_(Trigger warning: school.)_
Economists distinguish a spectrum between _rival_ and _nonrival_ goods. If you want to know more math than your school expects of you, all you need is a book, dedication, and time. If you want an Honorable Mention on the Putnam exam (and don't care about merely getting a better score if you don't make the list), you need to be _better than_ all but no more than 99 entrants. The payoffs in the competitive scenario have a significantly different structure from the scenario where you just want to learn stuff.
_(Trigger warning: school.)_
Economists distinguish a spectrum between _rival_ and _nonrival_ goods. If you want to know more math than your school expects of you, all you need is a book, dedication, and time. If you want an Honorable Mention on the Putnam exam (and don't care about merely getting a better score if you don't make the list), you need to be _better than_ all but no more than 99 entrants. The payoffs in the competitive scenario have a significantly different structure from the scenario where you just want to learn stuff.