New and Noteworthy Titles on our Bookshelf

December 2023

Note from the editor:

I couldn’t help myself! Given the similarity in titles, I felt compelled to review both of these books in the same month. Each book serves a different purpose and covers different topics, as you will see. This month, we ponder the realness (or not) of math!

As I perceive it, the goal of Eugenia Cheng’s latest book is to provide examples of why seemingly simple components of a typical math education are actually much deeper. She describes Is Math Real? as a “math emotions book,” and her audience is both math-lovers and math-skeptics. While reading, I was reminded of a former student who liked to jokingly ask me, “Have mathematicians figured out how to divide by zero yet?” This book provides a compelling explanation to this question that even math-adverse folks could appreciate.

It comes as no surprise that in a typical math education, there is too much emphasis on having students answer questions rather than learning how to ask them. Cheng would like to see students learn “how questions lead us on a journey, about where the journey is leading, and about why we might want to go on that journey, and what we see on the way.” She also advocates that math education should emphasize not only math’s direct usefulness and how it is a basis for studying other related fields, but also that math is a powerful way of thinking that is very transferable. She addresses popular memes, such as one which asks, “How many holes does a straw have?” Cheng’s response is: it depends on how you define a “hole.”

The mathematics presented is approachable and Cheng’s prose is conversational in tone. Readers who like to consider how the public views mathematics education would enjoy this book. There are some nuggets of wisdom that could affect your teaching philosophy as well, such as why to promote internalizing over memorizing and why you should relish the innocent questions students ask. Aimed more at the general public than mathematicians, this book would make a great gift for a K–12 educator or an intrigued but skeptical family member.

To most students, trigonometry seems self-contained. However, these functions model musical sound, ocean surges, and UV rays. While $\sin (x)$ and its siblings were used for measurements for thousands of years before mathematicians discovered their effectiveness at modeling natural phenomena, we are left wondering, “Why?”

Radulović takes on this assignment: provide examples of the “unreasonable effectiveness” of mathematics and pose insightful questions regarding this miracle. Throughout the book, the reader can expect forays into physics, set theory, geometry, and probability. We learn about the carefully balanced complexity of John Conway’s Game of Life, which serves as an example of the difficulty of building a self-contained and interesting universe. And axioms… there is much to say about axioms!

If you have wondered about the philosophical underpinnings of mathematics, this book is for you. It contains insightful queries for a mathematician to ponder and could definitely be the start of some enlightening conversations, perhaps in a departmental book club or seminar course. I found myself enjoying the many tangents (pun intended!) and digressions in this wonderfully unique and well-articulated book.