Having been doing a bit of math tutoring and seeing a modern math text book, I think the usefulness stuff has been oversold. The kids can’t even find the actual math in the book since it is so full of side bars, examples and the like. You’d think they’d at least use some typography and layout skills to make the book easier to navigate.

The problem is that math has always been useful. Even animals do simple arithmetic when it serves their purposes. Arithmetic started out as accounting and calendar keeping. (Writing started out as a way of keeping traders honest.) Geometry was basic to building and land allocation. Trigonometry was essential in astronomy and later navigation. Calculus was invented for astronomy and artillery. Math is uncannily useful. In many ways it is like magic. You manipulate symbols on a piece of paper and the world has to obey.