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Intuition in mathematics

  1. Sep 20, 2012 #1
    A funny thing happened to me recently....

    I solved a complicated math problem (for me anyway), and it was almost as if I had no idea of what I was doing. I just started writing.... and it kind of came out, unconsciously.....
    I think I know why Poincare said that intuition creates while logic verifies...

    Can anyone elaborate on intuition in mathematics?
     
  2. jcsd
  3. Sep 20, 2012 #2

    lavinia

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    my experience is that mathematical truths appear in the mind suddenly rather than coming from algorithms. Often insight even happens when you are not consciously thinking about math, I do not know why this is true,
     
  4. Sep 20, 2012 #3
    Hm... I think that is broadly true. I think that the mind produces such occurrences after plugging away at the problem while you aren't. However, it is important to note that the breakthroughs often come as a result of much conscious work.
     
  5. Sep 21, 2012 #4
    I think it's important to HAVE intuition, and to keep developing it. But at a certain point, intuition can be more of a burden than anything else. Intuition lies. Especially when dealing with things that don't behave nicely (infinity, for example).
     
  6. Sep 21, 2012 #5

    lisab

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    That's how it is for me, too - not with just math but with physical problems, too. But wrt math, I always thought that I get insight-all-at-once because I never took very advanced math (just up to advanced calculus).

    I've also found that getting solutions suddenly makes it very difficult to explain my problem-solving process to someone who's struggling. I mean, "Read the problem, think a bit, and then the answer just comes into your head!" is not very helpful :wink:.
     
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