New and Noteworthy Titles on our Bookshelf

How to Expect the Unexpected

Basic Books, 2023, 448 pp.

By Kit Yates

Cover is courtesy of Basic Books.

I’ll start by considering the word “unexpected.” What do you think it means? Does an unexpected event have an element of surprise? Is it a phenomenon that happens rarely or with low probability? In the book How to Expect the Unexpected, something that is unexpected plays into our personal biases of what we expect to occur. This nonfiction, general-interest mathematics book takes the reader on a journey of the biases, effects, and psychological phenomena that can often be explained or resolved with mathematics.

Yates starts the book by detailing common psychological tricks used by psychics to give a satisfactory reading and superstitious rituals utilized by professional athletes. While that sounds nonacademic, soon Yates begins to weave in mathematical topics to illustrate his points. As the chapters progress, the reader learns about more mathematical topics, such as linearity bias (the brain’s desire to extrapolate linearly) and illusory correlation (where one perceives a relationship when there isn’t one, such as finding a pattern in a random data set or attributing a deeper meaning to a coincidence). Bayes’ theorem and Nash equilibrium are discussed without technical definitions, and game theory is applied to both the plots of movies and the world’s political stage.

The book includes well-known counterintuitive facts and thought experiments such as the birthday paradox, the stockbroker scam, and the prisoner’s dilemma, where the results start to make sense after a careful analysis of the numbers. An instructor might use these examples to introduce a mathematical concept to the class, perhaps in a math for liberal arts course. You could add this recreational book to your personal library or gift to your graduating students for them to enjoy.

The Call of Coincidence

Prometheus, 2023, 192 pp.

By Owen O’Shea

Cover is courtesy of Rowman & Littlefield.

For many years, Owen O’Shea has been fascinated by numerical patterns and coincidences, and his latest book continues this tradition. The book features mathematical tidbits, ranging from arithmetic oddities to surprising number theory results that could be used in a discrete mathematics course. Parts of this recreational math book are more traditional; because historical anecdotes are juxtaposed with facts involving $\sqrt {2}$, including a proof of its irrationality, I believe the intended audience for this book is interested in the calculations as well as the musings.

The chapters in this book have whimsical titles, such “Geometry Gems,” “A Few Words about Simplicity, Mathematics, and Everything There Is,” and “Two Lightning Calculation Tricks and Sundry Other Matters.” Interludes with a fictional numerologist are entertaining. This numerologist is particularly skilled at finding numerical coincidences that might belong on memes or internet posts, such as “Martin Gardner was born on the 293 + 1 day in the year 1914. There are 293 $\times$ 1 primes less than 1914.” Some of the chapters discuss much deeper and possibly unanswerable questions, such as “Does mathematics exist outside of human minds?” and “Why is there something rather than nothing?” Examples from physics and philosophy are woven within the mathematical anecdotes, and O’Shea offers opinions and theories that will leave the reader thinking.

I enjoyed the inclusion of various puzzles and problems for the reader to solve, some numerical and others logical. After reading this recreational mathematics book, you are sure to believe that you can find “surprising” coincidences anywhere if you look hard enough.