I am PhD student and my research work heavily requires abstract mathematics . I have completed some of my coursework in mathematics.
I am currently reading a research paper which requires lot's of mathematics and I am doing that mathematics but it appears to me that I have been stuck in the proof of one theorem which requires the proof of 7-8 theorems. To understand the proof 7-8 theorem it took 2 weeks and when I read the required proof I get it but not entirely so I again read it 6-7 times till now each time although I have identified something new. But I have a problem here the whole process requires more than one month and it felt to me that I have been stuck there.
Question : Is my way to understand the proof fine or it can be improved so that I don't get stuck in one theorem
I have been there. In my opinion, the answer is simple and I remember my advisor telling it to me many, many times - and I remember myself refusing to accept it, because it involves so much work and for a long time seemed infeasible: Make concrete examples. For everything you try to understand, come up with the simplest meaningful example you can imagine. If you cannot do that - and this can be painful, take a step back and figure out what the objects are that you are interested in and search for ones that you can manage to comprehend by hand, or by computer. Once you have an example - understand the proof for this one example first. If you see how to generalize then, good! Otherwise, you should find another example and repeat.