I think the issue that until a budding mathematician reaches upper-level undergraduate classes, foundation must be built, and built quickly, in order to catch him up with the current rigor of mathematics.<p>It's the same with computer science – eventually you can learn the nitty gritty, but you don't start out learning the x86 ISA. You start out with some sort of high-level language, be it C or Python. Eventually, you can learn the details.