During a visit to Vanderbilt University last year, Billy Joel fielded a question from a freshman, Michel Pollack. To paraphrase: "My favorite song of yours is New York State of Mind. Can I play it for you on the piano while you sing?" To which Joel replied, "Ok." And off they went. It's a lovely impromptu moment. But it was a little too much for Pollack. A little overwhelmed by the whole experience, he got a 69 on his calculus exam the next day. But who could blame him. We have more impromptu musical moments below.