I have some personal criterion to choose my graduate students including PhDs. Here I would like to know what my colleagues' criterion are to choose their math PhD/MSc students. I hope this may help me to note some subtle points which are important but less well-known about choosing a math PhD student. In fact I would like to know more on those useful abilities which a math PhD student should have.
Question: What are nice criterion to choose a good PhD student in pure mathematics?