Hey, are you looking for a great mathy thing to do this summer? Try applying to PCMI. It's awesome, and Park City, Utah, is a fantastic place to be for three weeks of the summer. When you go there, you feel like the sky is bigger/cleaner and the days are way longer somehow. And there are some great math teachers who are passionate about teaching and doing math. Although you can find last year's problem sets here, it's hard to imagine the level of energy and camaraderie unless you've been to PCMI.
It's magic for three weeks, and you'll miss it when it's gone. There is also a generous stipend that covers most of your expenses.
Apply today! Deadline is the end of January, so you had better hurry.
PS. If you do go to Park City, bring your yoga mat if you've got one. It's utterly beautiful there to do yoga outdoors. Also bring your hiking shoes, your best karaoke persona, your fine dining belly, and your thinking cap. Just sayin'.