...when you do have a deep understanding, you have solved the problem and it is time to do something else. This makes the total time you spend in life reveling in your mastery of something quite brief. One of the main skills of research scientists of any type is knowing how to work comfortably and productively in a state of confusion.
Teaching, for me and several other people I know, serves the purpose of reveling in your mastery. In fact, Feynman said it best:
In any thinking process there are moments when everything is going good and you’ve got wonderful ideas. Teaching is an interruption, and so it’s the greatest pain in the neck in the world. And then there are the longer period of time when not much is coming to you. You’re not getting any ideas, and if you’re doing nothing at all, it drives you nuts! You can’t even say “I’m teaching my class.”
If you’re teaching a class, you can think about the elementary things that you know very well. These things are kind of fun and delightful. It doesn’t do any harm to think them over again. Is there a better way to present them? The elementary things are easy to think about; if you can’t think of a new thought, no harm done; what you thought about it before is good enough for the class. If you do think of something new, you’re rather pleased that you have a new way of looking at it.
Teaching helps me a lot in this respect, because I become very insecure sometimes when I do my research.
In my experience, if you find yourself in “a state of sheer existential dread”, that probably means you’ve done something wrong, most likely made a category error somewhere along the way.
-Anon http://www.quora.com/What-is-it-like-to-have-an-understanding-of-very-advanced-mathematics#ans873950
(emphasis mine)
Teaching, for me and several other people I know, serves the purpose of reveling in your mastery. In fact, Feynman said it best:
Teaching helps me a lot in this respect, because I become very insecure sometimes when I do my research.
I can’t tell if he presents this as a good thing or a bad thing.
At the very edge its also useful to be able to work while in a state of sheer existential dread.
In my experience, if you find yourself in “a state of sheer existential dread”, that probably means you’ve done something wrong, most likely made a category error somewhere along the way.