It's hard to be more descriptive with the title without making it excessively long.
What I'm wondering is this: what is the "right attitude" or "right psychology" when confronted with a mathematical question that one is not able to solve or get right (within a reasonable amount of time)? Maybe this sounds like a silly question, but I've struggled with it for a long time.
I'm an independent-minded person. I get more satisfaction from work when I am able to do it by myself. And mathematics is a huge body of knowledge that requires the student to depend on everybody else's work. Obviously that's the case with pretty much every discipline; there's always a certain amount that we always have to learn from others. But what makes it more difficult in math is that there is a culture or expectation of self-reliance. "The proof is left to the reader" is pretty much a meme. Math educators frequently and deliberately omit information. Also math is highly intuitive. It's conceivable that a person could get pretty far working alone.
I've had students who get frustrated at themselves for not being able to solve a problem. On one hand, I feel like this attitude isn't healthy. The frustration will just break down their confidence. On the other hand, I completely understand it and feel the same way sometimes. What advice would you offer those kinds of students?