<p>What has been discussed here are basic intro level college math classes for non-majors, such as multi-variable calculus, differential equations, linear algebra, essentially pretty basic stuff. Even calculus with proofs is considered basic as it is taught in many high school across the world. USAMO qualification is much more rare and IMO selection even more so. </p>
<p>A student doing advanced mathematical research on topological field theory under supervision of a well-known professor (I have interviewed such students) would clearly be considered an academic superstar. We are talking about a world of difference.</p>