I know that there are hundreds of posts exactly like this but posting my own just seems more satisfying. I am an undergrad sophmore at a pretty big university. I am majoring in mathematics. I've finished single variable, multi variable calculus, lower division linear algebra, probability, combinatorics, and diff eqs with all a's and b's. I'm currently in an into to proofs class and plan on getting at least a b.

By the time i graduate i plan on having completed abstract algebra, analysis, ud linear algebra, and a few other electives that interest me (number theory, topology, etc). I'm also doing a physics minor purely for interest.

with the proofs class i am in right now i am finding myself putting A LOT of work into it. more than I expected. i know that i must do well in this class to succeed in any further math classes. To me, mathematics is absolutely amazing and I would rather do nothing else. However, I am worried as a enter more rigorous courses that success is not entirely, but more than ever, dependent on creativity rather than interest and determination. I know that these usually go together but I guess what i'm getting at is to ask whether or not you think i have a shot at grad school.

I plan on graduating with ~3.6 and hopefully a few research experiences. i am a female which might give me a slight preference (even though giving preferences for things like that is just stupid, i guess i might as well try to benefit from it). As of right now I really don't ever want to stop studying mathematics, ever in my life. I don't want a real job, a lot of money, kids,, family, none of it. I really just want to use my life to learn as much as I can. Anyways to conclude, I guess my question is although I am in general pretty good at math I feel like compared to some of my peers my natural mathematical talent is a little lacking. I have to study more and try harder. Are motivation and interest enough, or is something like a math PhD only attainable to those with motivation, interest, and a VERY strong natural mathematical talent?
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 [QUOTE=AnIntegral;2605674I have to study more and try harder. Are motivation and interest enough, or is something like a math PhD only attainable to those with motivation, interest, and a VERY strong natural mathematical talent?[/QUOTE] For most students, and most courses, there isn't really any time for creativity at undergraduate level. You need to understand the framework and fundamentals before being in a position to play with it. It seems as though you're really just looking for re-assurance but one must be honest: a frank answer to your other questions is that, no, not everyone is capable of doing a PhD. There is no point in asking things like "VERY strong natural talent" as these things are very difficult to quantify: there are so many variables that comprise someone's viability for research that, in all but the extreme cases, there isn't any way to say that someone is just 'born with it'. For now, don't concern yourself with whether or not you have to work hard: do as much work as you feel you need to, and don't pay attention to the amount of time other people spend understanding problems. If you're able to get the grades, you're able to show graduate schools that you at least fit part of their application standard - someone that is able to put in the required work to get a high enough grade. There are also lots of other things that will be considered, however.

 Quote by AnIntegral I know that there are hundreds of posts exactly like this but posting my own just seems more satisfying. I am an undergrad sophmore at a pretty big university. I am majoring in mathematics. I've finished single variable, multi variable calculus, lower division linear algebra, probability, combinatorics, and diff eqs with all a's and b's. I'm currently in an into to proofs class and plan on getting at least a b. By the time i graduate i plan on having completed abstract algebra, analysis, ud linear algebra, and a few other electives that interest me (number theory, topology, etc). I'm also doing a physics minor purely for interest. with the proofs class i am in right now i am finding myself putting A LOT of work into it. more than I expected. i know that i must do well in this class to succeed in any further math classes. To me, mathematics is absolutely amazing and I would rather do nothing else. However, I am worried as a enter more rigorous courses that success is not entirely, but more than ever, dependent on creativity rather than interest and determination. I know that these usually go together but I guess what i'm getting at is to ask whether or not you think i have a shot at grad school. I plan on graduating with ~3.6 and hopefully a few research experiences. i am a female which might give me a slight preference (even though giving preferences for things like that is just stupid, i guess i might as well try to benefit from it). As of right now I really don't ever want to stop studying mathematics, ever in my life. I don't want a real job, a lot of money, kids,, family, none of it. I really just want to use my life to learn as much as I can. Anyways to conclude, I guess my question is although I am in general pretty good at math I feel like compared to some of my peers my natural mathematical talent is a little lacking. I have to study more and try harder. Are motivation and interest enough, or is something like a math PhD only attainable to those with motivation, interest, and a VERY strong natural mathematical talent?
I have an acquaintance who is doing their PhD in financial maths and he basically said that its more perspiration than inspiration (something that Thomas Edison said about inventing).

As far as research goes you are typically there to create an original contribution. It doesn't have to be in same league as say Einsteins 1905 paper (also remember how long he thought about and worked on that for to put that into context), but you will have a supervisor who's experience can be used to help guide you in the right direction: ie you are not expected to be a genius.

I believe that if you pursue your studies with the tenacity and dedication to that of most mathematicians you will find one day that you have become that very same person.