How/When do you get to the point of solving textbooks easily

[random_soldier]

So I was having a discussion with one of my teachers and they mentioned along the way in my PhD, I would learn how to formulate and/or understand where a question is coming from, be able to solve it and know exactly when I arrive at a satisfactory conclusion.

This would be quite a handy skill to develop from the get go itself, if I did not misconstrue the meaning. Any/all here know what I am speaking of and how I would inculcate such an ability?

 

[Klystron]

Categories help me determine the subject. Example: a lecture mentions "polarity". Term common in electronics, physics, chemistry, even psychology. Context helps determine the category; the category includes 'tools' to understand the subject.

Set theory helps me understand almost everything in mathematics. For instance, people have difficulty grasping "infinity"? My working definition involves 'some measure of a Cantor set'. Example: counting numbers, limited set of integers, cardinality of the set. Choose the set that matches the data and the metric applicable to the context under discussion.

Many concepts from math and physics such as limits and infinitesimals help me understand arguments and reasoning in other subjects.