TITLE: I lost my love of math; I'm getting it back. How can I determine if math is actually right for me?
QUESTION [80 upvotes]: This question has been on my mind for a very long time, and I thought I'd finally ask it here.  
When I was 6, my dad pulled me out of school.  The classes were too easy; the professors, too dull.  My father had been man of philosophy his entire life (almost got a PhD in it) and regretted not having a more quantitive background.  He wanted me to have a different life and taught me math accordingly.  When I was 11, I taught myself trig. When I was 12, I started taking calculus at my local university.  I continued on this track, and finally got to real analysis and abstract algebra at 15. I loved every math course I ever took and found myself breezing through all that was presented to me (the university was not Princeton after all).  However, around this time, I came to the conclusion that math was not for me.  I decided to try a different path.
Why, you might ask, did I do this?  The answer was simple: I didn't believe I could be a great mathematician.  While I thrived taking the courses, I never turned math into a lifestyle.  I didn't come home and do complex questions on a white board.  I didn't read about Euler in my spare time.  I also never felt I had a great intuition into problems.  Once you showed me how to solve a problem, I was golden.  But start from scratch on my own?  It seemed like a different story entirely.  To make things worse, my sister, who was at Caltech at the time, would call home with stories of all these incredible undergrads who solved the mathematical mysteries of the universe as a hobby.  Whenever I mentioned math as a career, she would always issue a strong warning: you're not like these kids who spend all their time doing math. Think about doing something else. 
Over time, I came to agree with this statement.  Coincidentally, I got rejected by MIT and Princeton to continue my undergraduate studies there.  This crushed me at the time; my dream of studying math at one of the great institutions had ended.  Instead, I ended up at Georgia Tech (not terrible by any means, just not what I had envisioned).  Being at an engineering school, I thought I'd give aerospace a shot.  It had lots of math, right?  Not really, or at least not enough for my taste.  I went into CS.  This was much better, but still didn't feel quite right.  At last, as a sophomore, I felt it was time to get back on track: I'm now doubling majoring in applied math and CS.  
My question is, how do I know I'm not making a mistake?  There seems to be so many people doing math competitions, research, independent studies, etc, while I just started to take some math courses again. What should I do to test myself and see if I can really make math a career?  I apologize for the long and possibly quite subjective post.  I'd just really like to hear from math people who know their stuff.  Thanks a bunch in advance.

REPLY [5 votes]: I interpret your question as how to determine
if you are good enough to be a mathematics professor
and to do academic research for a living.
Note: You may wish to ask your question on http://academia.stackexchange.com
as there are quite a few mathematician professors there
who would be able to give you their perspective.
My background:
My father has a PhD in pure math.
I had the privilege of taking part in the International Math Olympiad.
I wanted to be a mathematician just like my father,
but because there are so few tenure-track professor jobs in pure math,
he encouraged me to study something more applied but still math-y.
I ended up doing a double degree in CS and math,
just like the OP.
For graduate school, I got a PhD in operations research,
which is basically applied math
(we apply optimization and probability/statistics to real-life problems).
Question: How did I know if I am good enough to be an academic researcher?
Technically correct but useless answer:
When I have published lots of papers
and gotten tenure at a good university,
then I know that I am good enough to be an academic researcher.
More useful answer:

You take increasingly advanced math courses
including graduate-level math courses.
If you have a chance to do a UROP,
then do it to see what research math is like,
which is quite different from solving problem sets.
Also it is useful in getting a recommendation from a professor
for your application to graduate school.
As you get more advanced in your studies,
you will discover how good you are at math.
The reality is that it is very hard to get a job as a math professor
because there is much more supply (math PhDs) than demand (jobs).
To be a math professor is like being a professional athlete or musician
in that you have to be in the 0.0001% of your field.
Don't feel too disappointed if you can't make it,
along the way you may find something else that is challenging and that you like.
When you apply to math departments for graduate school,
if you are not good enough (in their eyes) to be a academic math researcher,
they will communicate that to you through their rejection.
That may be good news because you can try to do something else that is math-y
but less difficult to get into (e.g. CS, OR, statistics, financial math etc)
and your skills wouldn't have been wasted.
If you are accepted into a math graduate program, great!
Work hard on research.
However, due to the low probability of success at becoming a math professor,
I feel that it is wise to have an exit strategy;
i.e. develop skills such as programming
that will you to find job outside of math academia.