Okay, I'll bite. Apart from the same benefits one might attain from after-schooling in math (and if you're already such a stellar math student, what are you really gaining?), what are these benefits, and how are they different from those gained in any other extracurricular activity? Because you can win awards, pad a college application, and qualify for scholarships with any one of the other activities I already mentioned.
Hopefully the main benefit is that they enjoy the activity.
I am separating this last part of Dude's statement because so many people have this incorrect perception.
In addition, most college admissions officers prefer well-rounded applicants.
Selective colleges are NOT looking for well-rounded applicants. They are looking for a well-rounded CLASS. They can put together a well-rounded class by getting the star athletes, the champion debater, the musical prodigy, the politicians, accomplished actors, and yes, even the math and chess prodigies.