standard University Student, To Include All Examples, Illustrations, And A Comprehensive Index.
| 
| Thinking Mathematically
by J. Mason (Author), L. Burton (Author), K. Stacey (Author)
Thinking Mathematically unfolds the processes which lie at the heart of mathematics. It demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians. In this way, a deep seated awareness of the nature of mathematical thinking can grow. The book is increasingly used to provide students at a tertiary level with some experience of mathematical thinking processes.
| 
| The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs
by Antonella Cupillari (Author)
The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove...
| 
| The Mathematical Experience
by Phillip J. Davis (Author), Reuben Hersh (Author)
This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.
|
|
|
