Proofs from THE BOOK

图书介绍

This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals".
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

“… the style is clear and entertaining, the level is close to elementary … and the proofs are brilliant. …” LMS Newsletter, January 1999

This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler’s most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to “enumerate the rationals”.

Summary: this is THE BOOK!
Rating: 5
One of the most important mathematicians in the last quarter of a century was, arguably, Paul Erdos. At least we could say he was the one who travelled the most, and who had more collaborations with other mathematicians in the areas of Graph Theory, Combinatorics, etc.
One of his dreams was to assemble a collection of all the most beautiful proofs in Mathematics, in which God would maintain the perfect proofs in mathematical theorems. This collection would be called The Book. Unfortunately, he didn’t see his dream fulfilled while among us, but after his death Agner and Ziegler wrote this excellent book, “Proofs from THE BOOK”, as a nice excerpt of what The Book could have been.
Topics in this book range from Number Theory to Analysis, and also discussing Combinatorics and Graph Theory. Most of the proofs are accessible to everybody with some mathematical training, they are beautiful and surprisingly simple.
I just love this book, in the last five years or so I have bought several copies of it, as it has been my favorite gift for people who want to discover a little more about the beauty of Mathematics.