I attend a mostly liberal arts focused university, in which I was able to test out of an "Introduction to Proofs" class and directly into "Advanced Calculus 1" (Introductory Analysis I) and I loved it; I did great in the class. I was not very mathematically mature at the time, but I studied hard and started to outpace many of the senior level students who had a least a good year or more of experience than me. Furthermore, the professor teaching the course was apparently known to be particularly difficult, but I loved his course. I enjoyed the challenge and wound up with a B+, the 2nd highest grade given in the class. I took Advanced Calculus 2 and loved it even more. The professor even suggested that I take a graduate Complex Analysis course in the Fall. (Just a side note here, the undergraduate complex analysis course at my school does not use any theorem's or proofs. The grad version is similar to say, an honors undergraduate course at more traditional math program.) I took this as a high complement, and a verification that I was in fact doing well. I know I am not very deep into Analysis, but I feel comfortable with the subject, even with the more abstract parts.
However, I am really struggling with Abstract Algebra. I can't understand why. I study the material really hard. I am doing "better than most" in the class, and I am maintaining a solid B average, but I really have trouble thinking about Algebra like I do Analysis. I feel like I am mostly just regurgitating theorems and techniques just to pass the exams. I know I can pass the course, but I also know that this mindless memorization will eventually come back to haunt me later on in my mathematical career. Algebra is truly one of the "pillars" of math which is why I really feel terrible that I don't understand it.
Is this a sign that I simply don't have what it takes to succeed in math? I would love to go on to graduate school and hopefully get a Ph.D. In fact, a professor actually said to me "I think it would be a shame if you didn't go to grad school for math." He told me that before I took Algebra, but now I feel like my world is "crashing down" in a sense. Before I was a "good" student, now, I feel like a zombie in the back of the room. Any input is greatly appreciated but I really want to know if this has happened to anyone who has gone on to succeed in a Ph.D math program?