TITLE: Teaching abstract maths concepts to young children.
QUESTION [16 upvotes]: I am interested in opinions and, if possible, references for published research, about the pros and cons of teaching abstract maths concepts to young children. My younger brother (five years old) understands negative numbers and square roots so I was thinking of trying to teach him about complex numbers and maybe some other concepts, but my elder brother (who is doing a maths/stats degree) said it was a crazy idea (without elaborating, but that's what he's like). 
Update: I quizzed my brother on why his thinks it is crazy and his response was "Don't you think there is a reason why 99% of maths teachers have a degree in maths ?"  I'm at high school by the way.

REPLY [2 votes]: It really depends on what kind of a person your younger brother is.  If he has the mind of a mathematician (which sounds likely, given his advanced knowledge and your family history), then go for it.  It will intrigue him, and teach him to look at things in mathematically different ways.  On the other hand, if he is like 99% of the population, it would probably only serve to confuse and/or bore him. 
So I'd say go for it, and if he doesn't byte, then wait for him to get older.  It's not like you're making stuff up (there really are such things as imagainary numbers, and he probably will end up learning about them eventually).  
And remember that he is five, so unless he's a Gauss, he will need things explained slowly and in the most basic of terms.  He won't have taken mathematical concepts for granted yet that you probably have (for example, I remember when I was five or so, I did not yet have it ingrained in my mind that addition and multiplication must be commutative).
Finally, if he doesn't seem to be able to understand it, there are other "advanced" mathematical concepts that are more accessable to younger children because they are less abstract.  Prime numbers, for example.