TITLE: Advice on doing mathematical research
QUESTION [29 upvotes]: Please share any general tips or advice you have on doing mathematical research.
How do you identify good problems to work on or to think about? What do you do when you get stuck on a problem? Etc.

REPLY [6 votes]: Often, I find that the good problems come from errors in my work -- I write a proof of something that (at the time) I think is trivial and later find a counter-example.  Suddenly, the problem is non-trivial and interesting.
When I get stuck on a problem?  I work on another problem, a related problem, a broader problem, a more specific problem, etc.  Anything to try to understand why it is difficult to solve this problem.