I find a sense of curiosity important. It is unfortunate that students will spend years working on a PhD before they begin their dissertation, only to discover they hate research. While it is vital that a student can learn math that has already been done by others, intellectual exploration is necessary to continue on in research after graduation. We emphasize the need to solve problems, but in research, it is also important to have the independence to determine what you are interested and to ask your own questions.

While this is something that does not show up in the application itself, I would find my interest piqued by a reference letter that mention's a student's curiosity.