Almost no mathematical knowledge is needed to understand this book. It could be read by a willing high school student. It would probably be best appreciated by someone like a college math major wanting to see what lies ahead of her, but it could also interest non-mathematicians who want to see what the field of mathematics is all about.
This book consists of 193 pages of 50 brief essays on numerous mathematical topics. The book is divided into the following parts: Historical Tidbits, Unsolved Conjectures, Solved Problems, Personalities, Concrete and Abstract Matters, and Interdisciplinary Potpourri. Some essays have references to further reading. The essays are largely free of actual mathematics. Fanning through the pages will reveal no formulas or equations. The essays include short biographies of famous mathematicians, descriptions of important mathematical problems, and applications of mathematics to other fields. Mathematical topics include twin primes, plane tilings, computer-aided proofs, knot theory, chaos theory, group theory, elections, data compression, computer science, fractals, turbulence, and Bible codes.
This book was a runner-up for the 2005 Descartes Prize for Research and Science Communication. I almost couldn't put it down. (I read it in two sittings.) It is highly entertaining and original. The biographies were insightful and not just the same old standard stuff. A lot of the mathematicians mentioned were the standard famous ones that math students know about, but many "lesser" figures are also covered, including Coxeter and the contemporary Wolfram.
The essays describing mathematics itself were somehow thought-provoking and informative without the author hardly mentioning any particular formulas, equations, or proofs. Some specific theorems and results are given, however. The chapters on knot theory, computer-aided proofs, and the Collatz problem were especially fascinating.
The book does contain a few minor mathematical errors (that don't detract from the main points) and a few of the essays have some redundancies in them (as if this is a compilation of essays previously written). But who cares? This book went a long way to rejuvenating my mathematical spirit and it makes me want to study serious mathematics again.