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


closed as off-topic by José Carlos Santos, Lord Shark the Unknown, Math1000, Dietrich Burde, Matthew Towers Mar 30 '18 at 10:20

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  • $\begingroup$ Do you really need to understand the proof of the theorem, or do you just need to know how to apply it? $\endgroup$ – Lord Shark the Unknown Mar 30 '18 at 8:15
  • $\begingroup$ @Lord Shark the Unknown I need to understand the proof although I will be apply it. $\endgroup$ – user545172 Mar 30 '18 at 8:17
  • $\begingroup$ I'm an aficionado (I never did a PhD thesis), thus this is just my opinion as companion of previous answer. I know a video from the channel Sprouts in YouTube, with title The Feynman Technique. I think that your problem is the abstraction of your theory, thus another advice can be that you need to make metaphors of those tools-theorems or definitions used in the proof of your main theorem, draw of concepts f it is possible. Also you can make conceptual summaries on small cards. And it is good know the history behind this theorems (the preliminars in the articles that you are stuying). $\endgroup$ – user243301 Apr 1 '18 at 11:06

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.

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    $\begingroup$ Very good answer(+1). $\endgroup$ – Dietrich Burde Mar 30 '18 at 8:46