Question: Stack-Exchange,
I am a freshman in Mathematics Department.

I always learn mathematics the hard way. Everytime I learn mathematics on my own by reading from Mathematics textbooks, I would read the definition, try to figure out what it really means, stick new definitions which concepts that I already know, prove theorem without ever reading given proof.

But recently, I find this method cumbersome. In order to get a deep level of understanding those concept and solve a good amount of problems, I trade it off with a lot of my time, and my energy.

My seniors tell me that I should learn from different source of material to get more insight view, and separate the processes of learning theory and problem solving. I should read all the theory before trying to apply them to save times. But I'm used to the way of Pólya's mouse, so I am worried that I won't be able to catch up with all my classes like this. I want to try the way my seniors told me; that might be faster. But I want to know if the method would come with a loss of depth in understanding.

So I am asking for help. Also, please give me some tips to boost up the performance and the quality of learning mathematics all by myself. Thank you all very much.

Answer: 
I don't know why, but after reading the question, remembered this saying:

> 
> Theory is when you know everything and nothing works. Practice is when everything works and nobody knows why. In this office we combine theory and practice: nothing works and nobody knows why.
> 
> 
> 

Summing up. I agree with THE LONE WOLF. And do problems as much as possible.

I would add: if you have doubts, ASK.
I wish I had you for a teacher or a student. I am long past the age when I can take classes in school, and everything I do is driven by curiosity. Recently, I became interested in retro-tech and began with the table of four-place logarithms we were given in high school. (Before computers or calculators log tables were the one of the instruments by which human computing power could be amplified.) Wow! What a bunch of errors in that thing, but I am finding ways to weed out the worst mistakes and improve the accuracy. 

I think I have discovered things about log tables that nobody else knows. It is an empowering feeling. And some day, when some conference needs some kind of paper, I will have one pre-generated. Most likely this would be the HHC 2017 conference dealing with HP calculators.

It is a good way to learn. Never quit!