I am a student in the second year of a university majoring in mathematics. I am trying to publish scientific research. Of course I know that it will be very difficult to do it at this level of study. At this level I try to prepare myself to do it. I try to study anything in detail with the proofs, and to solve some diverse and difficult problems that are often from IMO.
Since I started doing this I have noticed that I find it very difficult to combine rigorous self-study with solving very hard problems. It seems that it is better to do one thing. By this I mean either I try to study without going too deep and without knowing the details, with solving difficult problems, or I try to study in depth without trying to solve very difficult problems.
As a note, by hard exercises I mean Olympic exercises, not medium-difficult exercises like the one in "calculus" Spivak's book. My question is this:
Do you need to be good at solving difficult problems or just enough to understand everything you have studied, in order to be creative in mathematics?
From your experience in scientific research, what is your advise for a student who is still trying to hone their skills to enter the field of research?