Vi Hart (a full-time mathemusician at Khan Academy) makes mostly short YouTube videos on a variety of mostly math and science subjects. She draws in a notebook while talking really fast, making insightful, surprising connections. She’s smart, funny, knowledgeable, and entertaining.
This brilliant video is, I think, a bit of a departure: a 30-minute piece explaining how 12-tone music works. Because of copyright law, she can’t play Stravinsky and Schoenberg, so she composes her own 12-tone versions of well-known tunes, with side-journeys into pattern recognition and the nature of art. By the end, she’s composed a four-part, 12-tone vocal version of “Mary Had a Little Lamb” that she sings herself. It’s a tour de force of music, science, art, and explanation.