When I was in physics grad school, we'd sometimes amuse ourselves with the game "grad student or homeless", which involved guessing the circumstances of a given person we might come across. It was surprising how often we were wrong... :) There was one guy who I had seen at the weekly colloquia for almost a year, who I had always assumed was a homeless, probably mentally ill guy, who was just there for the food. Then one day he asked an incredibly technical question in the middle of a lecture. I think he was actually from the math department.