Math competitions for high school and college students always kind of bother me. Not intrinsically so—if they’re approached with the right attitude. It’s a game and a decent excuse to practice some mathematical knowledge in a social setting. In that way it’s great! Kids having fun, who can be against that? Especially if they like math.

But often they’re not having fun, and there are so many ways in which competitions fail to exercise important mathematical skills. A fairly surface-level example is cooperation. The real business of doing math involves lots of conferences, emailing domain experts, and coauthoring papers. But a deeper example is that math is highly structured, theory is built on theory is built on theory. Competition math never needs to reach down more than two levels below the level at which the problem is pitched. In that way, competition math fails to incorporate the single most distinctive feature of math.

I copy this from a random person on a math chat room:

contest problems are sort of 'curated' as to have a solution that can be arrived at in limited time without any recourse to deep results. real life problems aren't like that. this isn't to say that contest skills aren't useful, because many real life problems do have contest-like subcomponents.

some people can be extremely good at leveraging a small bag of tricks but get bored/annoyed when a problem won't yield to them. that's not the best attitude for research. but many people have that feeling without ever doing contests.

- leslie townes