I have been doing mathematics for some time now. I am currently a UG in Mathematics and Computer Science. I like doing mathematics but as I progress, I notice that I don't remember certain theorems at all. I forget how to divide/multiply at times. I have forgotten almost all of the theorems that I learnt. And whatever I am studying I am likely to forget it soon enough too. So what are we expected to do ? Gain understanding and then move on, the theorems/results don't matter ?
All books on a subject have different theorems on a topic? Am I supposed to read all of them? I can write proofs but certain theorems are listed in the books that I hardly encounter again, why are they mentioned over others in the book ?
How do you know that you have proved a new theorem that hasn't been proved before ?