In 2012, a mathematician friend tipped off Kevin Hartnett, then a writer for *T**he **Boston Globe*, about a curious situation unfolding in the world of pure math research. The renowned mathematician Shinichi Mochizuki had released a series of papers claiming to prove one of the most famous problems in number theory. But the papers were over 500 pages long and were written in an impenetrable style. Mathematicians didn’t know what to do with them.

Hartnett wrote a story for *T**he **Globe*—one of the only pure math articles the paper has ever run, he says. Soon after, he heard from *Quanta Magazine*, an online popular-science publication that is committed to writing about math: Would he like to pitch them some stories?

Hartnett had stumbled upon an open secret among the small pool of journalists who write about math: Science editors are eager to cover more math. “There’s a huge hunger on the part of some editors, including me, for math stories,” says Clara Moskowitz, a senior editor at *Scientific American*. “But there just are not many journalists who seem to cover this field.”

Eric Hand, *Science*’s physical sciences editor, can’t remember having received more than a couple of pitches from journalists on pure math stories. “It’s been frustrating,” he says.

Compared to most STEM fields, mathematics receives scant coverage in the popular press. There’s no shortage of newsworthy topics, but they can be challenging to unearth, since mathematicians have built up little of the infrastructure other scientists have for disseminating their findings. And many journalists who fearlessly wade into complicated areas like climate change or astrophysics may shrink from covering pure mathematics with its reputation for arcane abstraction.

Yet writing about math isn’t that different from writing about any complex topic, says Siobhan Roberts, a Toronto-based journalist and a regular contributor to *The New York Times* who found her way into mathematics journalism even though math was her worst subject in high school. “You have to be willing to shamelessly ask questions,” she says. “But to some degree you can crack it open and tell a story.”

And math articles tend to be highly popular, say Moskowitz and *Quanta*’s editor-in-chief, Thomas Lin. Given the dearth of mathematics journalists, “I’m willing to take a chance on someone really trying to carve a role for themselves in this field,” Hand adds, even if they haven’t written about the subject before.

Hartnett realized after writing one or two math stories that the subject offered “an opening for me as a journalist.” And even though his background is in the humanities, he has found it “massively rewarding to wrestle these very complicated topics into something clear and understandable for a general audience,” he says.

## Finding Math Stories

Many of the standard approaches to generating science story ideas are ineffective when it comes to mathematics. The top journals never issue press releases on math breakthroughs, and the big mathematical societies and university press officers rarely do. Math papers are usually highly technical, making it difficult for lay readers to appreciate their significance or even what their main result says. And math research talks are notoriously hard for even mathematicians in other fields to follow.

If your goal is to write about research advances, Hartnett has found that “the best… and the only way” to find story ideas is to get mathematicians to share them with you. To some extent that can be done indirectly, by listening to what mathematicians say on Twitter and blogs. But Hartnett, who did a five-year stint as *Quanta*’s staff math writer and then editor, would routinely cold email mathematicians to ask if they could chat. Gradually, he built out a spreadsheet of more than 400 sources, and every week or two he would check in with a batch by email. Typically, he estimates, “30 percent respond, and two of those have ideas, [and] one of those works.”

But research breakthroughs are only some of the stories that can be told about mathematics. Roberts and Evelyn Lamb, a math writer in Salt Lake City, have both found story ideas at the annual Bridges conference, which focuses on the connections between math and art, music, architecture, and culture. Roberts also recommends the National Museum of Mathematics’ MOVES conference, MathFest, and the Gathering 4 Gardner, which she calls “an eclectic, circus-like conference” for lovers of recreational math.

Finding a math story can take effort; but once you’ve found it, you can usually feel confident that it’s yours alone.

One story often leads to another. After Roberts wrote for *The* *New Yorker* in 2016 about the debut of a 120-sided die at the Gathering 4 Gardner, she decided to keep an eye on one of the die’s creators, mathematician and mathematical artist Henry Segerman. This past January, she wrote for *The* *New York Times* about a three-dimensional sliding puzzle Segerman constructed to illustrate the geometric concept of holonomy.

Roberts says her limited formal mathematical training helps her recognize which stories will resonate with readers. “I use my own curiosity as a measure,” she says. “If there’s something that sparks my interest and imagination, then I think that there must be something there that a reader might enjoy.”

Sometimes, a result that’s not earth-shattering can still provide the jumping-off point for a deep mathematical dive. When Lamb spotted a tweet about how many Möbius strips fit in three-dimensional space, she seized the opportunity to write for *Quanta* about wild topological shapes and different types of infinity.

Lamb keeps on the lookout for math angles in current events. “When COVID started, there were suddenly some needs for explainers about exponential growth,” she recalls. From climate modeling to Bitcoin to the neural networks behind the latest chatbots, there is plenty of mathematics underlying today’s news.

Dilip D’Souza, a journalist in Mumbai who writes a weekly mathematics column for *Mint*, an Indian financial daily newspaper, generates story ideas by looking not just to daily news but also to archaeology, history, astronomy, and a host of other subjects. “There’s interesting things you can write about in math in every different subject,” he says. Mathematics “is like an ocean,” he says. “There’s endless stuff to write about.” Any time he spots a mathematical element to something he’s reading, he adds it to a file of potential story ideas, which he revisits periodically to see which stories are ripe for a column.

Finding a math story can take effort; but once you’ve found it, you can usually feel confident that it’s yours alone. Because so few journalists cover math, you are unlikely to get scooped (with the exception, perhaps, of especially topical stories). That means you can take all the time you need to understand the math.

## Reporting the Story

Since math papers and lectures are often indecipherable, in-depth interviews are essentially the only efficient way for a journalist to gain a thorough understanding of the material. Happily, I’ve found that mathematicians (most of whom have never talked to a journalist before) are extremely generous with their time. And when Hartnett was starting out as a math journalist, he was pleasantly surprised at their expository skill.

“[There’s] this stereotype of mathematicians as unable to talk to a general audience,” he says. Instead, he’s found, “mathematicians are many of the clearest thinkers and, in some ways, the most empathetic explainers of difficult material I’ve ever encountered.”

While most mathematicians you’ll interview for a story will come from the handful of experts in that subfield, it’s worth remembering the mathematicians who are especially good at letting you see into their thought process, Lamb says. “A lot of it is finding the mathematicians that you might go back to again and again.”

Even the most abstruse mathematics will have roots in something more familiar that you can use as a starting point.

But even given great expositors, every new story has a steep learning curve. For Hartnett, “the first, maybe, 20 articles felt every time like I was preparing to climb this really difficult mountain,” he says. Learning math is a highly non-linear process: Your first few interviews may seem like gibberish, but then your brain turns things over, and in the next interview a mathematician says something that makes everything fall into place. Math reporting requires a tolerance for feeling lost or even stupid, and the faith that things will eventually come together.

Hartnett tried at first to conceal his limited understanding from sources. But he gradually realized that this false front hindered his reporting. Nowadays, he says, “because I feel more confident about myself as a math journalist, I’m more willing to, in a sense, play dumb.” He tells mathematicians to imagine they’re talking to someone who hasn’t taken math since high school and didn’t like it then.

Even the most abstruse mathematics will have roots in something more familiar that you can use as a starting point. For example, when I was writing about a breakthrough in packing together spheres in 8- and 24-dimensional space, I thought about how spheres can pack together in ordinary space, and then got my sources to explain which of my intuitions carried over to higher dimensions and which didn’t.

I was determined to understand what made dimensions 8 and 24 special. So I asked that question in a bunch of interviews, and started building up a cloud of ideas; but I hadn’t found one that quite clicked. Then a mathematician told me that the configuration in a stack of oranges at the grocery store has an analogue in each dimension, and as you increase the dimension, the gaps between oranges grow in size. When you hit dimension 8, those gaps are suddenly exactly large enough to let you squeeze in extra oranges. *Aha!*

Continuing to ask questions until you’ve experienced a few such moments of illumination is valuable on two levels. First, it can signal that you’re reaching a deep enough understanding to start writing. And second, it gives you a small taste of the joy of being a mathematician. If you can pass on these “aha” moments to readers, they’ll light up with mathematical joy too.

## Writing the Story

As with all journalism, strong math articles are built on storytelling. Look for sources of tension, Lin recommends, to drive your narrative forward. Why was this problem hard to solve? Why do mathematicians care about it? What drew these particular mathematicians to work on it, and what challenges did they face along the way?

Many people find the life of a mathematician mysterious, though they can envision the daily work of a biologist or chemist. I’ve found that readers are fascinated by the human side of mathematics and excited to discover that the “solitary genius” is just a stereotype. Some of my most popular stories have had a strong human element, whether it’s the child prodigy who struggled with imposter syndrome in graduate school or the grad student who assigned herself a knot theory problem as homework and was unprepared for how thrilled mathematicians were when she solved it.

Look for ways to let your subjects live and breathe on the page. Do they have a favorite park bench where they think about math, or did they come up with a brilliant idea in the shower? What kinds of mathematics do they find beautiful?

So look for ways to let your subjects live and breathe on the page. Do they have a favorite park bench where they think about math, or did they come up with a brilliant idea in the shower? What kinds of mathematics do they find beautiful? How do the participants in a collaboration complement each other (or clash)?

While these details can enliven your story and sometimes even provide its connective tissue, in many stories your main characters will be the mathematical objects themselves. Don’t be afraid to give them their due. Hartnett has found that his most substantive stories are often the most widely read ones. “Talk up to your audience, respect them, and then by and large you will be rewarded,” he says.

It’s essential to create a story arc for these mathematical characters (and their applications, if you’re writing an applied math story). As an editor, Hartnett often found that new freelancers tried to explain too many concepts without connecting the dots. Instead, a writer should decide on two or three core concepts they want readers to walk away with, he says. “Build the story around those.”

For instance, after reporting my story on 8- and 24-dimensional sphere packings, I decided that the story had two key pieces. One was about the notion of higher-dimensional spheres, and the special sphere packings in dimensions 8 and 24. The other one was the narrative of the research leading to Maryna Viazovska’s discovery of a “magic” sphere-packing function for dimension 8 (and soon after, one for dimension 24). Identifying these two central story elements helped me figure out which mathematical details were essential to include, and provided a clear narrative structure.

Hartnett and Moskowitz have both found that sometimes writers lean on quotes to do too much explanatory heavy lifting. “There’s definitely this tendency to despair of your own ability to explain a concept, and so then just have a three-sentence quote from a source that’s fairly technical and detailed,” Hartnett says. “Don’t bail out and have quotes do the explanatory work that you really need to do yourself.”

A good editor can help a math writer figure out when they haven’t synthesized the story enough. When Roberts’s drafts lapsed into technical detail or were overly earnest, her *New York Times *editor, Alan Burdick, would tell her, “less Austria, more Italy” (a phrase he got from his own editor at *The* *New Yorker*, David Remnick). In other words, “don’t get too caught up in the particulars,” Roberts says. ”Don’t lose sight of the joy and the pleasure.”

Balancing these competing demands can at times feel overwhelming. Roberts sometimes asks herself why she subjects herself to writing about such complex and challenging material. She takes solace in something mathematician Peter Sarnak told her: “The steady state of a mathematician is frustration.”

“In a way, in engaging in the process of writing about mathematics, I’ve come to think that, vicariously, I’m experiencing the process of doing mathematics,” Roberts says. “Math is hard, and life is hard…. I comfort myself with that when it seems impossible.”

Erica Klarreich has been writing about mathematics for more than 20 years. Her work has appeared in *Quanta*, *Nature*, *The Atlantic*, *New Scientist*, *Science News*, and many other publications, and has been reprinted in the 2010, 2011, 2016, and 2020 volumes of *The Best Writing on Mathematics*. She has a graduate certificate in science communication from the University of California, Santa Cruz, and a PhD in mathematics from Stony Brook University. In 2021, she received the Joint Policy Board on Mathematics Communications Award. Follow her on Twitter @EricaKlarreich.