How the Other Half Thinks: Adventures in Mathematical Reasoning

In his preface, the author does a good job of explaining what he set out to do in this book; then, in the rest of the book, he does a good job of doing it! Stein has attempted to present examples of real mathematical reasoning that (unlike some of the most beautiful parts of math) DON'T require any math background to understand or appreciate--and in my opinion, he succeeds brilliantly. If you love a well-reasoned, clearly explained argument but never even took algebra or geometry, you will enjoy this book. On the other hand, even mathematically sophisticated readers are likely to find some things here that they hadn't seen before, so they should enjoy the book too.

This is a well written and much needed book. Of all disciplines, mathematics continues to be the least understood by the general public. Even among the scientists who use mathematics daily in their work, many are not fully aware of the true nature of the subject. One of the main reasons for this lack of familiarity is the absence of books that illustrate the mathematical way of thinking in a way that non-mathematicians can easily comprehend. In this book, Sherman Stein leads the reader through a number of genuine mathematical problems whose statements and solutions are presented in a way that requires no more than the use of common sense and, possibly, a few facts from elementary arithmetic. By reading this book, readers will have a chance to see how mathematicians think and what processes they go through before solving a mathematical problem.The book consists of eight chapters, each starts with a simple question that leads to others, and from the discussion of these a general question arises and an answer is developed. This question then is often related to others asked by other mathematicians or scientists and, on a number of occasions, some applications are pointed out. Although the eight chapters are basically independent and can be read in any order, there is similarity in the type of questions they treat. The best way to get a flavor of the book--the type of questions it discusses and how the material is handled--is to read the first chapter, where a question that seems so simple at first glance leads to an interesting and unexpected solution. This spirit continues throughout the entire book. I believe that the author's choice of topics and the clear and interesting way in which he discusses them make this book truly accessible to any intelligent member of the "other half." The book also has something of interest to professional mathematicians as well; they will find that many of the problems it discusses are new to them.Fawzi M. YaqubProfessor Emeritus of mathematicsSUNY College at Fredonia