I have found quite a bit of information of how, on a neurological level, we learn the most basic forms of maths. We seem to be hardwired from the get go, to deal with manageable quantities, can intuitively decide whether something is more or less and even add or subtract small integers together. There have even been tests that six-month-old children already have an intuitive sense of small numbers. Basically, this covers basic arithmetic on natural numbers.
However, I had a hard time finding anything about how we learn to deal with more abstract, higher level maths. What happens in our brain when we deal with functions and variables? Will they still be processed in the same region that is used for counting? - Especially when it comes to functions that do not even take numbers as inputs or outputs.
I am asking about math that can not be solved with simple arithmetic, and I wonder how an intuition of a generic mathematical concept would be represented in our brains. Has any research on this already been done? - Like something which isn't a numeric algorithm but rather symbolic manipulation.