- Hardcover: 215 pages
- Publisher: Springer/Sci-Tech/Trade; 2 edition (Jan 11 2001)
- Language: English
- ISBN-10: 3540678654
- ISBN-13: 978-3540678656
- Product Dimensions: 24.8 x 19.7 x 2 cm
- Shipping Weight: 862 g
- Average Customer Review: 5.0 out of 5 stars See all reviews (2 customer reviews)
- Amazon Bestsellers Rank: #1,766,696 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Product Description
Review
From the reviews of the third edition:
"... It is unusual for a reviewer to have the opportunity to review the first three editions of a book - the first edition was published in 1998, the second in 2001 and the third in 2004. ... I was fortunate enough to obtain a copy of the first edition while travelling in Europe in 1999 and I spent many pleasant hours reading it carefully from cover to cover. The style is inviting and it is very hard to stop part way through a chapter. Indeed I have recommended the book to talented undergraduates and to mathematically literate friends. All report that they are captivated by the material and the new view of mathematics it engenders. By now a number of reviews of the earlier editions have appeared and I must simply agree that the book is a pleasure to hold and to look at, it has striking photographs, instructive pictures and beautiful drawings. The style is clear and entertaining and the proofs are brilliant and memorable. ...
David Hunt, The Mathematical Gazette, Vol. 32, Issue 2, p. 127-128
"The newest edition contains three completely new chapters. … The approach is refreshingly straightforward, all the necessary results from analysis being summarised in boxes, and a short appendix discusses the importance of the zeta-function in number theory. … this edition also contains additional material interpolated in the original text, notably the Calkin-Wilf enumeration of the rationals." (Gerry Leversha, The Mathematical Gazette, March, 2005)
"A lot of solid mathematics is packed into Proofs. Its thirty chapters, divided into sections on Number Theory, Geometry, Analysis … . Each chapter is largely independent; some include necessary background as an appendix. … The key to the approachability of Proofs lies not so much in the accessibility of its mathematics, however, as in the rewards it offers: elegant proofs of interesting results, which don’t leave the reader feeling cheated or disappointed." (Zentralblatt für Didaktik de Mathematik, July, 2004)
From the reviews of the second edition:
"... Thirty sections treat results drawn from number theory, geometry (mainly combinatorial), analysis, combinatorics and graph theory; these can be follwed by one versed in undergraduate matheamtics including discrete topics. ... The authors have done a fine job of arranging diverse material into a thematic progression. ... The presentation is clear and attractive with wide margins for portraits, diagrams and sketches."
E.J.Barbeau, Mathematical Reviews, Issue 2000k
" ... This is a wonderful book that can be recommended to anybody who is in any way connected to mathematics. Those who have ever experienced the beauty of mathematics will experience the chill again. For those who have never experienced that, this book is just the right one to start."
Acta Scientiarum Mathematicarum, 1999, Vol. 65, 769-770
"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler do not claim to have presented the definitive collection of great mathematics. In their brief introduction they write: "We have no definition or characterization of what constitutes a proof from THE BOOK: all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the American Mathematical Society, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. Moreover, the exposition makes them transparent. ..."
London Mathematical Society Newsletter, January 1999
"... Clearly this second edition is dangerously suited to infect the reader with the enthusiasm of the authors."
J.Elstrodt (Münster), Zentralblatt für Mathematik 0978.00002
--This text refers to an alternate Hardcover edition.Book Description
A collection of proofs in honor or Paul Erdos, whose work included the mathematical approximation of The Book. Offers examples of selection of proofs that the editors consider proofs from the book, based on Erdos's work. Includes a number of illustrations.
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Most helpful customer reviews
5.0 out of 5 stars
A breath of pure air,
By
This review is from: Proofs From THE BOOK (Hardcover)
I stumbled across this book and am amazed that I had not heard about it before. Since buying it, I have kept it by my bedside and have now read the whole book four or five times, picking up more of the subtleties at each reading.The proofs are almost all magnificent (although I wonder how Buffon and his needles got in there) and even the well-known and time-honoured ones have a new twist or new extension. The level of mathematics required to follow the proofs is reasonably low (high-school 'A' levels in the British system, no idea about other countries) although the book gives a deeper explanation in some areas (e.g. trans-finite arithmetic) than in others (e.g. number theory). I wonder if this unevenness reflects the interests of the authors. But these are tiny nit-pickings. This is a wonderful and inspiring book and reading it should be made compulsory by the government in all high-school mathematics classes.
5.0 out of 5 stars
A fitting tribute to the great Paul Erdos,
This review is from: Proofs From THE BOOK (Hardcover)
Paul Erdos once remarked that you need not believe in God, but you certainly have to believe in the book in which God maintains the "perfect" mathematical proofs. Martin Aigner and Gunter Ziegler have certainly done a great job with this book, a fitting tribute to the great Erdos himself.I had purchased a copy of the 1st edition of this book and was plesantly surprised that the authors had come up with a 2nd edition, with a few more "perfect" proofs. My personal favorites are "The Shannon capacity of a graph". where the Lovasz theta number would eventually lead to semidefinite programming, Erdos' probabilistic method where probability makes counting sometimes easy, computing the number of trees in a graph, how many guards it takes to guard a museum, and the section on Turan's theorem. This book deserves to be on the bookshelves of both amateur and professional mathematicians.
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Most Helpful Customer Reviews on Amazon.com (beta) Amazon.com:
4.5 out of 5 stars (19 customer reviews) 72 of 72 people found the following review helpful
4.0 out of 5 stars
original,
By Giuseppe A. Paleologo "gappy" - Published on Amazon.com
This review is from: Proofs from THE BOOK (Hardcover)
This book was conceived as a tribute to Paul Erdos for his 85th birthday. It is clearly inspired by his aestetics and research interests. The proofs are from number theory, combinatorial geometry, inequalities, combinatorics and graph theory. The statements are very often easy to understand; for example "there always exists a prime number between n and 2n", "every set of more than 2^d points in R^d determines at least one obtuse angle". Theorems and proofs are chosen because of their simplicity and elegance, not their relevance to modern or past mathematics. The book is, graphically and stilistically, a gem.Overall, this is great reading for mathematicians and mathematically literate readers alike. It's also a bit odd, since the book is neither a reference nor a textbook. The only criticism I have is not directed to the book itself. It would be much appreciated to have similar books, but focused on different topics. For example "probabilistic proofs from the book", or "topological proofs from the book". 102 of 105 people found the following review helpful
1.0 out of 5 stars
Kindle edition is worthless: avoid at all costs,
By T. Smith "tzs" - Published on Amazon.com
NOTE: This review is JUST for the Kindle edition.The Kindle edition is completely worthless, because it is missing many symbols. It appears to have been done using OCR, and it was confused by mathematical symbols. For example, there are some places where I THINK it was supposed to be the greek letter phi, but it comes out as a left parenthesis and a right parenthesis. At least with that you can figure out what it was supposed to be. There is much worse--places where symbols are completely gone. E.g., there is a place where you just get a capital sigma with a subscript giving a summation limit, a blank space, a less than sign, and another blank space. So, the proof is saying the some of *something* is less than *something else*. This is a shame, because the book itself, from what I can see, is EXCELLENT. 87 of 92 people found the following review helpful
1.0 out of 5 stars
Do NOT get the Kindle edition,
By Dr. Hoenikker "drhoenikker" - Published on Amazon.com
Amazon Verified Purchase(What's this?)
The Kindle edition of the book is missing or misrepresenting math symbols in so many places it makes it completely unreadable.
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