Proofs from THE BOOK [Hardcover]

Martin Aigner (Author), Günter M. Ziegler (Author)

Book Description

ISBN-10: 3540636986 | ISBN-13: 978-3540636984 | Publication Date: December 31, 1998 | Edition: Corrected

The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory.
Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection.
The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background.

Editorial Reviews

Review

"...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." - Notices of the AMS

From the Back Cover

This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which  treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings,  but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem".   From the Reviews "... 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... write: "... 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 AMS, 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. ..."  LMS Newsletter, January 1999 --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 199 pages
• Publisher: Springer; Corrected edition (December 31, 1998)
• Language: English
• ISBN-10: 3540636986
• ISBN-13: 978-3540636984
• Product Dimensions: 9.6 x 7.6 x 0.7 inches
• Shipping Weight: 1.6 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (19 customer reviews)
• Amazon Best Sellers Rank: #2,052,543 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

71 of 71 people found the following review helpful:

4.0 out of 5 stars original, June 4, 2000

By 

Giuseppe A. Paleologo "gappy" (Riverdale, NY United States) - See all my reviews
(REAL NAME)   

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".

92 of 95 people found the following review helpful:

1.0 out of 5 stars Kindle edition is worthless: avoid at all costs, April 23, 2008

By 

T. Smith "tzs" - See all my reviews
(REAL NAME)   

This review is from: Proofs from THE BOOK (Kindle Edition)

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.

82 of 87 people found the following review helpful:

1.0 out of 5 stars Do NOT get the Kindle edition, July 7, 2008

By 

Dr. Hoenikker "drhoenikker" - See all my reviews

Amazon Verified Purchase

This review is from: Proofs from THE BOOK (Kindle Edition)

The Kindle edition of the book is missing or misrepresenting math symbols in so many places it makes it completely unreadable.