<p>Sorry for giving an incomplete story of my situation! This is going to be way OT, but I figure I owe people a full explanation…</p>
<p>I skipped ahead 4 grades in math when I was in elementary school… then sort of kept up the normal pace through 8th grade, when I took Calc AB. I did a fair bit of math competitions through then, and did fairly well at the state level (5th in state for mathcounts, in ohio).</p>
<p>In HS I took online classes at Ohio State, which were a bit of a joke, and also started to lose interest in the math I was taking (multivar, lots of vector stuff, all taught through mathematica). I took AMC and would qualify for AIME, but was lucky to get more than a question or two right there. I saw myself as being good at learning material (especially material that wasn’t super abstract), but not good at being a brilliantly creative mathematician who could conjure up leaps of logic to prove difficult things.</p>
<p>At Harvard, I shopped 23/25, felt totally out of my league. I’m sure I could have done alright, but I would have had to work incredibly hard to be anywhere above average in the class. I took Applied 21a at some point, just to prove to myself that I could still do math, and it wasn’t bad.</p>
<p>I guess my (uneducated) thoughts are, being able to get a 5 on AB or BC means you’ll be fine in 21a. But that doesn’t mean you’ll be great in 23/25/55… and math competitions like AIME are probably the best predictor of that.</p>