alt Hacker NewsIt's why the invention of teaching has been so important. Took a long time for humans to develop calculus. A long time to then refine it and make it much more useful. But then in a year or two an average person can learn what took hundreds of years to invent. It's crazy to equate these tasks as being the same. Even incremental innovation is difficult. You have to see something billions of people haven't. But there's also paradigm shifts and well... if you're not considered crazy at first then did you really shift a paradigm?
And yet it is still taught in less than optimal form, lacking algebraic closure in ways that are completely unnecessary.
It isn't a secret, but the percentage of people who don't know that, plus the percentage of mathematicians who vaguely or more directly know that, but habitually use the broken, more difficult (i.e. less algebraic) notation is ... virtually everyone.
I am not trying to pick on calculus, this is everywhere. Important and useful concepts are right in front of all of us, that we don't see even in the context of what we are relatively fluent with.
Because we learn quickly, where we have (almost always inherited) the right preparatory perspectives (earned over lifetimes by others), we vastly overrate our ability to reason independently.