TITLE: Making sure that you have comprehended a concept
QUESTION [29 upvotes]: I have a question that I've been thinking about for a long time.

How can you assure yourself that you've fully comprehended a concept or the true meaning of a theorem in mathematics?

I mean how can you realize that you totally get the concept and it's time to move on to the next pages of the book you're reading?

Thanks in advance for your responses.

REPLY [3 votes]: I usually consider myself understanding something, if I can implement it on a computer. I do algebraic combinatorics, so it is fairly easy to verify identities and bijections.
Basically, if I can teach my computer a concept - I must be understanding it myself.