Not sure about "VI - Thou Shalt Try Doing Most Things Inside Thy Head". It justifies with something I hear often: "Because over-relying on tools and technologies can have some nasty side effects — and those include mathematical atrophy and higher math illiteracy.", but I think that's just mathematical snobbery. I think this attitude of tool allergy hurts mathematics, and scares people away from the field. Tools like SymPy make mathematics more enjoyable, at least for me, because it helps you tackle harder, more interesting problems, instead of only the toy problems its possible to solve by hand.