# Book Review: Strength in Numbers

## Strength in Numbers: Discovering the Joy and Power of Mathematics in Everyday Life by Sherman K. Stein

Based on the subtitle of the book, one might expect Sherman Stein’s Strength in Numbers to discuss when and where we see and use mathematics in our daily living, but that is not the end result of this book. Sherman does include some basic mathematics, including chapters on the basic properties of numbers, “everything you need to know about fractions,” why a negative times a negative is positive and how mathematics is useful in business, industry and other walks of life. A good deal of the mathematics described in the book goes beyond what is commonly thought as “everyday” mathematics.

## A Little Probability

A discussion of mathematics in everyday life often contains a good deal of discussion on probabilities and statistics. However, Strength in Numbers only touches on probability slightly. Just one chapter is devoted to probability, though this chapter discusses a somewhat “classic” probability problem that drew a great deal of attention when it appeared in Marylyn vos Savant’s column in Parade magazine in the early 1990s. This “two-goats-and-a-car” (or the “game-show” or “Monty Hall” or “stay or switch”) question asks:

Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car; behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?

Stein does not give the answer to the question in the book. Rather he uses this question to demonstrate his point that it is important to explore mathematics to learn how to think mathematically. He provides several ways that one can experiment with this type of situation to arrive at the answer (which is yes).

## Onward to Calculus

A large part of the book is devoted to an attempt to make some rather complicated mathematics (such as the sum of an infinite series, finding the area under a curve and approximating the value of π) simple to understand. Stein does a very good job of showing how two separate branches of mathematics, algebra and geometry, are actually very closely related. He brings to life some findings from each area of mathematics by leaning on the other. He also presents some interesting and “elegant” proofs of the well-known Pythagorean Theorem: In a right triangle, the sum of the squares of the two shorter sides of the triangle is equal to the square of the hypotenuse of the triangle (or a2 + b2 = c2). This diagram from the MathisFun website is used to show one of the proofs of the Pythagorean Theorem that Stein included in his book. This is one of many connections between geometry and algebra.

But what Stein does, in not atypical mathematical fashion, is present “simpler” findings (such as the formula for the sum of an infinite series) to build up to more-advanced mathematics. He builds up to the point of using three results he presents in earlier chapters to show how calculus, which is employed in many fields of study that involve motion and changing quantities and which led to much of the technology we use today, is used to find the area under a curve and to show how π is related to the odd numbers (which is rather interesting): So while the subtitle of “Discovering the Joy and Power of Mathematics in Everyday Life” might be a bit off target, Strength in Numbers is a good read for anyone interested in mathematics.