Learning math by analyzing/proving theorems?

Hello I want to learn mathematics.

In order to do this 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 instead this is not a good/efficient idea would you be able to specify why not?

I define efficiency as (energy spent on gaining understanding in mathematics/ total energy spent)

• The answer to this may be opinion based reflecting the learning style of the students involved. For me learning by proving theorems just doesn't work. – Karl May 28 '15 at 8:42
• I do really hope that the answer to this question is not merely opinion based. I hoped to find educators or mathematicians who have experience with this approach, as I want to use it for myself but also teach more basic math to others using this method. Oh, and also my goal is not to pass exams, my goal is to gain a deeper understanding in math. – St.Clair Bij May 28 '15 at 8:46
• This is is better suited to the maths educators site. Personally I believe teaching especially basic maths with theorems is a bad idea and a mistake new teachers frequently make. Others will disagree naturally but I'd urge caution with this a approach – Karl May 28 '15 at 8:52
• Thank you for the suggestion. In the case of really basic math of course I'd rather have them being able to perform the calculations before going on to understanding theorems. – St.Clair Bij May 28 '15 at 8:56