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Here's what happens. I get stuck on some proof or some mathematical construction and I end up staring at the problem for hours, sometimes not making any progress. I do this because sometimes I think that I'm being lazy, I'm not thinking things through, or I'm just not thinking clearly. This approach is not practical because I only end up falling behind on other work. I don't like to look up solutions because I feel like, given enough time, I would be able to come up with the answer (or some good reasoning). But maybe I should start looking for answers after a shorter period of time. I don't know what the right thing to do is.

Do you guys have similar problems? Should I feel bad because I have to look at solutions? Or is this just part of learning?

  • 23
    If this never happened to you, you would either be a true genius or not challenging yourself enough.2012-02-21
  • 22
    The difference between you and professional mathematicians is that mathematicians work on a problem for months, indeed years, without fully solving it.2012-02-21
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    Good question. Well, reading different solutions and proofs is a part of learning, you can't go to a cave and invent the whole known math by yourself in one year. But it's always good to think on your own. I think it's a matter of common sense how much you should think yourself and how much time you should spend reading. Probably it depends if you're learning your favourite subject or something you're not particularly interested in. And of course what other duties you have, and how much time (and energy!) is left for creative thinking on your own.2012-02-21
  • 0
    If you are stuck with a problem for hours, then it usually is a good idea to get a little help. If looking up an entire solution bothers you, then (now that you are a member of MSE) you can always come here and ask for hints/ partial help. The people here are pretty good with not giving away complete answers if you explicitly mention in your question that you are not looking for complete answers. Also, if you are in a university setting (which is the case with me) you can always go to your professor or the TA and ask for hints.2012-02-21
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    I think every student learns the hard way (and I am excluding professional mathematicians here who work on problems that are still unsolved) that when you have a lot to learn, it is usually not a good idea spending days on one particular problem. But, sometimes spending some time on a problem can be really enlightening.2012-02-21
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    For the record I have been stuck on the same problem since late 2010.2012-02-21
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    Being stuck on understanding one theorem for hours, resulting in you getting behind in your other work, is not worth it. If you can't understand a proof or problem after 30 minutes, move on. Look at it again in a few days. Professional mathematicians may be stuck on one problem for a long time, but they're professional mathematicians doing something no one has ever done before. They are stuck on trying to come up with a proof that no one else ever has. If they spend a year on a problem that has already been answered, they are wasting their time.2012-02-22
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    I know how you feel: not long ago, I watched a YouTube video where a high-level mathematician pleaded his viewers never to look at the answer for a problem they got stuck on. Ever since, I have been overly hesitant to do so whenever I notice that I have hit a brick wall in the flow of my understanding. Last time that happened to me, I asked my professor instead, and he gave me just one hint, that little push that I so badly needed to put an end to my intellectual misery. Afterward, I never regretted having spent so much time on that problem.2012-02-22
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    Just a little advise : if you get stuck for hours it's probably time to get out and think at other things. The solution comes often without thinking consciously at the problem (read Poincaré)... Trying alternative approaches may be helpful too.2012-02-22
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    this is just part of learning math. My open book Number Theory class had just 5 problems. I finished the first 2 questions in an hour (they were computational). the third I finished after half a day more, the 4th i finished after the second day, and the last problem took the whole week.2012-02-21
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    If you really want to solve the problem and you think you can solve it if you really work hard on it, then do it. Otherwise I recommend you to forget it for a while and attack other problems unless it is really necessary to know the solution.2012-11-18
  • 0
    There have been requests that this be made Community Wiki. It looks like a good fit to me. If you have a problem with this, let me know.2012-11-18

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