Book Review: “The Joy of x: A Guided Tour of Math, from One to Infinity”

reviewed by Gabriel Chong

BookcoverWhen I saw the release of the first batch of The Joy of x in bookstores a few years ago, I wanted to get the book immediately. Prior to that, I had enjoyed Strogatz’s 2003 bestseller Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life, based on his highly influential research on synchronized networks and the first in a series of books which subsequently cemented his reputation as one of the most popular mathematics writers of recent years.

The ambitious subtitle, “A Guided Tour of Mathematics from One to Infinity”, led me to a false anticipation of the same erudition and scholarship that awed me in Sync. This book, however, was rather different from its predecessor. The culmination of a well-received column in The New York Times, The Joy of x is printed in a sparse and large typeface, written in a rudimentary style, and accessible to even the most mathematically illiterate reader. Though not intended to be remedial, it strives to communicate what mathematics is about to a demographic that might be otherwise intimidated by the discipline. This does not mean, however, that it is simplistic or completely irrelevant to the mathematically trained. In fact, some of the chapters gave me a fresh insight into the fundamental purpose of many of the most basic mathematical tools that I have been acquainted with since high school.

The Joy of x is divided into six independently arranged sections, “Numbers”, “Relationships”, “Shapes”, “Change”, “Data”, and “Frontiers”, of which the subchapters run the gamut from number theory to geometry, from calculus to set theory. The first chapter begins with the most elementary of mathematical concerns: why we need numbers, by referring a particularly adorable episode of Sesame Street. Humphrey, a dimwitted muppet working at a hotel, calls out as he takes the orders from a roomful of hungry penguins, “fish, fish, fish, fish, fish, fish”, until he realises that his exhausting repetition of orders could be avoided with the use of numbers.

However, once he applies the arbitrary symbol “six” to his amount of orders, he cannot escape its logical consequences (for example, that six plus six necessarily equals twelve). Herein, says Strogatz, lies the purpose and strange power of mathematics: “This is how mathematics grows. The right abstraction leads to new insight… Yet despite this infinite vista, there are always constraints on our creativity… Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences.”

From there, Strogatz introduces the various fundamental concepts and major branches of mathematics with the aid of visuals and anecdotes, many of which are staples of elementary mathematics books (the Y-shaped diagram of squares which illustrates the Pythagorean theorem, Hilbert’s Hotel which explains the paradoxes of set theory, etc.), but also some less-utilised analogies and creative allusions to pop culture.

In Chapter 3, “The Enemy of My Enemy”, Strogatz borrows the concept of balanced triangles to elucidate multiplication between positive and negative numbers. We can imagine the corners of a triangle to be represented by a number each, whether positive or negative, and that the relationship between these various corners must match the logical relationship of multiplication between positive and negative numbers. These triangles have been used by social scientists to model the complex behaviour of social agents and historical trends, such as World War I (see diagram).

Diagram demonstrating the shifting alliances between Great Britain, France, Russia, Italy, Germany, and Austria- Hungary from 1872 (modelled by unbalanced triangles) until the consolidation of two implacably opposed blocs (modelled by balanced triangles) in 1907, shortly before World War I. Source: The New York Times, 2010.

Diagram demonstrating the shifting alliances between Great Britain, France, Russia, Italy, Germany, and Austria- Hungary from 1872 (modelled by unbalanced triangles) until the consolidation of two implacably opposed blocs (modelled by balanced triangles) in 1907, shortly before World War I. Source: The New York Times, 2010.

In Chapter 7, “The Joy of x”, Strogatz comments on the misapplication of algebra in formulating common but nonsensical social rules, such as the rule stating that if your age is x, your date should not be younger than x/2+7.

In Chapter 23, “Chances Are”, he uses the trial of O.J.Simpson to introduce conditional probability. Alan Dershowitz, the defense lawyer, had infamously argued that a very small percent of men with a history of battering their domestic partners went on to murder their spouses. But, as Strogatz pointed out, this was not the relevant statistic to look at. Rather, the relevant question should have been, “What is the probability that a man murdered his wife, on the condition that he had previously battered her and the fact that she was murdered?” Sadly, elementary mistakes in counting probabilities such as these often tamper the process of justice.

In a more light-hearted Chapter 26, “Group Think”, Strogatz uses group theory in exploring the question, “How should you flip your mattress to get the most even wear out of it?” – as another curious example of how mathematics applies in even the most mundane experiences of daily life.

Though many popular mathematics books exist out there, the majority of them still have in mind an audience with some high school level mathematical knowledge, which alienates a large subset of society still struggling with even the most basic mathematical concepts. The Joy of x is perhaps the most accessible popular mathematics book written by a high-profile mathematician that I have come across yet, and though much of the content is hardly original, it fulfills a much- needed role to introduce elements of mathematics to the larger society. Perhaps more importantly, it debunks the perception of mathematics as an abstruse subject and inspires – as its title implies – a love of mathematics.

About the Author

YONG WEI CHONG GABRIEL is a philosophy student at Wellesley College. Her column aims to break down popular topics in science into digestible bits for the lay reader. Gabriel can be contacted at gabrielle[at] Find out more by visiting her Scientific Malaysian profile at gabrielle/ 

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