I’ve always felt like I don’t have a decent grasp on a topic until I can “play” with it. For example, I have lots of fun asking questions in elementary real analysis, and to some extent topology and linear algebra, which usually leads to nice problems and more fun questions.
But with certain topics, like complex analysis, abstract algebra, and basically anything at the grad level, I can’t play with them. I don’t know how to come up with interesting questions to ask, and I can’t create any problems. I can understand definitions on a surface level, and solve textbook exercises somewhat fluently, but I still don’t feel like I have enough intuitive understanding to play with the topic.
So, some questions:
1) Usually the best way to really get to know a subject is to play with it, but how do you get good enough to play when you can’t play yet?
2) Does anyone else share this view on playing? Are there also topics for you that you feel comfortable playing with, and some where you just feel stuck?