And a link from that page is about an atypical mathematician and his work on both "stochastic partial differential equations" and a sound editing program for DJs. I'd no notion that anybody was looking at PDEs with a random coefficient, but I guess I don't get out much--I think I can see how they'd come up in music amplification problems. (stochastic means random, in a precise sense) An interesting character, and interesting work--but I'm kind of reluctant to tackle his magnum opus right now. I think I get the idea of the shape of his project, but the abstract had about 8 terms I didn't understand and the table of contents was worse.
UPDATE The Brownian maps don't seem to be metric spaces, exactly, though their "geodesics" get as weird as my "lines" sometimes. Interesting, but it would take quite a bit of study to get up to speed on the subject.