Nah. Teaching doesn't make people smarter. Challenging yourself does.
There's a fundamental divide between those that think the best of us are only here to help the less fortunate. And those that think, the best of us should be out there expanding the frontiers.
Especially since the 'less fortunate' sometimes can be that way by laziness.
There is a fundamental divide, but it's not the one you draw. The fundamental divide is between those that view life as a solo race and those that think of it is a group endeavor.
"If you are the smartest person in the room, teach until you no longer are."