Mathematical Sorcery, by Calvin C. Clawson, Perseus Publishing, Cambridge, MA, 1999. 294 pp., $16.50 (paper) ISBN 073820496X.
Five out of five stars
This book is a popular history of mathematics with a catchy and slightly disingenuous title. For there is no sorcery or magic involved, it is the wonder and usefulness of mathematics in both the pure and applied form.
It begins with the emergence of the concept of counting and the historical context as to why it emerged. With the development of agriculture, both animal husbandry and crops, human groups became fixed in location. This led to the emergence of governments to organize and protect the populations, which led to the levying of taxes. All of this required the ability to count, tally and record, which meant the mental concept of numbers had to develop as well as a way to efficiently record and manipulate them. The last chapter of history covers the development of and basic applications of calculus, so the history essentially ends in the first half of the eighteenth century.
The journey from start to finish is an understandable tour through several of the most significant advances in mathematics, from the development and use of negative numbers, fractions, irrational and transcendental numbers to complex numbers. Clawson is to be commended for he does not skimp on the use of formulas, when one is needed one is used.
Math, science and the increasing complexity of societies have been married into a feedback loop for thousands of years. Sometimes the need led to the development of mathematics, for example, when society needed counting numbers, the math was invented. Other times the math had to be invented to explain the science. In other circumstances, the math was developed before society had a use for it.
In all cases, the development of the math proceeded and Clawson does an excellent job in explaining the new math concepts, the reason it was developed and the niche it filled in society.