Math.
Odd, I was worried about being bored while stuck in the middle of nowhere for a summer. I brought plenty of amusements to keep myself company: a shelf full of books, juggling balls, my flute, a computer.
And yet I haven't touched the books since I got here, and haven't been bored. Why? Because we've been doing math all the time. When we're not doing math, we've got two apartments full of fun students' stories to tell, but often enough because we're all working on problems together, the conversations devolve into working on math again.
My desk is strewn with papers, theses, pre-prints, book chapters. I'd never heard of the Stein Chen method, or of pebbling, and certainly not of forbidden minors. A graph is planar iff it contains no K5 or K33 minors. How cool is that? Unfortunately, nobody on the internet seems to know anything about coloring non-planar graphs. And speaking of which, "Why is a planar graph like a priest? They both have a finite number of forbidden minors."
Today a book delivery came: The Cauchy-Schwarz Master Class and Ramsey Theory on the Integers. The Ramsey theory book was for us. Anne actually jumped and squealed when she got to open it.
Last night we were up past 3 am, verifying a conjecture to one million (or, more importantly, refining our algorithm so it would actually be able to compute that high in a reasonable time period). Of course, we got lost in the number theory trying to actually prove it, but it was fun anyways. And all because Annalies realized there was more structure to what we were looking for than we realized.