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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!

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  • $\begingroup$ There's probably more than one way to prove the theorem you link to, and certainly some of the proofs are more clearly motivated. It's a very nice trick anyway, and mapping into a different group is a natural thing to do. Expecting this to solve the question isn't necessarily. $\endgroup$ Commented Feb 27, 2021 at 21:06
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    $\begingroup$ Do tricks really exist in mathematics? I'm not sure. $\endgroup$ Commented Feb 27, 2021 at 22:31
  • $\begingroup$ @PietroMajer By trick I don't mean a magical result, but a new method or a result I don't immediately see where it can come from... Completing the square is a trick we learned to solve quadratic equations for example. $\endgroup$ Commented Feb 27, 2021 at 22:47
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    $\begingroup$ There is this mathoverflow.net/questions/363119/… quite popular MO question ... $\endgroup$ Commented Feb 27, 2021 at 23:44

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