My son is 7 and half. One of his best friends is a 12 year old boy in his same private school. (BTW, I delayed my son for a year to go to school, he also has "late birthy month" like your son. It is great for him.). This 12 year old boy is very kind and smart. He talks everything in terms of numbers. When we were eating pizza, he would calculate the number of possible ways to divide the toppings for everyone at the table, and the number of possible ways that we could start eating the olive or sausage of the toppings. He does all these in his head. He is the best math kid is his 6th grade class, but noone in his class plays with him. His best friend is my son, a poor 7 and half year old boy who loves sports and cartoon drawing more than anything. But my son is facinated by his 12 year old friend's math talks.
We love seeing them together. So fun to watch a math genius growing up.