Is it useful to learn math by proving a formula/theorem?

Question

To learn mathematics, I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ask you whether this is a good/efficient idea to become proficient in math.

My theory behind this question is that a theorem reflects several things in mathematics.

1. It reflects the existence of a category of problems/ideas that is meant to deal with.

2. It provides a method or part of a method to solve a problem.

3. It reflects rigorous mathematical expression of the insight of a mathematician. This means that a theorem is the crystallized form of expressing an idea.
4. Being able to prove or to completely understand the proof leads to enhanced knowledge of methods used in proving mathematical ideas and give a greater clarity in what exactly the use is of the theorem/formula. (I contrast this with solving equations with a formula, which you can do without completely understanding the formula)

If this is not a good/efficient idea, would you be able to specify why not? I'm only asking about this as a complementary method.

Answer 1

Spending one day on each mathematical theorem is like spending one day in each settlement in the world. It is

1. Impossible, because there are simply too many theorems.
2. Impractical, because it makes no sense to spend one day in a 1000-people town, and one day in London. In the same way, some theorems deserve far more than a day, and others can be handled in a matter of minutes.