True enough, except it's also along the lines of memorizing the works of Cicero or knowing all of the books of the Bible off by heart: It's useful at developing a skill that the correct tools render obsolete (cheap books in the case of the memory feats, computers in the case of the arithmetical ones). Similarly, knowing Latin and Greek had a purely practical motive as well back then: It marked you as a member of the social elite, defined as people who had enough leisure to study objectively useless things such as Latin and Greek. Memorizing paradigms wasn't something a farmer's son could be expected to do, after all.

I suppose my point, which I expressed poorly, is that it can be interesting to examine how technology impacts coursework.

> that problem would take you hours to solve

I don't know, two Newton iterations are enough:

  *GHCi> let croot f x = x - (x^3 - f) / (3*x^2) in take 5 . iterate (croot 0.0093) $ 0.2
  [0.2,0.21083333333333332,0.2102957483409451,0.2102943717551532,0.21029437174614204]

Guessing 0.2 as a starting point is obvious enough because 0.2^3 = 0.008.