I am 47 now, a mathematician. My daughter is 8. Any kind of competition is wrong. Why in the World would ordinary people want to compete in such disciplines? We got stupid sports, like football, and every person in the World can understand the rules and regulations of the somewhat primitive competition. Introduction competition in science, especially in mathematics, is just wrong. No more, no less. It is fun for some people, but it can be profoundly intimate and personal.
We had a problem a few months ago as some kids started bullshiting as a division in calculus is complex and hard to understand. The parents probably told them so, but I would let them stick to football and leave others alone.