On a recent plane trip, I was reading a very abridged version of (the ten thousand page long!) Church Dogmatics by Karl Barth, and I found something totally beautiful.

Given a text in two languages, is it possible to uncover the meaning of individual words?

Today, I was about to sit down and read a paper (in French--I may not speak in tongues, but apparently I can read in tongues, so to speak!), and I thought to myself about how nice it would be to have a cookie. I went to Uncle Joe's, I went to the Classics Cafe, I went to Cobb's coffee shop, and then I gave up, for there were no cookies in any of those places, places which so often appear to be the source of cookies.

Someone contacted me with some questions about Bayesian document clustering; with that inspiration and a free afternoon a few weeks ago, I took a Hebrew bible and built a matrix $(A{ij})$ where $A{ij}$ equals the frequency of the $i$-th (Hebrew!) word in the $j$-th chapter of Genesis. I calculated its singular value decomposition (supposedly this is "latent semantic analysis"), and then took some dot products (calculating the "correlation" of chapters)...

There are usually courses at Mathcamp about surfaces; there should be courses about orbifolds! For instance, knowing that the smallest hyperbolic orbifold is the (2,3,7)-orbifold, having orbifold Euler characteristic $-1/84$, immediately gives that a closed hyperbolic surface of genus $g$ has no more than $84(g-1)$ isometries (preserving orientation); this is "Hurwitz' $84(g-1)$ theorem."

At a recent Pizza Seminar, Matt Day gave a lovely talk explaining why it isn't possible to classify 4-manifolds.

This is a question I wandered into accidentally years ago now, which I think other people might be amused to think about (or more likely, put on an abstract algebra exam).