<p>Yeah stuff like that – it doesn’t have to be quizzing applicants, but simply about what they think of various subjects, what they like, where they see the subjects being important to them/their courses of study, anything of that sort. </p>
<p>Tricky question, I think it’s hard to define “number theory” for me 
– only had exposure to algebraic number theory myself and that was really a special blend of commutative algebra, Galois theory. </p>
<p>But definitely, it’s about throwing around concepts to me – one could even ask about what some interesting problems that have been seen before are. Open-endedness is good, given it forces an applicant to actually come up with something on his/her own, rather than answering something pre-prescribed – tough to come up with something technical on your own and talk about it and fake passion about it, no?!</p>