Proofs from the Book

Rating:
Summary: Proofs from THE book!!!!!!!
Review: 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.

Rating:
Summary: Proofs from THE book!!!!!!!
Review: 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.

Rating:
Summary: A breath of pure air
Review: 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.

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Summary: A fitting tribute to the great Paul Erdos
Review: 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.

Rating:
Summary: A fitting tribute to the great Paul Erdos
Review: 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.

Rating:
Summary: One invaluable pearl
Review: This book is an invaluable pearl in mathematics.
Both content and appearance of the book are excellent.

Rating:
Summary: original
Review: 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".

Rating:
Summary: The ideal maths book for dipping into...
Review: 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!