This book might always have come across as a disjointed read (as it delves into four separate areas of mathematics) but it also suffers because these areas fail to hold the reader's attention. The four sections covered are number theory, shapes and topology, computer science, and the mathematics of voting.

Of the four, the number theory section is the most interesting, but a more in-depth and charming analysis of this area of mathematics can be found in Simon Singh's two books: Fermat's Last Theorem and The Code Book.

The chapter on computing machines is weakened by the fact that the book was published first in 1989 and consequently is rather dated.

Overall I would describe this book as a page-turner but only in the sense that I skipped pages to swiftly conclude certain chapters.

Most people have math-phobia, which is too bad, because math exhibits a certain beauty and perfection. The great thing about Paul Hoffman's "Archimedes' Revenge" is that he shows you the beauty and perfection without your having to be a math major to understand.

Moreover, for anyone who's wondered what use math is, Hoffman can answer that as well. Among the subjects covered are: cryptology (code making and code breaking), architecture, computer science, and political science.

The book is divided into a number of sections, ranging from number theory to topology to game theory. While these may sound like esoteric (and useless) concepts, Hoffman masterfully weaves in stories, such as the (in)famous Beale cipher, a secretly coded treasure map that has resisted all attempts to crack it for over 100 years.

I recommended to a colleague of mine that she buy this book for her teenage son, who is bright but a slacker. She reported that he raved about the book and was so eager to discuss it with her!

As an example of the sort of thing covered in this book, Hoffman describes a game where A, B, and C all have balloons and darts. A hits his target 80% of the time; B hits his target 60% of the time; and C hits his target 40% of the time. If each person attacks his strongest opponent, who wins most often? Surprisingly, the answer is C, because A and B concentrate their attacks on each other.

In summary, if you have math-phobia but would like to conquer it, this is a great place to start. There are no equations to speak of, just concepts explained in (relatively) plain English. It may take a couple of readings to understand it all, but it's definitely within grasp for those who progressed no farther than Algebra 2 in high school.

I found the book to be rather interesting, and not difficult to understand. A scientific or mathematical background is an added plus while reading the book. I felt that it got bogged down in some sections, but they were of little interest to me and skipping them did not hinder the overall effect of the book. Enjoyable light reading, for if you ever thought,"What the hell is math good for?". Good section on cryptology.