Mapmatics: A Mathematician’s Guide To Navigating The World

by Paulina Rowinska

The Belknap Press of Harvard University Press, 2024

The boom in popular science books has been going strong for decades now. The mathematics of maps is the latest topic to be mined from dusty textbooks for our entertainment. Mapmatics: A Mathematician’s Guide To Navigating The World is the last in the long line of the publishing world’s attempts to make everyone’s dreaded subject approachable. The mathematician of the subtitle is Paulina Rowinska, an aspiring science communicator with a PhD in mathematics and statistics from Imperial College London, whose “2017 Tedx talk ‘Let’s Have A Math Party!’ explained that math is all around us.” This is her first book.

A map, according to the Merriam-Webster dictionary, is “a representation usually on a flat surface of the whole or a part of an area”, also “a diagram or other visual representation that shows the relative position of the parts of something”. The word representation conceals the actual defining characteristic of a map, which is simplification or reduction. Mathematics, to which one plus one equals two whether that’s grains of sand or galaxies, is the supreme art of reduction and a natural tool for the map maker. “Maps”, says Rowinska, “have been fueled by mathematics and have also inspired numerous mathematical breakthroughs. Once we notice this connection between mathematics and cartography, we won’t be able to unsee it, and it will help us to understand how our world works.”

Mapmatics is written in the form of an episodic history, recounting said cartographical and mathematical breakthroughs. Embarking from the familiar sites of Christopher Columbus’ lucky blunder and the flaws of projecting our 3D globe onto a 2D map, we are guided through the mathematics of infinitely long shorelines, gerrymandering, troublesome Prussian bridges, searching for plane wreckage over the Atlantic and discovering the Earth’s structure. We learn about the vast mathematical subject underpinning the map of the London Underground as well as the injustices that result from the drawing of school district borders in the United States. Math symbols are kept to a minimum and relegated to the footnotes, along with similarly harmless things like references to the movie Shrek.

Rowinska’s tone is conversational and current. She often writes in the enthusiastic first person and at times, when writing about her personal experience, the historical style lapses into the journalistic. The focus throughout remains on the people behind the stories, but Rowinska competently blends the explanations of the science with her narratives. Conventionally enough for a science book, discovery against the status quo is the tentative theme drawing the narratives together. Another theme is that of the power of maps and the dangers that lie in their irresponsible use. It is set up in the introduction:

Maps represent reality, but we can take full advantage of these visual aids only when we understand the underlying math. Otherwise, we’re prone to draw wrong conclusions and inherit the mapmaker’s biases, whether intentional or not.

The needle is threaded with sentences like “Maps and math, together, save lives,” and “That’s the power of maps.” These are the instances where Rowinska’s unimaginative and student-like prose stumbles onto its peaks of awkwardness. The problem with humdrum prose is that it defeats the popular science writer’s purpose. If, as is almost always the case, the popular science writer does not come up with the science they’re explaining, what is their contribution other than to express the ideas in a simple and elegant, if not new and gripping, way? Some of Rowinska’s explanations are so commonplace and blandly communicated that we, at times, wonder why she doesn’t just refer the reader to a Wikipedia page and be done with it. If, for example, you’ve ever heard anything about graph theory or the Remarkable Theorem of Gauss, then you’ve already heard Rowinska’s explanations, and without having been spoken to like a child in the process. Rowinska is also guilty of having “impact” be her favorite verb, starting too many sentences with “but”, and the extensive use of cliché (“no hard and fast rule”, “game-changer”, “the truth lies somewhere in the middle”, etc.). Her bio informs us that she’s just joined the Graduate Program in Science Writing at MIT.

Just as maps are simplified representations of real space, so are popular science books of real science. Many of these books serve the same useful purpose as a child’s first atlas, if only the same care and art was put into them.

Mapmatics is a friendly and accessible introduction to the science that draws how we view our world.

Nikolas Mavreas is a reader living in Athens, Greece.