Customer Reviews

Proofs from THE BOOK

5 star:		(15)
4 star:		(2)
3 star:		(0)
2 star:		(0)
1 star:		(2)

 

 

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".

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.

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

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!

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.

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 probability or topology like the other reviewer mentioned.

As a final note I would like to give credit to the publisher for doing a good job on this one. The typesetting is excellent, the layout is clear with all the illustrations, the paper is of high quality, and the binding is oustanding. It has held up well to moderate use and still looks brand new. I only wish some of my more heavily-used reference texts were bound like this.

The famous eccentric mathematician had a theory that God (who he liked to call the SF-Supreme Fascist) had a book with every mathematical theorem and that the book had the most beautiful and elegant proofs for the theorems.
This book has that philosophy and presents great proofs for many beautiful theorems.
It is a masterpiece. A book that shows why mathematicians love what they do.

Most of this book could be read by an undergraduate with only background in calculus and basic discrete math. The proofs are mostly self-contained, and there are helpful appendices to each chapter when prerequisite material is needed. I think this would be a good book for undergraduates or enthusiastic high school students to read for fun, or for lecturers to draw interesting examples from.

The proofs, while "elementary," are sometimes quite involved, however, and do require some maturity to be able to appreciate the "big picture" of each proof, and it's tempting to "island-hop" (i.e., just check that each if... then... works out in the proof, without looking at the whole thing put together). This would be especially nice material for an undergraduate math club or for math enthusiasts to read at liesure. The problems are also highly "integrated," in that they make use of ideas from several different types of math, and are not usually straightforward, so they are good examples of creative solutions to challenging problems.

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.

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.