Nine Years of Blogging About Math

[This month’s post is a transcript of a talk I gave on March 13, 2024, as part of a UMass Lowell “Conversation Starter” event on the topic of scientific literacy and communication. I was addressing other members of the Kennedy College of Sciences, so I treated mathematics as a subfield of the sciences, though I feel that math is an art as well as a science.]

Quick: What 19th century mathematician is this?

If a journalist had buttonholed the nineteenth-century pure mathematician shown above and asked him what his revolutionary ideas about geometry were good for, and if the mathematician had answered “Someday people will use my ideas to figure out exactly where they are, not by looking up at the stars but by looking down at little boxes they carry around in their pockets,” the mathematician’s colleagues would have been justifiably outraged by such unscientific sensationalism.

No points awarded for recognizing this guy.

There was no way Bernhard Riemann or anyone else in 1854 could have known, guessed, or dreamed that his new kind of geometry would give someone named Albert Einstein the mathematical language he needed in order to express his theory of general relativity, which now is a key part of the geopositioning technology embedded in your smartphone, a century and a half later.

An image from my Mathematical Enchantments essay “Numbers Far Afield”

A lot of basic scientific advances have this kind of delayed payoff. By the time they transform the world in ways that a general reader can recognize, the breakthroughs aren’t news anymore, so journalists have little reason to write about them. But neither have the breakthroughs become part of what gets taught in high school science courses. So these stories fall between the cracks and don’t get told to enough people outside the scientific community.

An image from my Mathematical Enchantments essay “The Man Who Knew Infinity: What the Film Will Teach You (and What It Won’t)”

That’s why there’s a need for scientists to tell these stories, about what happened not last week but in the past century or two. Our great advantage over journalists (aside from the fact that we know the science really well) is that we don’t face press deadlines; we have time to get our facts right, and to situate discoveries in a broad human context.

The logo for my Mathematical Enchantments blog. To find out what the logo means, check out my essays “Between the World and the Mind” and “Chess with the Devil”

This is the kind of writing I’ve been trying to do in my Mathematical Enchantments blog over the past nine years. I write an essay each month, usually around 5000 words long, and post it on my WordPress site. A typical essay of mine gets read by hundreds of people, but only sometimes a thousand. Having that small a readership means I’m not having as much impact as I’d hoped. Still, I’ve developed some opinions about this kind of writing, which I’ll share with you in the form of advice.

An image from my Mathematical Enchantments essay “Will ’17 be the Year of the Pig?”

#1. Don’t be ashamed to grab people’s attention through the use of suspense. I did it in the opening sentence of my talk, when I showed you a picture of a mathematician but didn’t tell you right away who he was. The best advice on writing I’ve ever seen is this: In your opening sentence, raise a question in your reader’s mind. Before you answer it, raise one or two more questions. Keep doing that. At each moment, there should be at least one unresolved question to keep the reader hooked till the end.

#2. Lean on honest friends. I mean the kind who are willing to tell you when a piece of writing falls short of what you were aiming for. Honest colleagues can sometimes do this too, but they usually know too much. Friends are better proxies for actual readers, except that when a friend comes to a passage they don’t understand, they’ll mark it as difficult and move on to another paragraph; an actual reader will move on to another writer.

#3. Know your audience. Thanks to WordPress analytics, I’ve learned that some of my most successful essays have gotten publicized on Hacker News and Y Combinator. If you write an essay on a scientific topic, consider publicizing it there.

#4. Don’t be ashamed to grab people’s attention through the use of clickbait-y titles. Some of my most successful essays have had titles like “The Clatter of the Primes” or “Twisty Numbers for a Screwy Universe” or “Marvelous Arithmetics of Distance” — titles that make a reader wonder what kind of article would have that for a title. If you abuse this one cool trick for getting people to read your writing, eventually they’ll catch on and stop trusting you, so don’t do it gratuitously.

#5. Keep your eyes open for things you can use. I picked up the phrase “Marvelous Arithmetics of Distance” from a poster in a New York City subway car (it’s from a poem by Audre Lorde) and I jotted it down for future use.

#6. Be yourself and use your personal history. I’ve written pieces featuring myself, my wife, my parents, my kids, and my favorite teachers. Readers like to see links between our private lives and the work we do. This kind of anecdotal material, when it has connections with what we’re writing about and how we feel about what we’re writing about, isn’t just filler; it can add a human dimension to an abstract topic.

#7. Collaborate. I haven’t collaborated enough, but I’ve really enjoyed working with mathematical writer and cartoonist Ben Orlin.

A Ben Orlin cartoon, from my Mathematical Enchantments essay “The Null Salad”

One advantage of blogging is its complete freedom; you can explore a range of topics and styles, find a conversational voice of your own to use for discussing scientific topics, and take your time doing it. Learning to write like an academic took you years; un-learning some of those habits so that you can express ideas colloquially takes time too!

A disadvantage of blogging is the relative lack of feedback. WordPress allows readers to leave comments, but not enough readers do it. If you really want to have an impact on public understanding of science, you probably shouldn’t limit yourself to blogging as I’ve done, certainly not for nine years; you should try your hand at writing for publication, in outlets like Scientific American or Quanta Magazine. If you’re lucky, experienced and generous editors will help you improve. I’ve published abridged versions of some of my essays in a magazine called Math Horizons (for math enthusiasts at many levels), which is sort of a form of outreach. And unlike blog essays, they count as publications.

An issue of Math Horizons, which published an abridged version of my Mathematical Enchantments essay “Tricks of the Trade”

You could also bypass the written word entirely and make videos. Well-made science explainers get viewed by millions. Some stories are very well suited to animation. Check out Grant Sanderson’s YouTube channel “3Blue1Brown” and Derek Muller’s channel “Veritasium” for starters.

I haven’t made many videos, and my YouTube channel “Barefoot Math” is self-consciously low-tech. But in my blog I do sometimes find it helpful to make images. Most of the ones I’ve shown you were created with Mathematica or Omnigraffle, although a few were taken from the Web. If any of them have whetted your appetite, check out my blog!

An image I snagged from the web and discussed in my Mathematical Enchantments essay “How Can Math Be Wrong?”

I’ll mention two other forms of outreach I’ve engaged in. One of them is X, formerly known as Twitter. My most successful tweet was this one, reporting something my daughter said:

My other outlet for popular science communication has been the Festival of Bad Ad Hoc Hypotheses, or BAHFest, which was held quasi-yearly at MIT until the pandemic struck. It’s a celebration of deliberately bad science, but like all satire it has a serious side: by highlighting some of the shoddy forms of argument that can be used to bolster a dubious hypothesis, BAHFest can make us more alert to scientific bogosity in the real world. In my first BAHFest talk, I argued that what killed the dinosaurs was a brief reversal of Earth’s gravitational field.

In a similar satirical vein, I created a parody of creation science arguing that pi is 3.

My opening slides focussed on applications of math and basic science. That’s a hook that works for many readers, and it’s vitally important for the people who vote to fund science (or not to) to know that the payoffs for basic research, though far off in the future, can be huge.

An image from my Mathematical Enchantments essay “Here There Be Dragons”

But: I’m also writing for people like me who love math for its own sake but who for various reasons didn’t pursue that love professionally. One of my college friends who became a physician used to seek me out at reunions not just so we could catch up on each other’s lives but also so that I could explain to him cool bits of math he’d heard rumors about. Like me, he was exposed to the writings of Scientific American columnist Martin Gardner when he was young, and once you’re hooked on recreational math it tends to be a lifelong addiction.

A photo of Martin Gardner, whose writings inspired me to embark on this 30-year project of writing about mathematics for non-mathematicians.

If I’m honest with myself, people like my doctor friend constitute my core target audience. But over the course of years of blogging, I’ve dipped into applications of math and also into mathematical history, and to my surprise I’m finding them nearly as interesting as the math itself. So blogging can also be part of an academic’s continuing education.

Thanks for listening, and I’ll take questions now.