Insight: Sudden or special understanding of a topic.

One place where insight plays a special role is in mathematics, where one suddenly comes to see the crux of a proof or argument, usually because suddenly one's perspective alters, so that one can see the same thing in new terms.

There seem to be many different kinds and capacities for insight, as anyone knows who is quite intelligent and can play chess fairly well, but is not himself a grandmaster: Grandmasters in chess, although commonly quite intelligent also, have a special knack for understanding chess positions. In part this seems to depend on some special native ability or abilities, and in part it usually also depends on a considerable amount of knowledge and training.

Also, it seems always a fairly specific gift: Even the greatest mathematicians tend to be especially good in certain parts of mathematics. And grandmasters in chess tend to excel in chess, but not in other subjects (even if they are more frequently than average persons good in mathematics).