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I have encountered this quote along the way, "In mathematics you don't understand things. You just get used to them" -Johann von Neumann

This is a question for any one who allows me to see their point of view. But it is even more directed to those mathematicians who have studied this beautiful subject and have been capable of getting through the whole school cycle.

Ok in the last years I have very strongly advocated the idea for math having to be understood rather than “get used to”, but I do also have to say that through my scholastic years I have noticed that those who have not question the reason behind a mathematical idea have been the ones that have been outstanding in it.

Mind that mine is not a critique to the scholastic system. I respect my school and the teachers that are part of it.
Mine is rather an exploration towards understanding what math really represents to the people around me and how people think when utilizing it.

  • Oct 15 2013: "I respect my school and the teachers that are part of it."- emma rusconi
    This is biggest problem with the system we have today IMHO.
    "By the time that I could talk, I was ordered to listen"- Cat Stevens
    Instead of an educations system, we have a brutal dictatorship. We are taught to obey, instead of question (the very essence of education).
    Von Neumann was a crucial part of many mathematical advances including the computer, atomic energy, quantum mechanics just to name a few, not to mention his self-replicating spacecraft of the future. At the ripe ole age of six he could divide two 8 digit numbers in his head, in two more years he had learned advanced calculus, by the time most kids were entering college he had already published several papers and was offer a teaching position. While mathematics are hard for some people they were like a child's toy for Von Neumann, he had been playing with these toys since childhood. What he is saying here is mathematical problems are like family, you will never understand them, you just get used to them.
  • Oct 15 2013: I would highly recommend reading (one of my favourite books)- Fermat's Last Theorm. It's about the history of mathematics. How it was invented initially more as a tool for measurement, and not much 'understanding' put into it. Wasnt till much later did people start to think deeper about the relations and reasons for many equations that have been around for a long long time.

    I find mathematics in school a very similar way. You learn how to use the tools first, and you are graded accordingly. Also, there are different levels of 'understanding'. First you learn the 'how', then you learn how to apply things in different contexts, then you start to challenge the 'why', and eventually you even start to challenge the premise, the 'what' 's. A bit in reverse, really.
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      Oct 15 2013: I second the book recommendation.

      It is possible the quote refers to Da Way's scenario. It is traditional for calculus students to learn to use the tools of calculus before understanding with rigor why the tools work. Earlier than that students learn to use the "quadratic formula," typically before they know the mathematics for its proof.

      But those are statements about instruction of some concepts in school rather than statements about mathematics as practiced by mathematicians.
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    Oct 15 2013: every natural number is interesting. proof: take the smallest number that is not interesting. this number is interesting, because it is the smallest number that is not interesting. proof by contradiction.

    most real numbers can not be expressed in any way. proof: expressions are a finite string of symbols. since we have finite number of symbols, finite strings of symbols are countably many. at the same time, real numbers are continuum, which is strictly greater. thus does not matter what symbolism you choose, majority of real numbers can not be expressed.

    there is a way to cut a sphere to pieces, and assemble the pieces into two spheres of the same size as the original one.

    if a mathematical system is strong enough to be any useful, it must contain at least one statement that makes sense within the system, but can not be proven true or false.

    there are as many pairs of numbers as numbers.
  • Oct 15 2013: Emma,

    I would like to know the context but if I were to guess it is the difference between applied math and theoretical math. There are many things in theoretical math that have no practical uses but are debated for a 1000 of years. There are also paradoxes which makes little sense in the real world.

    Also, in applied math, if it works, use it. We use theorems but ignore parts of the basis of the theorem because it does reasonably approximate reality.
  • Oct 15 2013: One would need to understand the context. Apparently he had an interesting conversation with Godel though the latter advocated something very different from what John Von Mewman's life had been.
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    Oct 15 2013: the origine of it it's the static logic full paradox like the paradox of Russell for it ,i think it's missed the time like factor for to be dynamic for to be not right by mathimatical eyes but right by eyes of reality...to write the reality matimaticaly ,i think we need to change some principals for we give it a life...i am guessing only maybe i am wrong and the math must stay static.
  • Oct 15 2013: I like maths and comuters subject s very much.Enjoy!
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    Oct 15 2013: I would like to know the context of the quote. Von Neumann was one of the greatest mathematicians who ever lived.

    In my experience with mathematics students and mathematicians, it is not true that those who do not question the reason are the most outstanding in it. Mathematics is all about the reason, proving things with careful articulation of reasons.