I find it more important not to show that you are smarter than your boss
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Well seriously though. Apparently being smart isn't a necessity to get you promotions, i learnt that you do with patience and hard work. And education, but that's overrated. Anyone can pass education today with all the help and retests and crap. But it's almost always the most ambitious and driven people that succeed faster. And if you are ruthless to the employees whilst kissing asses above you, and not being afraid of stealing someones idea, lying etc etc. Then it's instant Success!. Bosses are a special kind of people, and you have to learn how to handle them. There are naturally the opposite, but great bosses seem to be rare commodities. And they usually never stay, those are the kind of bosses that are really smart and seldom makes misstakes, and never blame anyone else.
Just don't expect to find a genius in every office, my oh my have i asked myself many times how someone could have hired the bosses i've encountered.