Title: Proofs from THE BOOK Author(s): Martin Aigner, Gunter M. Ziegler Pages: 199 Publisher: Springer; 1st ed. 1998. Corr. 2nd printing edition Publication date: 1998 Language: English Format: PDF ISBN-10: 3540636986 ISBN-13: Description: 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 Erdos, 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.
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
Review:
this is THE BOOK!
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.
Review:
Fantastic exploration into mathematics
We used it for an undergraduate statistics seminar series; and that was largely a success. PFTB contains many of the most elegant proofs I have ever seen. Reading through it is, by itself, an enjoyable journey through some aspects of many branches of mathematics. A few of its chapters may not address the average undergraduate math population quite well, due to its depth of reasoning and assumption of prior knowledge in Abstract Algebra and Geometry; but those who reads it are likely to be more advanced anyway. In general, an excellent book.
Review:
Excellent, but bizarre and atypical book on mathematics
I agree with what most of the other authors have said. This is a wonderful book, if only a bit strange. The book is very clearly written and easy to follow, although many of the proofs require a great deal of contemplation in order to fully understand.
This is one of those books that a serious mathematician will probably enjoy picking up and reading from time to time. It is neither a reference nor a textbook, but more a source of mathematical inspiration, a collection of particularly elegant mathematical results. My favourite aspect of this book is the way it focuses on proofs and results that draw connections between different areas of mathematics. The interconnectedness of mathematics is too often ignored by researchers nowadays, who have become specialized to the point that their work is often inaccessible. This book is a healthy step in the opposite direction.
My only complaint about this book (and it's not really about this book at all) is that there are not more books like this. The book is heavily slanted towards number theory, combinatorics, and graph theory. The chapter on analysis is beautiful, but atypical of analysis as a whole. I think that it would be wonderful for people to write similar books in other topics, in particular, analysis, algebra, or
Title: Proofs from THE BOOK