Contrary to want others have posted though, IMO, even though high test scores may help in some college admissions, success in advanced math courses and success in competition math are not always the same thing. My son's professors have told him the same thing.
Looking at the thread, I'm guessing you mean me, but actually I didn't mean to imply that I thought any such thing - I don't. Plenty of great (and lesser!) mathematicians are not interested in competitions and/or don't have the particular talent it takes to solve a contrived problem under time pressure.
What is absolutely clear, though, is that success in school mathematics courses is no guarantee of having the ability to do genuinely original mathematics, or even of having the ability to do well at challenging university level courses. One of the ingredients that is generally missing from school maths, but provided by competitions, is experience with looking at a problem that you may or may not be able to solve, not being afraid of the possibility of failure, and trying some things that may work.
I wasn't interested in competition when I was at school, and so at the time I didn't mind that nobody made any attempt to introduce me to it. However, what this meant was that I started university with almost no experience of ever finding any maths hard. This was bad. Competition maths isn't the only way to provide that experience, of course, but it is often the easiest. That's why I'm encouraging DS to do competition maths - I don't care whether he ever competes at a high level, but I do want him not to freak out (the way I used to) when something's hard!
