There are several versions of this book; or at least books with the same title that are being reviewed together. The description of the book given by Amazon states that the text of the Amazon.com review refers to another, earlier, edition of a book with the same title. This earlier edition was written by Richard Mankiewicz, with a forward by Professor Stewart. It was published in 2001, whereas the book description lists a publication date of 2008. The one that I read was written by Ian Stewart and was published in 2008. However, it does not have the cover shown in the Amazon insert; it has the cover that was provided by a customer. I believe that the negative comments of some reviewers (small print and many pictures in place of text) refer to the 2001 Mankiewicz edition. I had no trouble with the size of the text, and I find it difficult to read books with small print. Furthermore, while there are pictures, they are not the focus in my edition and, unlike the 2001 Mankiewicz edition, none were in color. A prospective buyer should check to make sure of the edition that is being purchased. This review refers to the 2008 edition authored by Ian Stewart.
The book is an overview of the development of mathematics. It is part math, part biography and part history. It covers mathematics from the earliest ideas of the Egyptians, Babylonians, Chinese, Indians and Greeks, to the most modern ideas group theory, set theory, topology, and non-linear dynamics. Each chapter, starting with counting and numbers, is self-contained but there is a flow that relates each chapter to what has gone before and what will come next. The text is only 278 pages long, so only a brief overview of each topic can be provided. The development is generally chronological and historical and in addition to the development of the math there are capsule biographical inserts concerning the mathematicians involved with that development. Each chapter also contains a capsule summary of why this topic is important not only for the development of mathematics but also "what it does for us", so even if the reader does not completely follow the mathematics they can see why the topic is important and how it fits into the whole of mathematics.
This is a good book for advanced high school and college students who are interested in the way in which mathematics developed. Equations are provided, but are generally not derived or developed fully. The introductory chapters on numbers and the development of geometry and algebra are good supplements to what students are learning in math class, but many will likely find the latter chapters a bit too advanced. Be forewarned, however, that this is not a mathematics book in that it does not aim to teach the reader how to solve problems. The treatment is more historical and aims at describing how mathematics evolved.
Mathematics is a difficult subject to cover in a cursory manner and Professor Stewart does as good a job as any that I have read, but frankly I found that some of the latter chapters were somewhat incomprehensible. I guess this is unavoidable as there was just not enough space to include a more complete exposition of the topics. It is for this reason why I could give the book only 4 stars. Nonetheless, I did learn what the basic ideas were and why they were important, even if I could not completely follow the all mathematics. Mathematicians will likely find this book too elementary, but the historical and biographical elements will possibly interest them.