I'm a fairly new student in pure math, in my second year of studying analysis. In my first year, I took courses on basic real analysis using Rudin, and this year, I'm taking classes on measure theory (using Folland) and probability theory (using Durrett and Breiman).
Both years, I have/have been struggling to do well in the courses: I struggle mightily in getting proofs started and finishing them as well as coming up with examples/counterexamples.
I really enjoy pure math, but when it comes to actually solving problems/taking exams, I do rather poorly and really discourages me in pursuing the discipline. Could it just be that I'm just not cut out for pure math?
I'd appreciate any advice or comment. Thanks!
For me the overriding question here is: Do you enjoy the work (the intellectual struggle) and have you proven you're in the top strata of your cohort (classmates, students at the same level in other schools...)? Note that only those who persist and struggle, no matter what their intellectual gifts, ever really succeed. (Good Will Hunting is mostly fiction.) Look honestly into your future and see if you have a career ahead of you.