In the beginning of In Pursuit of the Unknown: 17 Equations that Changed the World, Ian Stewart claims that “you don’t need to be a rocket scientist to appreciate the poetry and beauty of a good, significant equation.” He subsequently dangles the provocative description “this is the story of the ascent of humanity, told through 17 equations.” What is a reader — regardless of whether that reader is a math phobe or a research mathematician — to do, but keep reading? After all, the math phobe has little to lose and the research mathematician has a tremendous amount to gain.
Does Stewart succeed with his bold claim? Absolutely! Stewart effortlessly strikes a conversational tone that makes accessible the content and context of some high level equations from mathematics, physics, information theory and finance. Maxwell’s equations on electricity and magnetism, for example, gave birth to radio, radar and wireless communication, which has since fueled an entertainment industry, enhanced military operations, helped doctors detect tumors, and helped archeologists locate ancient underground structures. The equation for the normal distribution has given society, for better or worse, a means to understand the “average” person. The Fourier transform has yielded insight into DNA and earthquakes. The Navier-Stokes equation gave us jet planes, quiet submarines, and medical advances concerning blood flow, while the wave equation has enabled us to find oil. Newton’s law of gravity birthed the Hubble telescope, the Mars rover, and GPS. The list of transformative events that have been fueled by equations goes on and on and on.
Stewart thinks highly of his reader. He neither dumbs down the math nor bombards the reader with highly specialized vocabulary or notation. To be sure, there are equations in this book — as the title acknowledges. But he includes pictures too, and lots and lots of prose.
The book is organized into seventeen chapters, each of which addresses the history, content and significance of a single equation. The first page of every chapter presents a graphic of the selected equation complete with arrows identifying the ingredients. Also included are brief answers to three questions, “what does the equation say?” “why is the equation important?” and “what did the equation lead to?” This reader-friendly introduction piques the reader’s interest in the topic as well as confidence in Stewart’s ability to get right to the point.
Once inside a chapter, the author does not hesitate to add a healthy dose of human-interest, telling us about the mathematical greats behind the equations. For example, rather than setting the scene for imaginary numbers with, “the variable i equals the square root of minus one…,” the reader is introduced to Cardano, the “gambling scholar,” whose “mother tried to abort him, his son was beheaded for killing his (the son’s) wife, … (who) gambled away the family fortune, … (and) was accused of heresy for casting the horoscope of Jesus.” In between, the reader is provided with a lay explanation of how imaginary numbers may explain airflow around airplane wings.
What is there in Stewart’s book for the experienced mathematician? In Pursuit of the Unknown offers a noteworthy example of how to write about mathematics for a wide audience. The book also offers a deep understanding of how equations have shaped modern civilization. Most mathematicians already know some of the facts and trivia that Stewart cites, but the incredible volume and breadth of Stewart’s book almost guarantee that even experienced mathematicians have something to learn.
In Pursuit of the Unknown could be a strong contender for a liberal arts math course, a course on the history of mathematics, or simply an enjoyable read on the beach. Stewart’s tone is inviting, his mathematical content substantial and his argument compelling. In the end, Stewart succeeds in breathing life into those immediately recognizable, but all too often little-understood, mathematical objects known as “equations.”
Susan D’Agostino is an Assistant Professor of Mathematics at Southern New Hampshire University. Her essays have appeared in The Chronicle of Higher Education, MAA Focus and Math Horizons. She is currently writing a math book for a general audience.