I don't know if here is the right place to ask this question but I would be glad if you could help me.
I am currently a first year PhD student in pure mathematics, and I have some issues that seem like are preventing me to try to become a mathematician, and come in my mind every now and then.
I start with my background, when I was in high school I tried a lot to be in our national IMO team but I didn't even get close to it, after that I tried a lot of university math books and almost finished undergraduate material in my high school, but after getting to university I didn't have any success in my first years, and after that I got to some "CV-filling" places, that I used to get to a rather good university in math for my PhD, but when I see young great mathematicians, almost all of them have had some of the great successes in their high school and undergraduate, and seems like everyone is looking at them like a great mathematician because of that, and they do not need to put a lot of effort on what they're doing, for example, one of my colleagues got to one of the best universities in math without trying to learn a lot of mathematics - even those that I knew from high school- but has a lot of "success" in mathematics.
In my undergraduate I tried to continue my way of reading mathematics, and learned a lot in my undergraduate studies (from books not courses, and for that I didn't have the best GPA in class), also worked with some professors and other things that not so bad undergraduate students usually do.
My questions are the following:
1) What is a mathematical success?
(for example, I know that in PhD working on good things and having great ideas about core problems in mathematics is a success, but it seems that I'm doing something wrong because it seems that I will not get good things in math by just doing what I'm doing)
2) how can I have motivation to become a great mathematician and be sure that all my efforts are not in vain?
(for example, in my department, everyone talks about having some number of papers published to get to a better place (which I think is something bad to be someone's goal in math) , and when I see former graduate students of my department, almost all of them are in big data analysis and stastics and these non-pure mathematical jobs, even after having a good understanding of some part of pure mathematics)
I would be happy to see other questions similar to this, if there are any in this website, but I would be happy to not put duplicate to this one, if there are duplicates, I would be happy to see answers in my case.
Regards, Sorry to put anonymous, I'm a little insecure when asking these questions!