A gem from reddit.
In Abstract Algebra, we were discussing normal subgroups. A student asked how it was possible that two isomorphic subgroups might differ with respect to their normality. My professor, without missing a beat, responded:
Being normal is not about who you are, but rather where you live.
— Professor Shahriar Shahriari of Pomona College
(I linked to inner automorphism since I think it is easier (at least to me) to grasp the concept of normal subgroup if we start reading there. Then, if we understand inner automorphism all we need to know is that: In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group of which it is a part.)