To communicate successfully, it’s necessary to consider the audience’s knowledge and interests and the communicator’s relationship to the audience. These determine how much motivation to give, how much detail to include, how much content to try to convey, and even what to choose as the main point of the communication (this list is by no means exhaustive!). Without a conscious awareness of these effects, students may inappropriately try to apply strategies successful in one situation (e.g., math problem sets) to all situations. So students can benefit from some guidance about how to communicate mathematics to a variety of audiences. Communicating to a nontechnical audience can be particularly challenging.
Teaching students to target math writing to the audience
Math writers talk about writing math for the public:
 Blogging about math for the New York Times, a presentation by Steven Strogatz
In this presentation, Steven Strogatz discusses the authorial decisions he made when writing a math column for the general audience of the New York Times.  “How to Get Into the Newspapers,” from the blog Devlin’s Angle, by Keith Devlin
Eleven tips written for university mathematicians about how to get a mathematics story into the local newspaper.  “OutwardFacing Mathematics: A Pitch” by Jordan Ellenberg, from the Early Career Section of Notices of the American Mathematical Society, March 2019
 “Communicating Mathematics to a Broader Audience.” This AMS blog post by Vanessa RiveraQuinones provides advice on communicating mathematics to an outside audience.
Assignments To help students to understand the importance of tailoring communication to the audience and context, students can analyze math writing from a variety of contexts and genres and can be asked to explain the same mathematical concept to different audiences.
Examples:
 A recitation and writing assignment about audience awareness from M.I.T.’s communicationintensive offering of Real Analysis
 In M.I.T.’s Principles of Discrete Applied Mathematics, Recitation 7 focuses on rhetorical analysis of communication situations and writing to a nontechnical audience. The prerecitation assignment asks students to read some news articles about mathematics and analyze the genre and context for news articles. During recitation, these are contrasted with the genre and rhetorical context for math journal articles. For the assignment, students write a news article about the solution of Kepler’s Conjecture by Tom Hales. Concurrently, they work on a longer assignment in the journal article genre.
Courses and Workshops
At East Tennessee State University, Ivars Peterson taught a course about Communicating Mathematics [to the public]. The course website includes assignments as well as lists of websites and books about mathematical topics for the public.
The following AMS Early Career Notice by Jordan Ellenberg discusses running a writing workshop for generalaudience mathematical writing.
Examples of math communication for a general audience
A wealth of math communication is available for a general audience. A few examples are below:
 Vi Hart’s math doodling videos
 Steven Strogatz on Elements of Math (New York Times column)
 Devlin’s Angle, by Keith Devlin (blog)
 The Math Guy sound archive (Keith Devlin on NPR’s Weekend Edition)
 The Math Factor Podcasts
“University of Arkansas Mathematics Professor Chaim GoodmanStrauss and KUAF 91.3 FM Radio Journalist Kyle Kellams have been mathematically entertaining children all over the world for nearly forty years.”  Logicomix: An epic search for truth, a graphic novel by Apostolos Doxiadis and Christos H. Papadimitriou, art by Alecos Papadatos, color by Annie di Donna, Bloomsbury, 2009, New York Times book review, by Jim Holt, Sept 27, 2009
 The Best Writing on Mathematics, By Mircea Pitici (book published annually by Princeton University Press)
 The JPBM Communications Award
This award is for communicators who, on a sustained basis, bring mathematical ideas and information to nonmathematical audiences. The website includes a list of recipients.  Albert Leon Whiteman Memorial Prize
This prize “recognizes notable exposition and exceptional scholarship in the history of mathematics.” The website includes a list of recipients.  Here is a list of some popular books about mathematics written for the general public from East Tennessee State University’s MATH 4827 Communicating Mathematics.
 Here is a list of some websites about mathematics for the general public from East Tennessee State University’s MATH 4827 Communicating Mathematics..
 Tova Brown’s Hotel Infinity presents Hilbert’s hotel paradox in a series of short videos that engagingly present the concepts of countable and uncountable infinity.

“The Mysterious Disappearance of a Revolutionary Mathematician” b Rivka Galchen, the New Yorker Magazine, May 16, 2022.
“Alexander Grothendieck was revered for revealing connections between seemingly unrelated realms. Then he dropped out of society.” This article illustrates effective strategies for communicating mathematics to the public: e.g., using metaphor to convey mathematical ideas, and captivating the reader by starting with a hook, telling a story, and using quotations.
General resources about audience awareness (not specific to math)
 Correcting misconceptions and convincing others to change firmly held incorrect beliefs can be notoriously difficult. In the May 16, 2014 New Yorker article “I Don’t Want to Be Right,” Maria Konnikova summarizes some recent research into how false beliefs are affected by conception of self and how selfaffirmation enables more accurate understanding. These results suggest that convincing a reluctant audience may require affirming the audience rather than simply presenting facts.