I think it wise, and only honest, to warn you that my goal is immodest. It is not my purpose to "transfer knowledge" to you that, subsequently, you can forget again. My purpose is no less than to effectuate in each of you a noticeable, irreversable change . I want you to gain, for the rest of your lives, the insight that beautiful proofs are not "found" by trial and error but are the result of a consciously applied design discipline.,...
Your obligation is that of active participation. You should not act as knowledge-absorbing sponges, but as whetstones on which we can all sharpen our wits.
I fear that the force of this as a "school of magic" will be lost on anyone who hasn't learned the difference between a proof and a heuristic, or rule-of-thumb, or hopeful dependence on the sun's having risen every day so far. Indeed, I am told that most people think of mathematics as the exact opposite of magic; although, looking at the wild-haired oddities represented doing both, there must still be an undercurrent on my side.
They even share the tragedy that we don't really live in that world; we probably live in a world of best guesses and rules-of-thumb. (Philosophy and applied science attack me from opposite sides; I duck.)
I don't know how much a capacity for joy in proof is inborn. I hope math (and philosophy and science) try harder than the Ministry of Magic to share the wealth. I know I judge modern representations of magic by whether they are at least as numinous as my (not impressive) experience of science; really, I think that's fair. Doesn't have to be the same, but has to be as gripping. And that's the thing that disappoints me most in the Harry Potter novels and the widest reactions to them; they are claimed to be fascinating because they are magical, and people are being palmed off with tinsel.
and some summaries of her essay think the magic fails psychologically, by not being attached to the development of the character's sexuality; I have my doubts about it politically, since the wizarding world seems pretty much parasitical on the mundane one. These might be ensubtletied in later books; anyhow, there are plenty of arguments about what art and power should be used for. Sex and freedom are only two of the favorites. The Potter novels are doomed to being library books in my household because the magic is neither art nor science; power at worst and marketing at best. Anyone reading this, as I write it, in summer, could see a larger world in a bean-seed in a cup of dirt. (You could even live bounded in a nutshell and think yourself master of infinite space, if it were not for the negative curvature.)
Dijkstra archives, URL: http://www.cs.utexas.edu/users/EWD/