So, he probably needs to be aware of how easy it might be to move into CS if he starts in math and later decides he wants to change.
Typically, CS can either be in the College of L&S or College of Engineering (or both like at Berkeley). Usually at privates it is easier to change from a non-engineering major into CS. But, for example, at CMU it would be very difficult to change from math to CS (though it would be easy to minor in CS).
He sounds similar to my son, except my son is a physics/CS guy who took Calc BC in 10th and started research around 10th.