The Story of Mathematics

Mathematician and scientist Ian Stewart writes some popular books on the subject (I keep meaning to read his annotated Flatland). The Story of Mathematics is devoted to an overview and history of Mathematics, and what it was good for in the past and what its good for now. With lots of sidebar digressions on figures and topics, this volume reminded me, in some respects, of my beloved "The Math Book" textbook that I recently found for sale again, used and purchased. The Story of Mathematics takes on Mathematical topics of increasing complexity and difficulty. Each topic is placed in context with how and why it was invented and developed. So the volume begins with tallies and basic number systems, showing how tallies turned into Babylonian and Egyptian number systems. We progress through basic geometry, our own number system (with sidebars on things like the Mayan and Chinese systems), trigonometry, logarithms, algebraic geometry, number theory, calculus, differential equations, and all the way up to modern chaos theory. In less than 300 pages, this means that no topic really is done in depth, a strength and a weakness. Similarly, too, the book remains at a high level overview strictly for non-mathematicians. This is not a volume by Eli Maor! In fact, the Mathematically trained might feel this is a bit dumbed down. So, I believe that intelligent readers who are completely math-phobic and yet have an urge to know more about how it works and where it came from (without doing any math skull sweat) will be happiest with the book. Those fully trained in Mathematics might be frustrated at some of the lack of depth in topics (and probably would be happier with a volume on a more specific subject that they are interested in). As for myself, I learned some things about fields of mathematics of which I am not very conversant. Stewart has a relatively easy style to follow, but its nothing special. As a production value, I do mention that to keep the volume under 300 pages, the print in the book is relatively small. Still, despite all of this, I enjoyed reading Stewart's Mathematical overview.

Light mathematical history is the best phrase to describe this book; it has too much math to be considered as mere history and not enough to be described as mathematics. It begins with the earliest of representations of mathematics, which was of course numbers. After that came the geometry of area representations for land surveying and the beginning of abstraction, where the idea became the mathematical concept traded rather than physical objects. Most of the general ideas of mathematics developed since antiquity is at least mentioned, and Stewart is to be commended for including formulas when needed. His style of exposition is effective in presenting complex ideas in a manner that makes it very readable. Any reader with knowledge at the level of high school algebra will be able to understand the fundamentals of the concept even if the particular details are beyond their grasp. This book could also serve as a text for a college level history of mathematics class for the elementary or middle school education major. If used as a source of ideas for classroom presentation, it could also be used as a text in a history of mathematics class for the math major.

Mankiewicz has given his readers exactly what the title promises -- The *Story* of Mathematics. As such the book doesn't bog itself down with illustrating the very mathematics it talks about. This might seem like a major absence for a book about mathematics, and maybe it is, but I get the feeling that the book assumes that the reader doesn't need or want a refresher. I appreciate the approach taken by Mankiewicz because it successfully keeps the story moving forward...as all good stories are inclined to do. More commendable is that Mankiewicz's book gives the most historically balanced view of the early origins of mathematics that I've yet encountered. I am, of course, referring to the controversy that still surrounds Egypt's influence in the subject. I've read an entire spectrum of biased claims. Some of them over-crediting Egypt's contributions, but most of them under-crediting her legacy. Mankiewicz's view that "Our knowledge of Egyptian mathematics is necessarily limited by a genuine lack of artefacts" resonates as both sincere and true. He goes on to write that "It is therefore tempting to see the mathematics of the Egyptians as a step backward from the level reached by the Babylonians. But this probably unwarranted, especially given their precision in pyramid-building and their management of such a vast empire....the ancient Greeks widely acknowledged that their mathematics, especially their geometry, originated in Egypt." Those words seem to avoid the usual sensationalizing that I've encountered in other works on the topic. This balanced reportage precipitates throughout the rest of the book, giving due space to all the key players, regardless of their geographic origins, in the story of numbers. The writing style is very accessible and, thankfully, with personality. Hopefully, this book is a hallmark of more to come. I think the world deserves a proper and balanced view of mathematics.

So much intellectual output, so much practical significance, so diverse a spectrum of imagination -- this book is tough to put down. The most provocative theme: there may be a world of mathematical genious lost forever to time, decay, and obscurity. So much of today's mathematics descends from manuscripts that were buried in dust for centuries, or thoughts that were expressed but not firmly grasped until much time had elapsed.Perhaps a more thorough investigation of ancient/medieval math is warranted. Who knows what new ideas might emerge?