In the Preface, the author indicates “Since I’ve claimed that the book is for those who want to know about mathematics and why it matters, I’m at least implicitly saying that this is a book aimed at the nonmathematician.” Very good start, I fit that category. Later he states, “This does not mean that he or she actually knows any mathematical techniques or procedures.” Good, still there. Further on, the statement “Just about anyone who’s had a course in high-school algebra or geometry, and who retains at least a modicum of enthusiasm for mathematical ideas fits…” Sehr gut. With such promises, I dove into this exploration and explanation of what the author has determined to be the five finest achievements of the mathematicians’ arts in the 20th century.

All I can say is that I am glad I never took a high school course from Mr. Casti if this is his idea of what I might have learned. This is not a quick dip into the shallow end – this is a head-long high dive into shark infested waters. If you want to truly understand the concepts and ideas proposed (and if you are, like me, passingly familiar with and interested in the concepts of mathematics), be prepared to set aside great amounts of time and grey matter for this one.

There are interesting concepts and ideas. Casti does a good job of taking these mathematical pie-in-the-sky ideas and applying them to everyday concepts – you understand why they matter. But delving into the logical discussions and proofs (and, keep in mind, I lost count of how many times he indicates that, if you want a more rigorous proof [a more rigorous proof!!], you can check the books in the bibliography) I nearly drowned.

A mediocre to bad rating for this one because…well, I cannot say this is a bad book, because I cannot understand (or just don’t have the time to understand) everything that is being portrayed. But because of the promise of something simpler (no, I’m not asking for Dick and Jane, but at least don’t give me Dostoyevsky in the original Russian), I am greatly disappointed. And maybe someone with a better mathematical bent might be able to tell you it is as good as I suspect it to be, or incredibly bad – I just don’t know. Read this if you have the time and inclination to devote. Skim it (always dangerous in a math book) if you want to see a glimpse of how some of these concepts have changed our understanding of the world. But do not go swimming if you have no desire to even look at deep waters. ( )