Proofs from THE BOOK [Hardcover]

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

Book Description

Publication Date: December 31, 1998 | ISBN-10: 3540636986 | ISBN-13: 978-3540636984 | 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: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #477,176 in Books (See Top 100 in Books)

Most Helpful Customer Reviews

76 of 76 people found the following review helpful

4.0 out of 5 stars original June 4, 2000

By Giuseppe A. Paleologo

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".

16 of 17 people found the following review helpful

5.0 out of 5 stars The ideal maths book for dipping into... April 9, 2000

By Mr Andrew Mullins

This is a beautifully produced book with very elegant proofs of theorems from a variety of areas. The proofs require little previous knowledge, but be warned: if you haven't got undergraduate mathematics then you will not find it easy to read. On the other hand, if you have then you will find this book truly delightful. Top marks!

17 of 20 people found the following review helpful

5.0 out of 5 stars Proofs from THE book!!!!!!! August 26, 2000

By "quais_100"

An excellent book which looks at all branches of mathematics - graph theory, combinatorics, even logic. Contains some of the most spectacular proofs to math's most interesting conjectures. I highly recommend this book for any student interested in pursuing mathematics beyond high school. -I am sorry for my broken english, I speak French.