How we communicate mathematics is an essential part of making mathematics accessible. You’ve probably experienced communicating with peers and faculty in your area of specialization, taught a few math courses, or even been involved in outreach activities with younger students. All these types of audiences shape how we communicate mathematical ideas and require different types of skills. While I consider all of them an important part of our growth as mathematicians, there is still one more type of audience I want you to consider, the general audience.

Last summer, I had the amazing opportunity to participate in the Mathematical Association of America (MAA) MathFest. Each summer at MathFest one of the largest communities of mathematicians, students, and enthusiasts comes together to talk about the latest advances in mathematical research and education. One of my most memorable experiences was participating in the session Great Talks for a General Audience: Coached Presentations by Graduate Students. Here graduate students get coached by more experienced communicators on how to make their research accessible to a general audience, give a 20 minute presentation, and receive individual feedback by an undergraduate student and faculty member. Here I want to highlight some of the insight I gained through this experience.

Ask yourself, who is your audience? Are they kids, young adults, non-mathematicians, scientist, non-scientist, a combination? When addressing an audience you may not know its exact composition. I’ve always thought the best thing to do what to teach my audience my work. Make it accessible by treating it as a student-teacher interaction. However, in the limited time available may be impossible to achieve! Instead, advertise your work. Talk about what drew you to your problem, what are the big ideas, why do you find it interesting?

Less is more. For anyone who has met me, they know when I am excited about an idea I tend to ramble. I used to think my presentations needed to stand on their own. Every detail I thought was important should be precisely stated in writing. Truth be told, audiences have a limited attention span and a presentation is a tool to highlight ideas. Your use of slides or board space is what brings your talk to life! Make it your story.

Avoid jargon. When you spend a lot of time talking to specialist in your field, it is hard to imagine changing how you talk about your work. However, using layman language is necessary to make your ideas engaging outside of your field. You can use a picture to build ideas. Be generous with using more simple examples that motivate your result. I am sure at many stages of your academic moment you’ve experience that ‘A-ha!’ moment. Give that gift you your audience.

If you’ve found yourself eager to learn more about communicating mathematics, I encourage you to apply to MathFest (deadline April 30) this summer! Below are additional resources: