Granted that this book is intended for non-mathematicians and is, according to the author, descriptive rather than precise, it still should not purvey misleading information.

E.g., on p.43, he calls spherical geometry "Riemannian geometry" and then claims on p.44 that "actual space is not Euclidean but rather more nearly Riemannian." That is incorrect if we adopt his notion of "Riemannian." It becomes correct when one provides the correct definition of "Riemannian" found in any advanced text on the subject.

On p.73 he misstates the Gelfond-Schneider Theorem, writing ab when it should be a to the power b that is transcendental. And on p.72 he misspells Mahler as Maher.

I doubt that most laymen will be enlightened by his discussion of the law of signs on p.73ff. He does show that it follows easily from other algebraic laws, and if the layman finds those laws acceptable, then the law of signs must be accepted, unintuitive as it may be.

His discussion of Fermat's Last Theorem on p.89 was unfortunately written before Wiles corrected the initial error in his proof. He needs a second edition to update this.

On p.88ff he argues that Appel and Haken's solution to the Four Color Problem was ugly because they used a lengthy computer calculation that cannot be surveyed. I and other mathematicians thought it was quite beautiful the way they reduced the problem to a finite computation.

That's as far as I've been willing to read in this book.

This is really a wonderful book. It's one of the reasons I went to grad school.

Dr. King really does a great job of explaining what math is really all about. His analogy to sculpture is perfect: If you want to appreciate a statue, you can't stand too close or too far away. Those in liberal arts are standing too far away from math to see it. Those in engineering and the sciences are standing too close -- they use pieces of math as tools but never see the beauty of mathematics.

And I must respectfully disagree with Dr. Greenberg -- the Appel-Haken proof of the four color theorem really is a travesty. It's not a question of being ugly: it's invisible. It's not a proof at all -- it's an "argument from authority" and hence is inductive, not deductive.

I happend to pick this book up by chance and enjoyed every page. I agreed with everything the author had to say. I suggest this book to anyone with ANY interest in Math. It is best suited for those trying to understand why other people enjoy/understand Mathematics so much