Another thing that is often missed is that we think we “understand” something when in fact we just got used to it. Even such simple concept as “number” would probably be very difficult to explain to someone (who either doesn’t know what a number is or wishes to “really understand” it).
Oh yeah. The history of numbers is long and complicated. I think today we take for granted the idea that numbers are objects (in some abstract sense). In the past, there was simply no concept of number as a thing. Numbers were used for counting or measuring, so they existed only as adjectives attached to their objects of counting/measuring, not nouns in their own rite.
Well the natural numbers are the decatigorification [1] of the category of finite sets.
I won't speak to other kinds of numbers but it's funny how category theory helps answer that question as well.
