When is something "obvious"? I try to be a good student but I often find it hard to know when something is "obvious" and when it isn't. Obviously (excuse the pun) I understand that it is specific to the level at which the writer is pitching the statement. My teacher is fond of telling a story that goes along the lines of 

A famous maths professor was giving a lecture during which he
  said "it is obvious that..." and then he paused at length in thought, and then
  excused himself from the lecture temporarily. Upon his return some fifteen minutes later he said "Yes, it is obvious that...." and continued the lecture. 

My teacher's point is that this only comes with a certain mathematical maturity and even eludes the best mathematicians at times.
I would like to know :


*

*Are there any ways to develop a better sense of this, or does it just come with time and practice ?

*Is this quote a true quote ? If so, who is it attributable to and if not is it a mathematical urban legend or just something that my teacher likely made up ?

I believe the famous mathematician was G. H. Hardy, and I am sure he had a different view as to what is "obvious" compared to lesser mortals (like myself). 
I would say that "obvious" should only ever be applied to things that the speaker believes that his listener should find "simple" ..
