TITLE: I take it so long everytime I learn mathematics myself. What should I do?
QUESTION [35 upvotes]: 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.

REPLY [2 votes]: 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!