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Now, I'm no mathematician but I really want to become one in the near future. I primarily want to ask people who've attempted to do mathematical research, how was it like? And also, how hard was it?
Another question is, what are your best tips for anyone attempting to do mathematical research? Also, if possible, how different it is from competitive mathematics or "problem-solving".

  • And what do you want to research? – FShrike Sep 03 '21 at 07:13
  • @FShrike Whatever I happen to excel at... I won't research things I'm not qualified to research... or at least up to my own standards of myself. It's not like I want to do research now... just that I want to have a projection. –  Sep 03 '21 at 07:14
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    First and foremost, you need to be willing to be frustrated 90% of your time, so unless the remaining 10% make you feel really great it is not worth doing it. – asdq Sep 03 '21 at 07:20
  • @asdq I spend days on proofs, and I'm fine. I think I can pull through. I feel really happy when I finish a proof after some hours, and I don't know if I'm being naïve by assuming I'm going to feel the same way there... but who knows? –  Sep 03 '21 at 07:24
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    Fair warning: the frustration of finishing a proof after some hours is peanuts compared to finding a counterexample to what you were trying to prove after four months. – 5xum Sep 03 '21 at 07:49
  • And also the solution to an important problems after a few years pales in comparison to a few hours for a proof. :) –  Sep 03 '21 at 08:07
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    @5xum Even worse is to work years on a problem, find a great result just to find out later that someone has done this already. – Peter Sep 03 '21 at 09:17
  • @Peter That reminded me of this MO post which, granted, goes somewhat in reverse of what you describe. But still. – Arthur Sep 03 '21 at 11:21

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