Agreeing to give a lecture on a subject is often a great way to push yourself to learn and distill as much as you can about it.
It’s a commitment device, putting an actual timeline on an otherwise-nebulous process. It’s also a way of creating a stronger emotional connection to the material, which in turn can help you understand it more deeply: Deep understanding requires (and is a result of) intense personal connection.
This strategy seems most helpful when you understand something only moderately well. If you don’t yet understand it well at all, the pressure may just push you to crystallize shallow thinking; if you understand it extremely well, you’re less likely to be emotionally connected to a class on the subject.
Related: The best time to write about your lecture’s topic is around the time you deliver it
Hofstadter began developing the ideas for Gödel, Escher, Bach by teaching a course at the University of Oregon. He credits several interested students with helping him considerably develop the ideas (p. P-10):
These three students simply devoured the ideas, and we talked and talked endlessly about them. My course thus turned out very well, both for the snag gees and for the snagger.
The great mathematician Andrei Kolmogorov described an interesting trick that he used to get around being intimidated by big problems. Rather than investing all his time and effort on attacking the problem, he’d put the problem into a larger context. He’d announce a seminar series in which he’d lecture on material that he thought would be related to the problem. He’d write a set of lecture notes (often turning into a book) on material related to the problem.
Q. What trick did Kolmogorov have for attacking hard problems?
A. He’d give a seminar series on related material and write lecture notes on the topic.
Q. How did Kolmogorov’s lecturing strategy hedge his bets when working on hard problems?
A. At worst, he’d end up producing some valuable lecture notes.
Hofstadter, D. R. (1999). Gödel, Escher, Bach: An Eternal Golden Braid (20th Anniversary ed. Edition). Basic Books.
MN tells me that Kolmogorov famously used this strategy to solve problems, but I’m having trouble finding references to this!