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John Von Neumann once said to Felix Smith, "Young man, in mathematics you don't understand things. You just get used to them." This was a response to Smith's fear about the method of characteristics.

Did he mean that with experience and practice, one obtains understanding?

  • 69
    No, he means that with experience and practice, one obtains experience and practice.2010-11-21
  • 22
    Anyway, I have always thought that this is unnecessarily pessimistic. I don't know why people are so fond of quoting it.2010-11-21
  • 5
    There is some truth in it. Of course, it's not a mathematical truth. More like wisdom. But everybody who has been a teacher and had trouble explaining things to students who were genuinely trying to understand must have somehow felt the meaning of the dictum.2010-11-21
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    I remember being dumbfounded when math students (I took it as minor) juggled around with integrals without being able to explain to me what they were doing and why the steps were valid. Fubini's theorem was among the more prominent things.2010-11-21
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    I think it means "no matter how much practice or experience you get, you will still suck!"2010-11-21
  • 1
    I think it means that experience and practice are not sufficient to obtain understanding, and that understanding is not necessary for manipulating mathematical terms and symbols to prove a statement or derive an equation.2010-11-21
  • 23
    A more constructive interpretation of von Neumann's cute rhetorical flourish is that experience and practice _change_one_, so that what may have once seemed alien becomes familiar. This psychological aspect of "learning" is very often grossly under-estimated, I think. So, yes, as far as I can tell, after I've seen a dozen examples of a phenomenon that at first seemed bizarre and counter-intuitive, and had some months to let it percolate into my head, I "understand it" in the sense that it now seems reasonable, and I can "act" with it as part of my reality.2011-07-08
  • 1
    This quote is too often used by people who find math weird and supposedly non-intuitive, which is very painful. I don't know in what spirit and why Von-Neumann said this. If you really track why somethings are done in mathematics, you will figure out/understand why things are done the way they are. And definitely in the case of the method of characteristics, you can explain why things make sense!2011-12-07
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    Maybe we're over-thinking this. It could just have been an insult to Mr. Smith.2012-09-21
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    lets not forget von neumann was highly involved with quantum mechanics, where this quote has many parallels eg with famous assertions by bohr, who said it was not the physicists job to _understand_ nature which in turn seems to have conceptual ties to [logical positivism](http://en.wikipedia.org/wiki/Positivism). another similar quote by my old math teacher [not sure origination]: "you never understand the last math class you had". in other words, math builds on itself, so it is difficult to see the big-picture mid-picture. another key aspect is math _abstraction_ outside of human experience.2013-12-27
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    Ironically enough, I just ran into this quote while learning method of characteristics. I, personally, think it is a great quote. I often find myself over-thinking a problem instead of just getting use to it. When I stop myself from trying to understand it and just get use to them, I found myself understanding it a lot better.2014-09-15
  • 9
    Young man, with von Neumann you don't interpret quotes, you just get used to them.2016-11-22

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