This compact explanation of the Discrete Fourier Transform is a few years old, but it's new to me; from Stuart Riffle via David Smith:
Putting the DFT into a single sentence is nice, but the magic is in the color coding. It really helps connect your physical intuition to the math. I love how this draws your attention to the different mathematical machinery at work (spinning, averaging, etc).
If you have no idea what I'm talking about: this is the core math behind "frequency decomposition," the technique that allows you to take a recording (or time history of data) and figure out the frequency content. As you might imagine, this is pretty important. Check out the Wikipedia entry for Fourier Series; it's got some gorgeously animated illustrations.