(…or a good talk of any kind.)

I recently read an excellent article called Giving Good Talks, by Satyan L. Devadoss, in the Notices of the AMS. The timing of the article was good, because just last week I gave an invited research talk at the University of South Carolina. I was able to use the advice given to improve my talk beforehand. The Devadoss makes many good points, and I recommend reading the article. Here, I’ll just list my take-aways.

• Tell a story. Do not deviate from that story, even if the deviation seems interesting to you. Stay focused! Your audience needs to be able to follow along without too much jumping around.
• Do the work for your audience. Distill major points down to their essence, so that they are clear and memorable. It’s okay to ignore subtleties and exceptional cases. Use intuition and images over precise definitions and explanations.
  • A note here: it is very tempting when creating a slideshow based on a research paper to cut-and-paste from the paper into the slides. Do not do this. Language that is appropriate for a paper is often too verbose for a slideshow. Your audience can’t go back and re-read definitions or mull over the statement of a theorem, so it needs to be presented simply and memorably the first time.
• Use your lecture slides wisely. Just because you can cram more info onto a slide, or run through many slides quickly, doesn’t mean you should. Less is more here (and pretty much everywhere else).
• The most important one: Speak slowly and end on time. If you’re running behind, do not just talk faster. Rather, leave out some stuff (in fact, decide beforehand what can be left out). Do no go over your time. DO NOT GO OVER YOUR TIME.

Most of these lessons apply to giving any type of talk, not just a math talk. Also, they apply when lecturing to a class. When I teach, I try to connect the lesson to what we’ve learned already and what we ultimately want to learn, so the lessons build a kind of story. I first present intuitive explanations and pictures (often through an example) before giving technical definitions and theorems. And of course, I try to speak and write slowly, remembering that my students are hearing this information for the first time and need time to process it.