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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!

closed as primarily opinion-based by Brian Tompsett - 汤莱恩, Buzz, Coder, padawan, user3209815 Oct 9 '17 at 6:41

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    What level of success are you looking for? Fields Medal or bust? Good enough to have prove some theorem that is worthy of publication in Annals of Mathematics? Good enough to get a job at a top math department? Good enough to get a job at some research university? Good enough to prove some theorem someone else is interested in? – Alexander Woo Oct 7 '17 at 16:56
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    Life is not a competition, and neither is mathematics. (Unfortunately, the job market is a competition.) If your goals are based on comparisons to others, you're pretty much doomed to a sad life. – Alexander Woo Oct 7 '17 at 17:09
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    You should measure success by having measurable, reachable goals. Being "the best mathematician" is not such a benchmark, and setting that as your goal, as Alexander Woo mentioned, will almost certainly guarantee you will be unhappy in your mathematics career. Moreover, not pursuing a career you want because you can't be "the best" in that discipline seems shortsighted. – aeismail Oct 7 '17 at 19:22
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    If success requires being the best mathematician, then everyone on this site is a failure. – Andreas Blass Oct 7 '17 at 22:34
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    'Good enough to be the best mathematician' Not to be cute, but the set of mathematicians is not well-ordered! – Charles E. Grant Oct 8 '17 at 2:44

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