> building intuition is the same thing as struggling to solve a problem. Not necessarily. Intuition (borne out of Imagination) is for understanding the domain

> building intuition is the same thing as struggling to solve a problem. Not necessarily. Intuition (borne out of Imagination) is for understanding the domain concepts even before there is a problem to solve. This is the reason i am against the oft repeated advice "solve a lot of problems to learn Mathematics" which merely leads to mechanical "plug and chug problem-solving" with no real understanding. Instead one should spend a lot of time trying to grasp the concepts well, map them to the appropriate notations used and then study a few fully-worked out problems to grasp the "applications".