“Arithmetic,” by Paul Lockhart, Belknap Press, 2017, 240 pages, $22.95

Math is hard. Or is it? Most master the basics of arithmetic by grade school. Arithmetic is what most people use, comfortably living without everyday use of algebra, calculus or other mathematics, except perhaps a dash of geometry. Arithmetic is so familiar it is viewed as mundane.

“Arithmetic,” by Paul Lockhart re-examines arithmetic. It reveals there is more to arithmetic than meets the eye.

Lockhart goes beyond arithmetic as rote calculation of numbers. He despises memorization. Rather, he looks at arithmetic as a means of organizing and manipulating information. He starts examining the basis of counting, looking at how people organize collections of items, from rocks to aircraft. Lockhart also shows how and why commonly organizing by groups of 10 is arbitrary.

He plays games showing how counting by different arrangements, groups of six, eight or 12, for example, yields different interpretations of information. He also shows the importance of using a single base. Twelve pence makes a shilling and 20 shillings equals one pound invites confusion.

Lockhart builds on this foundation. He takes readers through different counting systems — Egyptian, Roman, Chinese and finally the Indian-Arabic numbers used today, and shows how they simplify organizing basic arithmetic functions. One example: Lockhart shows how adding using Roman numerals is straightforward if you do it the way the Romans did rather than by mentally using Arabic numbers.

He progresses to tools for counting, from the abacus to modern mechanical and electronic adding machines. Today’s computer is at its heart an arithmetic device. Along the way he shows how subtraction, multiplication and division fold in.

His presentation is intended to lead readers to reassess commonly held assumptions about arithmetic. His examples are straightforward, accessible even to those who had difficulty with the subject at school.

Those who love mathematics will want to read “Arithmetic.” Those who hate math should read it. Not because reading it is “good for you.” Rather, because “Arithmetic” causes the reader to view that subject differently. Lockhart’s ability to explain the inner machinery of arithmetic as a simple, entertaining and uncomplicated language makes understanding arithmetic much easier; fun rather than hard.

Mark Lardas, an engineer, freelance writer, amateur historian, and model-maker, lives in League City. His website is

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