This question is motivated by this one that I posted on math.stackexchange.
When I fail to solve a hard math problem (like the ones I presented in the linked post), I read a solution and I noticed that many times it includes a trick that I didn't see. I try to memorize it and make it mine, but sometimes it's very hard to do so because I don't see the thinking-process behind the trick (like for $\phi$ here). And this frustrates me. My questions are:
- Is it a common feeling in research?
- I wonder if I should write a list of tricks (that I'll update every time I see one), is that a good idea?
- Do you have any advice on how to get better at solving such problems? (I know that experience and mathematical maturity help a lot)
Thanks for your time!