I LEARNED A LOT from Raphael Rosen’s *Math Geek*, not just about math, but about how those who like math are perceived and how to reach those who don’t much enjoy it. These are topics we need to consider as we figure out how to better educate Americans about science, and how to get more students and more diverse ones ready for careers in science and technology.

Rosen, who has worked at San Francisco’s hands-on Exploratorium science museum and writes about science for various outlets, has produced an unusual math book. For one thing, rather than written in chapters, the book features brief essays about math and its appearances in daily life, which makes it more suitable for dipping into than for sustained reading. For another, *Math Geek* may be the first math book ever to explicitly welcome “geeks” and “nerds.”

This made me wonder: those two terms are used a lot, but what do they really mean? Both can claim distinguished lineage: “geek” traces back to Shakespeare and Jack Kerouac, and “nerd” may come from an old Dr. Seuss story. They also share dark undertones, especially “geek,” which once meant a circus performer whose act consisted of biting off the head of a live chicken. Now, according to the Oxford English Dictionary, a geek is an “unsociable person obsessively devoted to a particular pursuit” and a nerd is “socially inept” and exclusively dedicated to “an unfashionable or highly technical interest.” Neither suggests bizarre circus acts but they carry similar less-than-complimentary connotations. (You can, of course, find plenty of online discussion about subtle differences between a “geek” and a “nerd.”)

Yet there’s also some underlying admiration for nerds and geeks in our society. Unsociable and obsessed they may be, but in today’s hi-tech world, they can be highly successful too. As one online commenter put it, “A nerd is the guy you made fun of in high school who you work for today.” I don’t know if anyone ever made fun of entrepreneurs like Bill Gates or Elon Musk when they were teens, but the dedicated focus of technology gurus like these has produced companies that employ lots of people and, besides that, are changing the world.

In addressing *Math Geek* to nerds and geeks, Rosen and his publisher are on to something meaningful that may also sell books. If so, is he preaching only to the already converted who pursue the “unfashionable” area of mathematics? Rosen’s answer would be “no,” because as his introduction makes clear, his intention is to reach a much larger audience. He wants to convince anyone who reads his book that mathematics is not “just a series of rote exercises performed in a classroom.” Instead, it is “built into the fabric of reality [and] is a living feature of the world we live in […] Math has a beauty that can stop you in your tracks.” Rosen’s hope is to turn non-nerds and would-be geeks into true appreciators of the mathematics in their lives — and maybe, who knows, that will encourage some of them toward careers in math or science.

Rosen’s goal raises another question the book inspired me to explore: how do you get math, or appreciation of its wonders, across to readers who are interested but lack the tools to really get into the subject? Math is expressed in a special, highly symbolic language that must be learned, starting with algebra. That may be one reason why “math anxiety” often gets between people and their engagement with math. It isn’t clear that this special kind of anxiety is a well-defined mental state, but anecdotal evidence suggests that some people feel a kind of mind freeze when confronted with a mix of numbers, letters like the dread algebraic unknown “*x*,” and exotic terms like “cosecant” and “differential calculus.”

As a result, math is harder to popularize than other categories of science. People are awestruck by the megaphysics of black holes and galaxies and the nanophysics of quantum mechanics and the Higgs boson; space exploration is always exciting; the natural wonders of our Earth, from volcanoes to exotic animals, elicit strong interest; and much of the science in biomedicine, like the current explosion in neuroscience, has the twin draw of illuminating our own nature and producing useful medical outcomes. But even though mathematics is a substrate and a framework for science, its abstractness and its special language make it hard to access and hard to link to the everyday world.

Still, mathematicians and science writers have done their best to popularize math. Looking at their efforts provides lessons in how to get math across, and shows how writing about scientific ideas has evolved in the digital age, as exemplified by *Math Geek*.

One early popular math book I tackled as a kid wanting to be a scientist will celebrate its 80th birthday next year. It is Lancelot Hogben’s* Mathematics for the Million: How to Master the Magic of Numbers*. In 1936, Hogben, a British zoologist and medical statistician, produced a classic that can still be found today as a paperback for sale on Amazon, where it continues to get admiring reader’s comments. Its blurbs on the back cover, old as they are, are hard to beat. One is from Albert Einstein, who says the book “makes alive the contents of the elements of mathematics”; the other is from H. G. Wells, who calls it a “great book.”

At over 650 pages, it is also a big book, and no wonder. It teaches math through the long history of the subject, from the first insights into numbers and arithmetic by ancient civilizations to the great 17th century developments of calculus and probability theory by Newton, Pascal, and others that underlie much modern mathematics. Well-illustrated with figures and equations, the book even has mathematical exercises, with answers supplied, so the reader can test his or her knowledge. By current standards, it is more a textbook than a popular work, though enlivened by Hogben’s discourses on mathematics and mathematicians through the centuries. Hogben himself understood his book as no easy read. His prologue exhorts the reader in capital letters, “WHAT YOU GET OUT OF THE BOOK DEPENDS ON YOUR CO-OPERATION IN THE SOCIAL BUSINESS OF LEARNING.” It is a “social” compact between reader and author to work hard to gain understanding.

This contrasts with a recent math book, Steven Strogatz’s *The Joy of x: A Guided Tour of Math, from One to Infinity* (2012). Strogatz, a working mathematician at Cornell University who specializes in applied mathematics, extended his series of popular columns about math for *The* *New York* *Times* into this book. Like *Mathematics for the Million*, *The Joy of x* begins with the basics of numbers and arithmetic, then follows an ascending arc to higher levels but not necessarily in chronological order. Rather its chapters appear under headings that give a flavor of the basic areas that math covers: Numbers, Relations (algebra and beyond), Shapes (geometry and mathematical proof), Change (calculus), Data (probability theory), and Frontiers (miscellaneous topics, from prime numbers to Moebius strips and infinity).

Rather than intersperse historical tidbits with mathematical explanations, Strogatz gives vivid examples of math in daily life, tied to today’s world and its pop culture. For instance, he writes “The best introduction to numbers I’ve ever seen […] appears in a *Sesame Street* video called *123 Count with* *Me*,” then uses the video to comment on some of the deeper philosophical meanings of numbers. Strogatz has a light and entertaining touch and his chapters, typically under 10 pages long, are easy to digest. This makes the book eminently readable in a way that *Mathematics for the Million* is not.

That is a plus for a popular book about mathematics. It did, however, make me wonder about the much-touted loss of concentration and inability to do “long reads,” supposedly engendered by our obsession with reading short online click-worthy pieces. Is this affecting how we all read and write now, and does writing about science and math need to change to accommodate this newer style of absorbing information?

This trend seems more pronounced in Rosen’s book than in Strogatz’s. *Math Geek *is similarly organized under major headings — Shapes, Behavior, Patterns, and Special Numbers — but instead of chapters, it has 100 short essays about mathematical topics. Typically a couple of pages long, the essays could work as a screen’s worth of reading if they were downloaded from the internet. Compared even to short, easily digestible chapters, these are bite-sized.

Their topics will be familiar to anyone with a math background, but Rosen makes them enticing to beginners by writing in a relaxed conversational style, assuming little math knowledge, and relating the math to pop culture and ordinary events. The essays have intriguing or provocative titles, such as, “Why are manhole covers round?” (because they can’t fall through their own openings); “Are you living in the fourth dimension?” about the mathematical oddities called Klein bottles and the shape of the Universe; “Your social media jealousy has mathematical roots,” about the result called the friendship paradox that explains why everyone else has more friends than you do; “What the subway map leaves out,” an introduction to topology; and “Did you inhale Caesar’s last breath?” a statistical analysis of the odds that air molecules that Julius Caesar exhaled when he died still linger in the atmosphere.

Consistent with his strategy of short pieces, Rosen has mostly picked topics in the theory of numbers, geometry, and so on that do not need long exposition. He does cover infinite series and the concept of infinity, but nowhere in the book do you see calculus or very many equations. Illustrations help, and also, to provide more heft, each essay names the mathematical concept that it covers and is followed by a short note that extends the concept or otherwise adds meat to the discussion.

Packaging mathematical ideas into short essays means that they cannot be covered in depth, and the connections among them do not jump out. What makes the book appealing to the casual reader might diminish its value for those inspired to dig deeper. One easy fix would be to add specific outside references to each essay in *Math Geek*. These could be discreetly tucked into the back of the book for those who want to delve further, without making it look like a scholarly rather than a popular work.

This does not mean, though, that I’m advocating for a tome like *Mathematics for the Million *as the only right way to popularize math. It’s a good thing to have a spectrum of approaches available. While some readers in the digital age respond best to short pieces, others gravitate to long detailed discussions. All will become more scientifically literate and some will go on to become scientists, when they will really have to grapple with dense and serious writing. But it doesn’t matter if they get there by first plowing through Hogben, or by feeling that “zing!” of passionate interest through reading one of Rosen’s essays — they will be on their way to becoming the best kind of geek or nerd, the kind that our society needs.

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