What is understanding the concepts he's presenting in comparison to being able to explain them to someone else? It's not nothing, to use a double negative, but you get the idea. It's of course not the only difference between professors and students, but if you can find someone interested enough, try explaining it to them, and you'll never forget the lesson. If you're not a professor, one difficult task is finding someone who's interested, in order to practice. Normally, the way to do this on your own is to write proofs.####[]