In many fields of science and engineering, any technical argument must be formulated mathematically if it is to be taken seriously. In contrast, in popular writing--even about science and engineering--including a single equation is a known recipe for getting many readers to click on to the next story. Understanding this discordant reaction to math reveals a lot about how popular and technical writing differ.
Back in 2003, when I was thinking about morphing from a practicing scientist into a science writer, I seriously questioned how I could possible to explain scientific arguments without variables and equations. Without the precision of a mathematical description, I wondered, how could I really know whether readers interpreted ordinary English phrases the way I intended? Moreover, without a algebraic description, how could readers judge how well a model matches observations?
Interestingly, in the years since, I've almost never felt hobbled by not being able to explain things with equations.
A lot of the difference arises from the different goals of journal articles and popular stories, and their very different sources of authority.
In a journal article, the goal is to convince other experts. In other words, the article should ideally be self contained, assembling all the relevant details so that an independent observer can make up their own mind.
In contrast, a popular science story aims merely to describe the conclusions, not prove them. As David Ehrenstein, the editor at Physical Review Focus, once told me, the goal is to present a plausibility argument for the conclusions: to give enough context and explanation that readers can appreciate what's being claimed and who's claiming it.
The last point is also critical: by and large, popular writing gains its authority from the quoted judgments of experts, not directly from the model or observations. Indirectly, of course, this authority comes from the reputation of the writer and the publication (that is, the editors), because they are the ones who decide which commentators are worth quoting. (Of course, those commentators must also respond to emails or phone calls!)
Since the goal is plausibility and a qualitative understanding, the limited precision of ordinary writing is usually good enough to convey the message.