But now honestly in topology, I breeze through the course although I find it completely fascinating so I just study so much and love every moment of it. I just don't find it difficult at all (note, I don't say any of these thing to brag, just trying to give a complete picture of my current situation. Again, I really sucked so much at all of this originally which is why I'm confused)
Anyway, is it even worth it to pursue a PhD in mathematics or do you need to be one of these people who just don't have to work and it's all cake from the first moment?
I wanted to also comment on this. People give very conflicting answers, and I wanted to reconcile the different ones.
First off, it is GOOD that you are finding it easier to follow topology. That is more abstract material, and it is not easy. But do not expect your next class in mathematics to be easy - you can have good and bad moments.
What is going for you is that you appreciate the value of bashing your head against something (for the love of doing it) until it makes sense. That will help in the PhD.
Be careful, however, or you will get discouraged - expect
it to be tough in the program. Expect yourself to have moments when you feel it isn't worth it, and you won't make it. Remember to never forget that it's meant to be enjoyable
. If you get to the point where you're learning it like swallowing medicine, you will 100% burn out.
It is most important to have a consistent climb.
All said though, you can't be someone who enters the program finding all the basic material hard. With some significant work, you should find it doable.
And remember that some day, if you strive for faculty positions, given they are even harder to come by than PhD spots, you will end up competing with people who did
find it all cake when they started. The beauty is nobody finds it cake when they get far enough. And if you want to prevail, the important thing is to prevail at that particular point - when everything is insanely hard for everyone, not at the point when stuff is easy for some people and not for others.