Finite Simple Group of Order Two

Apologies in advance for the high nerdiness content of this post.

Someone forwarded me this video, which brought back memories of my years studying math...



Some people find something in adolescence that engages them, gives them order and saves them from the banality of the world (and from themselves). For me, it was mathematics. I attended math camp for a summer during high school, and became enamored with number theory, where powerful proofs followed from simple axioms. We were taught to think deeply about simple things, as we explored the world created by Euclid, Fermat, Gauss, Galois,...

I studied math in college and then continued to math "boot camp" (the first year graduate program) at the University of Chicago. It was a small but highly academic and cohesive program. One of the highlights of the U. of C. math program was a tradition in which second-year graduate students put on "beer skits", a collection of skits and musical parodies. One song I remember was a parody of "Simple Gifts" called "Simple Groups":

There are groups that are simple,
There are groups that are free,
There are groups that have order exactly thirty-three

For the non-math majors: In group theory, groups have ordinary-sounding mathematical properties such as being "simple" and "free" and having "order".

Bonus: Here are "New Math" and assorted math songs by Tom Lehrer.