Mathematics for the Millions - How to Master the Magic of Numbers, by Lancelot Hogben, 1999.
Review by John Loofbourow, MD
The first Hogben book I read was called "The Mother Tongue" (1967), now long out of print. From a utilitarian orientation, it is a coherent exposition of the inter-relationships among Indo-European languages, which provides an insight into the diverse grammars to be found within English itself. (The British Isles was conquered and ruled by Romans, Nordics, and French, each layering their grammar and syntax onto the Celtic native language.) This left the conquering languages embedded in English. In the 1500s, the English discarded Latin grammar. Because of these advantages, Hogben makes the case for English to become the lingua franca of the modern world. Voila! (Sorry francophiles.)
However, Hogben first became widely known for his book Math for the Million in 1937, and it has gone through more than 40 editions since. It is a math textbook, but one with a broader message. The subject of course is mathematics, but the message is revealed in the organization of the book as well as through direct comment of the author, who notes that every advance or new development in mathematics, is the result of people doing things. It is people who do things who change thought rather than people who think things who change how we do things.
People counted, measured the size of their fields, navigated the seas. Measuring fields, for example, led to Euclidian (used to be more aptly called plane) geometry, and the navigators expanded to trigonometry, and so on. Being no Platonic purist, Hogben introduces each development in mathematics within its historical or cultural context, rather than through didactic or theoretical concepts. It is good reading, filled with historical detail, related with typical British humor; but it gets right down to serious math.
Each chapter is followed by exercises, which can stretch the reader's patience. I enjoyed the book, but felt like I was back in college and needed to do the homework, even though I am unlikely to use the skill. Come to think of it, that's the same with most of what I learned in college. Maybe reading math books is a form of entertaining regression.