The Garden and the Jungle
(1)
I love the place I'm working this summer. (A smallish proprietary trading firm in lower Manhattan.) It has one of the most vibrantly intellectual atmospheres I've seen anywhere, and the problems that we're working on really are interesting, often novel, and eminently practical. For a place that aims to compete in international financial markets by hiring the best mathematical talent that (1) cool math problems and (2) money can buy, it's...just about exactly what you might expect.
In particular, I'm in love with my current research project, which is easily the coolest thing I've been asked to do yet. (I also interned for all of last summer there.) What exactly it is is proprietary (sorry), but it has me mixing machine-learning and stochastic calculus in some really cool ways that have me alternating between coding furiously and filling up whiteboard upon whiteboard with math. Also, I recently got yelled at for taking up too much computing power on the shared intern server, so I got upgraded to supercomputing-cluster