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40 of 41 people found the following review helpful
5.0 out of 5 stars Proofs from THE BOOK, 14 Jan 2002
By A Customer
This review is from: Proofs from "The Book" (Hardcover)
If you are at all interested in mathematics, and your background is anything from undergraduate to Fields medallist, then this is the one book you really must have. Paul Erdos, the most prolific and creative mathematician of the 20th century, had no need for the hypothesis of God. He nevertheless liked to believe that this non-existent deity kept a book in which were recorded all the most perfect and beautiful proofs in mathematics, and that, just once in a while, mere mortals were permitted a brief glance at some of the pages. As a tribute to Erdos, who died in 1996, Aigner and Ziegler have made a guess at what those pages might contain. They have compiled an A to Z of what they regard as the most elegant proofs from a wide range of mathematics, including Number Theory, Geometry, Analysis, Combinatorics and Graph Theory (all subjects close to Paul's heart). Many of the results are remarkably easy to state, for instance the theorem that there are infinitely many prime numbers, but all require some ingenuity to prove them; this particular example is given six different proofs, three of them direct, two involving Analysis and Topology, and one based on a neat counting argument. Similarly, in Combinatorics we get four totally different proofs of Cayley's formula for the number of trees on n vertices, each of them a real classic, and one (perhaps the best) very recent.
This book is superbly written and produced. Each chapter has a brief but clear historical introduction to the problem at hand, some excellent illustrative diagrams, a discussion of the proof or proofs, and a selection of references for further reading. There are portraits of many of the mathematicians, ancient and modern, whose ideas appear here, while Karl Hofmann's witty cartoons are an extra and unexpected joy.
Even if you have only a modest mathematical training, you can dip into this book, almost at random, and be guaranteed to come away a few minutes later wondering "Where on earth does an idea like that come from?". You cannot read this book and fail to be inspired to create mathematics yourself. If there were six stars available for reviewed books, this would get them. Buy it.
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11 of 11 people found the following review helpful
5.0 out of 5 stars quite excellent, 31 Jan 2003
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D. Bevan - See all my reviews
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This review is from: Proofs from "The Book" (Hardcover)
If you have ever been excited by the beauty of pure mathematics - or wondered at people who were - this book is for you. Not only do the authors exhibit a variety of the most elegant proofs around, but their presentation is of the highest quality - and in a very attractively designed book too. Recommended for even the most half-hearted maths lover.
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5.0 out of 5 stars Brilliant!, 19 Mar 2014
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Andrew Kelly "AK" (London, UK) - See all my reviews
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This review is from: Proofs from THE BOOK (Hardcover)
Anyone looking for a book of wonderfully complex yet beautiful proof could not do better than this book. I thoroughly recommend this to anyone in undergraduate maths with a love for proof.
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5.0 out of 5 stars Its simply amazing book, 2 Nov 2013
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R. P. Maciol - See all my reviews
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This review is from: Proofs from "The Book" (Hardcover)
It's a beautiful book that highlights the beauty of mathematics. Everyone with high school level of maths should be able to appreciate it.
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5.0 out of 5 stars Fun gift for a mathematically-inclined person, 27 Aug 2013
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Mr. J. Youngman (Europe) - See all my reviews
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This review is from: Proofs from THE BOOK (Hardcover)
Not being especially mathematical myself, I didn't get that much out of it. But fortunately I didn't buy the book for myself. I bought this as a birthday gift for a mathematician. He really likes it. If I had other mathematician friends, I'd buy it for them too.
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Proofs from THE BOOK
Proofs from THE BOOK by GŁnter M. Ziegler (Hardcover - 13 Oct 2009)
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