The Magic of Math is a fantastic book, as one would expect from Arthur Benjamin. Benjamin's enthusiasm shines throughout the book, mathematical ideas are beautifully explained, and each chapter is surprisingly hard to put down! Moreover, the book is appropriate for many different audiences, including:
-- Anyone who wants a better understanding of what it means to do mathematics, or wants to see the beauty and creativity inherent in mathematics
-- Middle and High School students who want to see some of the mathematics ``behind the scenes'' of what they're learning in school
-- Burgeoning mathematicians who want to see mathematics beyond the scope of the grade school curriculum
-- Tutors and teachers who want an easy source of fun material to engage their students
-- Anyone who wants to really understand *why* the math they learned in grade school is true.
People familiar with this genre of mathematics outreach books (e.g., Here's Looking at Euclid, The Joy of X, Love and Math, etc.) often find that many of the books are very similar, and that their contents tend to overlap greatly. While readers will certainly find common topics like the Pythagorean Theorem or the Fibonacci Numbers in Benjamin's book, I think they'll also encounter quite a substantial amount of new material in this book. In particular, Benjamin goes into more mathematical depth with much of the material he discusses. Further, a quick skim of the contents reveals a lot of beautiful mathematics that is not commonly in outreach books, including an especially thorough discussion of exciting topics in a field of mathematics known as combinatorics. If you're interested in understanding the kind of thinking a mathematician does, then you'll find these chapters especially novel!
At the same time, Benjamin's book is very readable. He clearly motivates the mathematical ideas he shares, and then proceeds to explain them in concrete and understandable ways. Of course, as with any good book, this book will make you think! However, you'll have Arthur Benjamin supporting you along the way, and you'll find yourself learning quite a bit of mathematics with that support. Benjamin is also sure to include a few optional and sometimes particularly robust mathematical ideas, but he clearly marks these as ``asides,'' explicitly indicating to readers that grappling with these ideas is not necessary for understanding the material. Instead, these aside sections serve to make the book more interesting to people who might reread sections of the book, or who already have an especially strong background in mathematics.
The Bottom Line: This is a great book that can (and should!) be read by people from a huge variety of backgrounds. Beautiful mathematical ideas lie waiting to be discovered, and readers will encounter both engaging prose and crystal-clear mathematical exposition.
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