Smith’s book, The Great Mental Calculators, is a curious work. As per its subtitle “The Psychology, Methods, and Lives of Calculating Prodigies” it is divided into three distinct sections. The first third of the book reviews the scientific and popular literature associated with various members of this group. The author quotes and offers commentary on sections of scientific papers written about mental calculators and highlights in detail many of the mental tests these people were given by various investigators (primarily in the 19th and early 20th Century). As a statistician, the one thing I found particularly frustrating about those researchers of yore and their calculating tests was their nearly uniform focus on maximum speed or average speed of mental calculation with no thought given to the variability associated with these measurements. As a result, those investigators typically rank ordered the mental calculators on the basis of averages only. As any statistician will tell you – averages, without taking into account the associated variability, are meaningless and provide zero information with respect to actual differences in performance.

The second part of the book goes into the computational methods used by the various mental calculators. Again, the author provides enough detail to allow the reader to understand how the various calculations were performed. This reader was surprised to find out that, contrary to what some have said about mental calculation, these people did not start each calculation from scratch. They possessed excellent memories and memorized many things such as the square and cube of every number from 1 to 100, the logs of the same span of numbers, etc. All of which helped increase the speed and precision of their mental calculations.

The last section of the book is a collection of short biographies of a number of the mental calculators. In addition to the usual facts provided in a short biography, the author has, where information was available, provided examples of the mental dexterity of the calculator being profiled along with measured times and a commentary on the ease or difficulty of some of the feats of calculation.

I found the book to be an interesting read about an obscure aspect of the human condition. ( )

This is a fascinating look at mathematical prodigies, both past and present, and the techniques they use to solve incredibly complicated problems in their heads. The book also provides an easy method of calculating days of the week for any date 400 years in the past or future. ( )