Customer Reviews

The History of Mathematics: A Brief Course

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Approximately every three years, I teach a course in the history of mathematics. It is one of my favorite math courses to teach, because it allows me to delve into the historical and cultural context of the development of mathematics. Among other things, I was a history minor in college, and if you learn anything in that field, it is that events are never isolated. Everything takes place in a social, economic, cultural and historical context, and that includes the development of new mathematics.
Cooke is obviously as much a student of history as he is of mathematics. The technical structure of the mathematics is explained within the historical and cultural settings. There are many exercises at the end of the chapters with solutions to some of them included at the end.
The coverage of the development of mathematics in the western world is fairly standard. Cooke is to be commended in that he includes sections on what was going on in the rest of the world. Section II contains the following chapters:

*) Mathematics of the Hindus
*) Chinese mathematics
*) Korea and Japan
*) Islamic mathematics

Many mathematics books mention the role of the Islamic nations in keeping the ancient mathematics alive. However, there is little acknowledgement of what was going on in other cultures. If there is a mention of mathematics outside the western sphere, it is in reference to the creation of our modern numeration system.
It may be some time before I teach the history of mathematics again. If I do, I will once again place a great deal of emphasis on the history, something that Cooke does so very well.

Oh, what a disastrous disappointment this was! The book was generously sprinkled with history and chock-full of mathematics but basically fell silent in the "history of mathematics" department. I emerged with a vague idea of the interrelationships among these theorems or these techniques, but nothing of a useful _conceptual_ nature was to be gleaned from these academically spiffy pages. Honestly, I got the impression that the author was trying to impress me with the scope of his mathematical knowledge (a difficult task given the shocking limits thereof: a handful of theorems, more or less correctly stated, cannot substitute for a meaningful sub-corpus of math-craft). Yea, he expended not the first breath in trying to show me how the approaches and, yes, psyches of various civilizations empowered them to construct bodies of knowledge atop thitherto weaker or less finely structured bodies of knowledge. Nowhere could I glean any thread whereby I could declare, "Aha! It's amazing how culture X managed to cobble together idea P by subtly restructuring culture Y's notion of Q!" Friends, look for "The Crest of the Peacock" by George Geverghese Joseph and really, _really_ enjoy. (For a bit more detail of one particularly interesting tangent [no pun intended], explore Petr Beckmann's "History of Pi" also.) In retrospect, I can't imagine what motivated me to shell out $100 for Cooke's pseudo-opus in the first place.

I've spent a long career trying to establish a few solid relationships between mathematics and the sciences of mind. Thus, it is truly a great pleasure to read a book on such a vast and deep subject as the history of mathematics and be thoroughly able to trust the author's knowledge of it through chapter after chapter.

This book is a fascinating look at the history of mathematics, and is sure to inspire even the most devout haters of numbers.