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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.

Edit:

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.

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The parietal area and prefrontal cortex from the neocortex are the source of ones ability to perform algebra and most other logic and analytic intensive tasks.

In a brain imaging study of children learning algebra, it is shown that the same regions are active in children solving equations as are active in experienced adults solving equations. As with adults, practice in symbol manipulation produces a reduced activation in prefrontal cortex area. However, unlike adults, practice seems also to produce a decrease in a parietal area that is holding an image of the equation. This finding suggests that adolescents' brain responses are more plastic and change more with practice. These results are integrated in a cognitive model that predicts both the behavioral and brain imaging results.

-The change of the brain activation patterns as children learn algebra equation solving

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Thanks, very interesting! This doesn't fully answer my question, but it is a start. This is still basically arithmetic, even if it's more sophisticated than direct questions. I'd like to know how we form connections on a more abstract level of maths, when things are basically entirely symbolic and numbers increasingly go away. I suppose the answer will always be that this happens in the neocortex, though how is it represented in the brain? Is there anything on that already? –  kram1032 Jan 23 at 22:48
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@kram1032 the parietal area holds the symbols while the prefrontal cortex manipulates them this includes purely abstract logical equations like diffy eq. –  caseyr547 Jan 23 at 22:58
    
in retrospect, I asked this question rather poorly. I'll check your answer as correct - you did pretty much answer the question I asked - though I will try to think of a better way of asking what I actually meant. Thanks. –  kram1032 Jan 29 at 21:12
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