>>11770610>is there any gain to trying to improve your AMC/AIME scores?Depends how much you improve. There's gain to be had from doing very well, in that people who make it to the olympiad level make lots of useful connections to mathematicians/future mathematicians and are offered opportunities that plebs will never hear about (also admissions, olympiad-level competitors are almost guaranteed admission to MIT and Harvard), but this is a perverse way of looking at it.
Do you think the "real math" you're talking about was created by mathematicians thinking "well I COULD prove this theorem, but what will I gain from it?"
Nobody thinks like this. People do math because it's interesting.