Last month, the folks at Lab49 explained how to compute the derivative of a data structure. This is a great example of how to write about mathematical subjects for a casual audience: They draw analogies to well-known programming languages, they follow a single, well-chosen thread of explanation, and there's a clever payoff at the end.

The Lab49 blog post is, of course, based on two classic papers by Conor McBride, and Huet's original paper The Zipper.

If you're interested in real-world applications of this technique, there's a great explanation in the final chapter of Learn You a Haskell for Great Good. If you're interested in some deeper mathematical connections, see the discussion at Lambda the Ultimate.