A roundup of advice for writing about mathematics

April is Mathematics and Statistics Awareness Month, a time for increasing the understanding and appreciation of those fields. One way to communicate the joy and importance of math and stats? Through our writing.

Just last month, the Early Career Section of the Notices of the AMS published several articles on the theme of writing, including “Outward-Facing Mathematics: A Pitch” by Jordan Ellenberg, “To Write or Not to Write… a Book, and When?” by Joseph H. Silverman, “Preparing Your Results for Publication” by Julia Hartmann, “The Art of Writing Introductions” by John Etnyre and “Writing, and Reading, Referee Reports” by Arend Bayer.

“There’s really only one form of outward-facing math I personally know well: writing about math for general-audience publications, which I’ve been doing for more than twenty years now. And I meet a lot of graduate students and early-career mathematicians who are interested in doing it too. So let me tell you some of the lessons I’ve learned,” wrote Ellenberg. He gave this advice on getting started:

“Social media drives attention, but no one has yet figured out a great way to tweet or Snap about math. That’s why blogging is still alive for mathematicians, even as blogs have withered somewhat on the whole. I think best practice for getting started is to blog on a platform like Medium or WordPress, then use social media to bring readers to your writing. When you want to pitch a piece to a more formal publication, they’ll want to see what your writing looks like: with the blog, you’ll have something to show them.”

Etnyre’s piece focuses on writing introductions to mathematics research papers, but much of his advice is relevant for anyone who wishes to write well about mathematics.

“A common problem writers have, especially early in their career, is to overestimate what everyone will know about their work and how it fits into the research world,” Etnyre wrote. (I think this common problem often also occurs when mathematicians write about mathematics outside of the realm of their own research.) He added this advice:

“Assuming that everyone will understand the context of your work, and why it is really interesting, is not a good idea. Most work is focused on some part of a bigger program or problem, and even experts in a field might not, in any given moment, recall the subtleties and details to every interesting problem in their field. So tell them, and all the other readers who will have no chance of appreciating the context without some help from you. Explain the big picture.”

Hartmann’s piece is also intended for folks who are writing research papers but contains advice that’s useful for anyone considering writing about mathematics.

“Decide what the story is you’d like to tell. There is usually more than one way to present a result and the work that leads to it…Talk about your work to other people. Consider giving a talk at your home institution. This will force you to come up with a way to “pitch” your story. You might also receive helpful feedback on your results and comments on connections to other existing work. During the process of writing, you may find that your conception of the story has changed, and this may change the idea of how to best present it,” she wrote.

The “On writing” section for Terence Tao’s blog includes links to many pieces (written by him and others). Many of these are geared toward people who are writing research papers, but some of this advice could be helpful to folks who want their mathematics writing to take the form of blog posts, news articles and more.

Francis Su’s 2015 MAA Focus piece “Some Guidelines for Good Mathematical Writing” shares both basics and advice “toward elegance.” While the piece is written at a level that’s accessible to students, it also contains gems that will serve even experienced math writers. For instance, he advises that writers “Decide what’s important to say. Writing well does not necessarily mean writing more” and “Observe the culture. Good communication is inseparable from the culture in which it takes place.”

In “Mathematics for Human Flourishing,” Su discussed the importance of valuing public writing about mathematics:

“I would like to encourage institutions to start valuing the public writing of its faculty.  More people will read these pieces than will ever read any of our research papers.  Public writing is scholarly activity: it involves rigorous arguments, is subject to review process by editors, and to borrow the NSF phrase, it has broader impacts, and that impact can be measured in the digital age,” he noted.