For example, imagine that one day you mention a difficulty you're having to your office mate, who tells you about a wonderful theorem that's relevant. If you're feeling insecure, this is awful: you think about the time you wasted not knowing about this theorem, and you worry that your office mate knew it and therefore you should have. On the other hand, if you're confident in yourself, then it feels great: you learned something beautiful that will help your research, and how can it be a bad day when you learned something like that? This confidence can take time to develop, but as you feel more relaxed and bolder, everything will become more enjoyable.

Another thing to keep in mind is that progress is difficult to measure when you don't know where you're going (which is what research is!). Grad students sometimes feel bad because they don't think they're en route to solving their thesis problems. Often they're right, but that's not a problem. If you knew in advance that you were going to solve it, then it wouldn't be research. The goal isn't to solve the problem you started with, and indeed you often won't. Instead, the goal is to find something exciting along the way. Once you're used to this, you can say to yourself, "OK, probably I'm not going to solve this problem, but it's worth a try, and in any case I'm sure that if I think hard enough about it, something interesting and worthwhile will come out of that work."

Anonymous Mathematician, here