i agree for the most part. i believe our abstract mathmatical concepts are more archaic than school learning.
school learning 'civilizes' those understandings if you will with the systems of math that mankind has standardized. probably you realize this as well and it may seem i'm more or less nit picking. but i think it is something more than that. i can never forget an experience i had in elementary school. the first formal math class i can remmember. the teacher taught us how to solve some addition problem. i didn't pay much attention but took the lecture in just as a result of being in the class room.
the teacher assigned us a problem to solve. i wrote the answer down on my paper and that is all. the teacher comes by my desk and says that is correct but how did you get the answer. i couldn't even explain it to her other than i'd figured it out in my head. she told me that was fine but she wanted me to write out the solution to the problem on paper so she could see that i learned how she had shown how to do the problem.
i barely passed that class with D's i think.
i think what the difference is with this learned concept of number that you speak of and the abstract things i'm trying to refer to is that one is force fed then regurgitated on demand and the other stems from ones natural ambition to understand and from ones creative activity.
it is surprising that you would take a stance that "then an abstract entity is about the world". i don't disagree with this but if i remmember correctly in a past post arguing against Dr. Dick's paper i thought you took a stance against the idea that mathmatics has to do with mapping reality.