What do mathematicians think of themselves, and what do others think of them? These musings, the theme of a special session at the San Jose MathFest of 2007, resonate with a large and diverse group of mathematicians and students, for these are the questions that govern the way that mathematicians live. A large and diverse group of mathematicians and mathematical people were assembled to offer their views on these matters. The contributions represent a vast array of perspectives on the psychology of the mathematician. It is hoped that readers will find the thoughts assembled here stimulating and cause for further rumination.