Coincidences, Chaos and All That Math Jazz - Edward Burger (****)

Making Light of Weighty Ideas!

What a wonderful motto for learning! To understand deep things simply, investigate simple things deeply.

In "Coincidences, Chaos and All That Math Jazz", Burger and Starbird take that motto to heart and bless their readers with an entertaining, irreverent, always amusing yet eminently readable and completely understandable exploration of some of the frontiers of mathematics.

In the opening chapters, real-life numbers - the roulette wheel, nature vs nurture studies of twin's characteristics, e-mail stock picking scam and spam artists, air safety standards, HIV testing and the puzzle of coincident birth dates at a party - are used to put meat onto the bones of the familiar saying "lies, damned lies and statistics" and to introduce the modern concept of mathematical chaos.

A simple straightforward chapter on the nature of numbers that almost effortlessly leads us into a basic understanding of much more complex topics such as cryptography, the Goldbach and the Twin Prime conjectures closes with the interesting comment,

"... our instinctive desire to wonder about the world of numbers has paid enormous practical dividends in the past - abstract ideas about primes and factoring unexpectedly led to public key cryptography and security in Internet commerce. Somehow human curiosity about numbers from ancient times to the present seems to be in synchronicity with the universe."

Counting spirals on pineapples and sunflowers and the simple act of folding and unfolding a strip of paper is used as a springboard to take the reader, who is now thoroughly engrossed in the enjoyable style of the book, to a basic understanding of the Fibonacci sequence, the golden ratio, chaos and fractals. But for me personally, the most interesting section was the last one. Burger and Starbird used extremely simple notions of counting, matching and a hotel with an infinite number of rooms to guide the unsuspecting reader to a brilliant "aha" moment - a concise, clear understanding of Cantor's ideas regarding the cardinality of infinity, the completely counterintuitive idea that some infinities are bigger than others.

Mathematics is fun and beautiful and this wonderful little book will show even the most math-phobic reader why! Highly recommended.