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Ever since I was a child numbers have fascinated me. I had a genuine interest for mathematics, and a couple of tests I was forced to do as a child indicates that my cognitive abilities are suited for the field. However, "one needs to start early" is a phrase that's often heard in these "competitive fields." Reading about modern, great mathematicians, you often see them labeled with the word "child prodigy" and great results in competitions such as the IMO.

Due to several unfortunate situations, I didn't attend school as much as I'd ought to as a child. While I fell behind, I didn't have a hard time catching up or even surpassing my peers. However, my mind was elsewhere at the time. Once I started high school, I acquired the basic skills for each field quickly, using the rest of the time looking up things that piqued my interest further. For example, while doing basic trigonometry, I spent most of the time looking at complex numbers, which is completely outside of the curriculum. While I did this after learning basic trigonometry, many of the tests have some questions where you'd need some experience solving some of the trickier tasks. I obtained good, but not extraordinary grades.

I just started university, and I am doing well in single-variable calculus, seeing as my going off-topic during high-school often included subjects described there. Looking at the curriculum for the coming years, I feel reassured, like I am finally given the tools to do math the way I've always liked to do. I am currently 19.

This became quite a stroll, but given the nature of the question, some information on my background might be necessary. Lately, I have felt that I've been able to grasp new mathematical concepts with ease, but I think its going to slow. I'm hungry to acquire knowledge, and I feel at incredible ease when challenged with a problem that is just out of reach given my current knowledge. However, right now, I'm just a 19-year-old kid with mathematical knowledge that is slightly above his fellow students. Given the situation that I've described, is it unrealistic to hope to become a publishing mathematician that makes real contributions to a field?

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I don't think its at all unrealistic. –  user18921 Sep 30 '13 at 13:33
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There is as yet insufficient data for a meaningful answer. –  Isaac Solomon Sep 30 '13 at 13:33
    
Andrew, if you look -->, there is a "related" section with many similar discussions, such as math.stackexchange.com/questions/237002/… –  The Chaz 2.0 Sep 30 '13 at 13:34
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You're 19. You have like 3 lifetimes ahead of you. –  Bruno Joyal Sep 30 '13 at 13:34
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You're 19. 19! I don't think you should worry about being "too old" for anything, let alone math. –  Prahlad Vaidyanathan Sep 30 '13 at 13:35
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marked as duplicate by Gerry Myerson, Isaac Solomon, njguliyev, Macavity, Lord_Farin Sep 30 '13 at 13:51

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Don't worry: the 99% of the "publishing mathematicians" were not children prodigy at all! You are young and you are learning mathematics, and you have a lot of time to understand if you really want (and can) become an active mathematician.

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