1. What’s going on mathematically?
Often I have to give a talk about my research, or a survey talk about relatively advanced mathematics. This post is not about giving the talk, but preparing it.
2. What is the emotional and logistical context?
Before starting to prep, there’s always some degree of nervousness and anticipation, depending on how important the talk is and how comfortable I am with the material.
I’ve experimented with a wide range of logistical contexts for prepping talks. This is one experience for which the math culture permits a significant amount of flexibility and alchemy. Among mathematicians, “He/She has to prepare for a conference talk next week” translates to “he/she is going to be acting a little strange; give him/her some extra space.” I’ve tried locking myself away until it’s done, or prepping during a long hike without writing anything down, or sitting in front of a waterfall and practicing my words for hours. There isn’t much common context.
3. What thoughts are there?
The goal is to develop a human connection to the content of the talk, in order to figure out how to communicate the content so it can be best understood by the range of people in the audience. There is usually some learning and relearning of material, piece by piece. But the biggest challenge is in reorganizing the ideas into a story that is linear enough to flow as a narrative, but nonlinear enough to convey the robust intuitive interconnections. The second-biggest challenge is aiming for your audience – including the right balance of detail and metaphor, rigor and exposition.
A good starting point is immersion in the subject – getting comfortable with all the important ideas, the different perspectives on those ideas, the history of the ideas. I recently spent 15 hours preparing for a one-hour talk. Then it’s necessary to zoom out, try to see the big picture, and from a good vantage point to construct your story. Towards the end of the preparation, the talk becomes more gestural in my mind – it has organized itself into parts, with transitions, and an engaging structure and flow. The talk is ready when I can see it all in my head – all the information batched into articulate clumps, which are batched into sections, each section occupying a place in a conceptual outline whose shape I see clearly in my head.
4. What quality of awareness?
The hardest, but perhaps most important, task is to constantly and consciously shift between the different levels of detail. Zooming in, zooming out – the talk needs to work on multiple levels, so that the audience can comfortably engage the talk and follow it, from a range of backgrounds and focus. It’s easy to passively let the math lead you, while prepping a talk, but the result usually lacks perspective and is boring.
I try to see the content for the first time, to be my own audience. I try to forget that I already know how the story ends, so I can perfect the story-telling. It feels like trying to hear your own voice, from outside your head.
Each expository challenge starts with a tension, which is broken by a moment of freshness and newness, which then rearranges itself into an enjoyable obviousness.
When the talk is ready, I feel like I’ve transcended the math/non-math boundary. I’m holding, in my mind, an object (the talk) that is mathematically rigorous and true, but crafted to interface with the multi-dimensional, non-rational, colorful and robust real world.
5. What emotions?
There are the emotions associated with the impending performace – fear, adrenaline, excitement, nausea. The preparation itself is, while usually an anxious experience, also very pleasant. It is a gradual shift from confusion to certainty, confidence, familiarity, and friendship. They say that you don’t really understand something until you’ve tried to explain it to someone else.
6. What does it resolve to, after how much time?
It might take 30 minutes or 15 hours to prep the talk, but it’s clear to me when it’s done. I stop thinking about it, move on to something else.
7. How frequent is this flavor?
About four times a year. There are lots of lectures to prepare when I’m teaching a course; the experience is similar to prepping a research talk but much more mellow, since I’ve only taught 300-level courses.
8. What are good/bad ways to change or follow it up?
I have a strict post-talk-prep routine, which consists of actively doing nothing. I’ve found it’s important to rest, not worry, get sleep, do enjoyable things like listen to music or eat, maybe meditate or get some exercise. The talk is prepped; there’s nothing to worry about. It’s out of my hands, and now my job is to be the best performer I can be. If the talk was prepared well, the performance of the talk is really fun. The worst thing to do is to indulge in nervousness and anxiety.