And while I'm recommending things, I would be remiss to leave out
Harry Potter and the Methods of Rationality, a truly glorious piece of fanfic. It starts from the premise that Harry's stepmother, instead of marrying an abusive jerk, married a university professor. Hence, Harry was raised in a supportive environment for a gifted child, and learned lots of science, math, and a great respect for the scientific method. When Hogwarts presents itself, he is determined to discover the rational basis of this seemingly irrational magic. And maybe take over the world, depending how things work out.
My only significant complaint with it is that it's a work-in-progress, and I desperately want to know
what happens next! I know no higher praise. It hasn't yet made me cry, but I suspect that it will. It *has* made me literally laugh out loud in many many places.
It does take for granted a certain level of familiarity with the basic Harry Potter story, but having been exposed to the first three books and/or movies should cover all but a few references.
(h/t to
siderea, who in turn got it from
nancylebov.)
Then I went and read Harry Potter and the Wastelands of Time, which Less Wrong (is it, in fact, Eliezer Yudkowsky?) recommended. It's very good, but also lacks being finished.