Giving a math talk
Here are Henry's tips for giving a math talk.
- The majority of your talk should be understandable by the majority of the audience!
- Figures are perhaps the best way (or perhaps the only way?) to allow even the non-expert audience members to get an intuitive understanding of your main points.
- It is possible to speak to both the expert and non-expert audience members at the same time; this takes practice.
- For a board talk, my classic mistake is to not plan ahead-of-time how to trim the text down far enough, meaning I run out of time during the talk. Spoken words are easy to add in spontaneously, but I must plan and trim my written words (and notation) very carefully.
- For a slide talk, my classic mistake is to include too much material in the form of text. The amount of text in a slide talk should not be more than the amount of text that can fit in a board talk. Slide talks can often allow for many more figures, however.
- For a slide talk, I like to use a metal extendable pointer to point at my slides (instead of a laser pointer) whenever possible. I think the metal extendable pointers are much easier to see, and they allow me to add physical emphasis to the point I am trying to illustrate.
- I also like giving "combo" talks where I use slides, but also write on the board a fair bit (if the room accommodates this).
- Don't say things like "I don't think my results are good" or "My talk was bad" or "My figures are bad" publicly while giving your talk, or during the question period after your talk. One (of several) reasons why not is that there may be more junior mathematicians in the audience than you, who look up to you. You don't want to unintentionally give them the impression that you are saying "I don't think my results are good and therefore there's no way I would think your results are good", even though this is definitely not what you intended to say! It is fair to say things like "I'd like to improve this result in the future by ..." or "I'd like to improve this figure by ...". Of course, it is important to be able to express doubts with friends and advisors after the talk and the question period are over.
- Don't go over time. Instead, plan ahead how you will succinctly give a 2-minute overview of your last main point, probably without introducing any new notation or definitions, which you can automatically resort to if you realize that you're running out of time and have only 2 minutes left.