Does a janitor really need to know Pythagoras's theorem?

There is a debate which comes up very often, of whether it is worth teaching people any more than is strictly necessary, or whether there is any benefit to learning a wide range of subjects at school and university.

"Do you really need to learn about glaciers or the quadratic equation at school?" I will answer this question with another: "Does a soldier really need to do push-ups?" The motion of a push-up itself is near useless just about anywhere in life, military or otherwise, but it is a valuable physical exercise. In the same way, rigorous academic study is central to exercising the brain. Mathematics in particular is as important to develop logic and critical thinking as push-ups are to strong muscles.

In the modern world, no job is "brainless" (except, perhaps, for reality TV). There is so much automation and connectivity that it's impossible to be illiterate or innumerate in the workforce. Car mechanics increasingly need to be proficient with an oscilloscope; farmers increasingly internet connected. Even besides economics, our democracy and society requires informed individuals.

I think that this point reaches even further. There is often a question of whether university degrees are "worth it" when there are already so many graduates in the job market. Should our society invest in pumping out so many graduates? When every one of its members is responsible for taking part in its politics, looking after the environment, representing it internationally, I don't think it can afford not to.