I have looked around quite a bit on Math Overflow and haven't found a similar question, so I'm posting it here. I understand that this isn't the typical forum for such a question but it's as good as I can find.
Basically, I'm a rising 9th grader and this past year I finished a standard single variable calculus course. I've also had a fair amount of exposure to discrete mathematics and number theory, through through my own 'exploration' and not olympiads, like many other studenst of my age
At the moment I am quite certain that I will want to be doing research in math in some flavor or another. My dilemma at the moment is one torn between spending time channelling into the depths on undergraduate math or working on problem solving skills in preparation for a competition like the Putnam. I have found many a site on the web saying that a top Putnam score is now a rite of passage in this day and age and few low-scorers end up, for some reason unknown to me, doing research at a top level.
I love math for its elegance and ubiquity and the prospect of working through hundreds of mechanical olympiad problems for a single-day competition seems rather dull. When I contrast that to getting an understanding of some of the basic underpinnings of math through books like Axler and Artin, I find myself seriously doubting the merit in that approach.
Does anybody have any advice for someone in my position?