Really!!! They are (or were, anyway, when they made that recording) a group of math grad students at Northwestern University. Reportedly that video was taken at a department meeting, and the people laughing are their fellow grad students and advisors.

They recorded some other stuff at one point in time and it appears you can still buy the CD (http://www.kleinfour.com/) through a couple places, and I have this hilarious Christmas mashup of songs which they also did.