In the US and Canada, later on the (undergrad) college students can also take the Putnam Exam, an equally optional and fun but *horrendously* challenging competition for talented students, which essentially ranks them at the country level before they can go on to grad school (US + Canada together). I used to be smart as a kid (every year I made it to the Italian finals at the Math Olympics! ), but alas, that's pretty much the end of the fun in Italy for a student. I believe other subjects (chemistry, physics, etc.) also have their competitions if you are good and bored enough in school. Years later, one of the satisfactions of my career was to direct the research of a couple of Putnam Fellows (the national winners) while I was teaching at MIT, and there you can REALLY see genius in its purest form and in full display.....folks WAY smarter than I, who were starting to publish in the top international journals as undergrads! ;-)))