<p>Transfer admissions to top schools are extremely competitive because of their high retention rates. But a T20 university may not be the place for someone as single-mindedly academic as yourself; their admissions tend to focus less on academics than on personal qualities and initiative/promise shown through ECs (which isn’t to say that academic “requirements” for admission to top schools aren’t stringent, but that they aren’t the focus). A LAC may be a much better place for someone who really loves learning rather than doing.</p>
<p>Still, there are plenty of ECs that would appeal to a more academically-minded person. As others have mentioned, math/science competitions are a great way for you to demonstrate your prowess/creativity/devotion outside of your school curriculum.</p>