I'm a teenager hoping to become a mathematician, but math isn't my forte. Is it possible? I am a sophomore in high school and have discovered the joys of mathematics.  However,due to sheer irony, at times I find the subject difficult. I am what one could label "lopsided" in my faculties, excelling in languages but always floundering with numbers. This may be biological, for I was psychologically tested and found that my linguistic skills were abnormally high but my spatial reasoning...wasn't (I was diagnosed with Asperger's Syndrome). I do not want this to deter me from pursuing a degree in physics/math and finding work in the field. On the other hand, what if I just don't have the ability and fail? I see the mathematics geniuses at my school (or other students who are just better than me) and I feel horribly discouraged. Recently, I took a math test and felt completely lost, even though I studied diligently and received high scores on other assignments, which may be due to the anxiety I felt as I received the exam. The mere thought of that test kills me, as if it is a reminder that I shall never succeed in the subject no matter how hard I try (I was given a B last semester).  I was wondering if those in advanced mathematics have had the same experiences, and somehow overcame their struggles. Is it optimal I should just study a humanities subject even though this is what I like, or is there some way I could find a path in the field? Also, as an aside, what gives you your passion for math? What is the best thing you find about this subject? Perhaps that can force my motivation to the point where I become proficient...

P.S. If you could point me in the direction of some math/physics related extra-curricular/summer activities and programs, it'd be much appreciated.
The title of your question presents an interesting dichotomy.  It is of course true that a necessary condition to succeed as a mathematician is that one be "strong at mathematics"...but exactly what that means is less clear-cut.  And whatever "strong at mathematics" means, it is something that can be developed (or not) over time: it is not something that either inheres in one's soul or doesn't like some sort of Calvinist election.


  This may be biological, for I was psychologically tested and found that my linguistic skills were abnormally high but my spatial reasoning...wasn't (I was diagnosed with Asperger's Syndrome). 


Wondering as a teenager what one may or may not be "biologically capable of" is not something that I would recommend: you are placing too much stock in biology and testing.  (Frankly, I am skeptical even of the Asperger's diagnosis.  I am by no means professionally trained in psychology, but in my opinion there is a faddishness in the diagnosis of such "syndromes".  I believe that Asperger's diagnoses are based on measurable cognitive differences, but worry that the implications of these differences may be exaggerated.  To quote from the wikipedia article on Asperger's: "Some researchers have argued that AS can be viewed as a different cognitive style, not a disorder or a disability, and that it should be removed from the standard Diagnostic and Statistical Manual, much as homosexuality was removed.")  Also there is much, much more to mathematics than "spatial reasoning": I am a research mathematician with some kind of international reputation, but my inherent spatial reasoning abilities are no better than average.  I bought a bookcase a few months ago, but delayed assembling it and seem to have lost the instructions: without them, I think I would rather buy a new bookcase than worry about how to assemble the one I already have!  When it comes to applying spatial reasoning to mathematics, I can see that I have to work harder than many of my peers but I can still do it: for instance, when I discuss finding volumes of revolution in calculus I can always identify a few students who can visualize the regions more easily than I can...but overall I am still better at these problems than almost any calculus student I have ever taught because (i) I have so much more experience with these problems than they do and (ii) there are aspects of solving these problems other than spatial reasoning.  I think that if you want to work in certain aspects of low-dimensional topology then it is important to have strong spatial reasoning skills -- sometimes I have seen talks or read papers in which proofs in these areas are done with the aid of pictures that look very confusing to me -- but even here I think that other skills are just as important or more as naked spatial reasoning.  (In fact I did undergraduate research in low-dimensional topology, really enjoyed it, and would be happy to do more of it some day.)  


  I do not want this to deter me from pursuing a degree in physics/math and finding work in the field.


It is good to keep an eye on the future, but if you try to deal with the future as if it were the present then you're bringing a lot of unnecessary stress on yourself....we simply don't know so well what the future will bring.  Having a goal of getting an undergraduate degree in physics or math is a good level of future planning for a high school sophomore.  You can also start looking into the various careers that make use of this degree: there are many, and most of them would not go under the name "mathematician".  The best way to stay on track towards this goal is simply to take challenging math classes, do your best to get what you can out of them, and also feed your interest in mathematics by reading up on whatever outside of class mathematical material interests you.


  On the other hand, what if I just don't have the ability and fail?


We all worry about that.  I still worry about that (maybe my definitions of "ability" and "failure" have been adjusted, but the emotional effect is much the same).  I feel very confident that the world's leading mathematicians have these thoughts as well.  They're helpful up to a point -- the point where they drive us to improve ourselves and have lofty goals -- and then they stop being helpful (at the point where we uselessly worry about our innate abilities or future success rather than try to figure out what to do next).  


  Recently, I took a math test and felt completely lost, even though I studied diligently and received high scores on other assignments, which may be due to the anxiety I felt as I received the exam. The mere thought of that test kills me, as if it is a reminder that I shall never succeed in the subject no matter how hard I try (I was given a B last semester).


It happens -- none of this is proof positive that you are not cut out for a mathematical career.  When I was in school I usually did very well in my math classes but not always: I remember one "honors precalculus" course I took: the teacher was just very intense and had a way of making things tricky and complicated.  I think he was probably a very good teacher, but his high ambitions and intensity did not translate well for me: I remember when we started a unit on linear equations, a subject which I had seen in several previous courses and knew was easy to understand.  But somehow he made that material complicated as well: he discussed at least four (!!) different forms of equations of lines, and the exam managed to contain questions on linear equations that were really difficult!  For one of the four quarters I got a $B$ in this course, and it was a bit discouraging.  The next year I took calculus and it was both easier and more interesting than the precalculus course I had taken the year before: but I remember that though I found that most everything in the calculus course came very quickly, I also spent more than two hours a night solving calculus exercises...which must have been much more time than I had put into the "harder" precalculus course.  


  I was wondering if those in advanced mathematics have had the same experiences, and somehow overcame their struggles


In the first graduate level mathematics course I took, I studied "the wrong version of the Radon-Nikodym Theorem" for the final exam and was unable to do anything with one out of the three questions.  I got a $B$ in that course and later found out that there had been some real question as to whether I should be allowed to continue with the graduate analysis sequence.  In the end I got an award for being one of the best undergraduate math majors.  Being "strong at mathematics" doesn't mean that you are inhumanly perfect: virtually everyone has at least a few lack-of-success stories to tell. 


  Is it optimal I should just study a humanities subject even though this is what I like, or is there some way I could find a path in the field? Also, as an aside, what gives you your passion for math? What is the best thing you find about this subject? Perhaps that can force my motivation to the point where I become proficient...


What I find interesting about your question is that while you sound very confident about your skills in language and the humanities, you seem very intent on pursuing a mathematical field....but you don't really say why you like mathematics better than humanities.  (I'm not blaming you: such things can be hard to explain.)  I can identify with this, because all throughout my pre-collegiate education I had skills in the humanities which were as strong as those I had in mathematics and more consistent: I never had a day where e.g. I tried to read Shakespeare and failed!  Perhaps I had the sense that mathematics was deeper and more challenging than the humanities and was drawn to the idea that there was more clear room for improvement.  As a high school student I learned a bit about calculus and saw that there were interesting things that lay far beyond -- like number theory, which I have been interested in since my sophomore year of high school -- and I'm not sure what is the equivalent in the humanities of "gunning for number theory".  On the other hand I took creative writing as a high school sophomore, enjoyed that immensely and felt approximately the same infinite challenge as I did (and still do) with mathematics.  I am somewhat regretful that I gave that up...although, given that I have more than 2000 pages of "extra" mathematical writing on my webpage, perhaps I have not really given it up so completely.  So I wonder:

What is the right path for a high school student who is extremely talented and ambitious in the humanities?

I didn't know the answer to that question then, and I still don't now...but I wish I did.  You might want to look into it.  If you feel much more confident in your abilities in the humanities, shouldn't you at least think about going into the humanities?  

Let me also say that the phrase about "forcing my motivation until I become proficient" worries me a bit.  You also ask what gives mathematicians their passion for math and what they like about it.  To me this sounds a little like someone who is thinking of becoming engaged asking an older married friend exactly what it was about her spouse that made her decide to get married.  If you have to ask, then maybe you should be dating someone else!  My passion for mathematics comes from the fact that I love it...it is not really something that can be further analyzed or explained.  If you love mathematics, spend more time with it and develop your knowledge and skills.  Otherwise keep taking mathematics courses at least until you get to college, but keep your mind open to finding the true object of your affections.  It will be out there somewhere...
Been there, done that. Let me explain...

At high school (I'm from Australia so I don't know what all this sophomore/freshman stuff is.. Senior years here) I just barely scraped through my maths classes. At uni I did bachelors of education and science majoring in mathematics. I did not do very well in the math classes. Most of them I just managed to pull passes or the odd credit ( 4 or 5 from a max of 7 with 4 being the pass). However, the education classes I was getting 6 and 7's for. What was different? The assessment. For the education classes most assessment was essay based; the maths was exam based. I have a very bad short term memory. I cannot multiply or often even add two 2 digit numbers in my head. Not because I don't know how, but because by the time I get to the second number I've already forgotten the first. This problem showed in my work at uni; I understood the content and could do it, but when it came to the exams I really struggled. Especially since most of the course's assessment was 80 - 90% in one final 3 hour exam at the end of the semester.

To cut a long story short, I decided that I liked the maths better than teaching and so started looking for a job in that field after I finished. Now I work as a developer/mathematician on an agricultural simulator for a large research organisation. Now, I'll be the first to admit I'm not a pure mathematician. A lot of what I do is actually data analysis, but as you probably know that includes a lot of mathematical and statistical work. I am quite fluent in the language of mathematics but I still have a desk reference of the meaning of math symbols because I can't always remember them. I can do a fourier or solve a system of differential equations but I need a reference manual to help me. Mostly because I do them so rarely I need to jog my memory. 

And therein lies my main point. Many jobs in mathematics (excluding academia of course) don't actually require you to do maths. They require you to understand it. All those algebra equations and integrals and matrices they have you do? After you graduate you will probably never do one by hand again. We have computers to do the heavy lifting now. But you need to understand how the equations and integrals, etc work. You need to be able to set up the problem for the computer and understand the output that comes back. You need to be able to communicate your results to others. That is primarily what (in an ideal world) your classes are setting you up for. The exams where you have to do the calculations yourself from memory are to show that you have that understanding.

Now, having said all that. Do your best to do as well in your classes as possible. While it sucks that two people with the same ability can get wildly differing grades simply due to the form of assessment, that's the world we live in. And up to a point, especially when you're a recent graduate, employers will judge you on the basis of those grades simply because you don't have any work experience behind you yet that you can point to. But in the end, realise that your grades do not have to reflect your ability and as long you understand the content, don't let lower grades discourage you from a career in mathematics. The field is much larger and diverse than most people realise, which is probably another topic in and of itself, really.

So the tl;dr version: I sucked pretty hard at maths through school and university. I didn't expect to get a career in it but I did and I love it. Final grades are not always an indicator of mathematical success. If you understand what you're being taught but have trouble when it comes to assessment that can be for reasons other than a lack of ability. If you enjoy, keep going and you will be successful.

Best of luck,
Justin