Well, it's not something I normally have a lot of opportunity to think about. At first glance, I think he says a lot of things that are new to me, but ring true. So... I'll buy. For now. :-)

As for Inspector Holmes, what I hear when I read that is my students using it as an argument for NOT having to learn math, since they don't plan on ever actually using it in "real life".

At this age, their "little rooms" do have "elastic walls". They are still making neural connections in their brains. If I don't help them stretch those walls, then their brains—and their abstract thinking and reasoning abilities—will not develop to their fullest capacity.

But even with the math education bit aside, I still don't agree with the good Doctor. I believe there's value in the breadth of one's knowledge as well as its depth. Too much of either one—or too little—is a bad thing.