<p>I'm in my last year of high school but have started thinking about what major I'd list on my college applications...</p>
<p>Math is interesting to me and I've done well in my classes so far (up to Pre-calculus), but clearly this is only the most basic entry into the subject. I'm not really very distinguished in contests, only made a 5 on AIME, although I'm great in standardized tests which I find much easier (perfect math on PSAT and SAT II).</p>
<p>I was curious to know what it takes to be a math major in schools like Princeton, Stanford, or Columbia; hopefully I'll be heading to one of these schools >_<</p>
<p>It's hard to predict success just from AIME scores, but if 5 is representative of your overall ability, it won't hold you back. That said, even very good problem solvers, which is basically what the AIME tests, get to college and discover that they couldn't write a proof if their life depended on it. I'm a math major at Princeton, so feel free to ask me any questions you have.</p>
<p>My son is doing theoritical math as a sophmore at Michigan. He got some interesting advice from his prof when he asked him about what it took to get a PhD in math. The prof got his PhD from Chicago and did his post-doc at Harvard, so he's knows from whence he speaks. The prof said it was all about hard work ("glue your butt to the chair"). My son has already found this to be true, spending hours upon hours writing proofs. If you want to major in math at a top program, be prepared to work, work, work. The prof also said that often times it is not the clever students - those who do well in math competitions - who ultimately have success. Mamy times they are just not willing to put in the hours. Hope that helps.</p>
<p>I don't know if I'd go that far. I's say that a reasonable degree of innate mathematical aptitude is a necessary condition for majoring in math, though by no means a sufficient one.</p>