If you have a colleague to hand who doesn't know about the idea you're trying to understand but has the appropriate background, then that's brilliant, because you can test your understanding by trying to explain it to them. Similarly, when I've had occasion to write up brief expositions or notes for a talk on a topic, I find it allows me to efficiently identify and dispel many of the little uncertainties and misunderstandings that pop up in great numbers when you first learn about something. It may be overkill, but if you can do that kind of thing rigorously and thoroughly without your intuitions changing, then you can certainly congratulate yourself on knowing what you're talking about.

Making sure that you have comprehended a concept
What are people's views on this?  To be specific: suppose a PhD student has produced a piece of original mathematical research. Suppose that student's supervisor suggested the problem, and gave a few helpful comments, but otherwise did not contribute to the work.  Should that supervisor still be named as a co-author, or would an acknowledgment suffice?

I am interested in two aspects of this. Firstly the moral/etiquette aspect: do you consider it bad form for a student not to name their supervisor?  Or does it depend on that supervisor's input?  And secondly, the practical, career-advancing aspect: which is better, for a student to have a well-known name on his or her paper (and hence more chance of it being noticed/published), or to have a sole-authored piece of work under their belt to hopefully increase their chances of being offered a good post-doc position?

[To clarify: original question asked by MrB ]
