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Doubting

  1. Mar 3, 2005 #1
    Hi everybody,
    I didn't know where to post this, but it seems to me here is quite a good place. I would like to share some of my thoughts-questions about mathematical thinking and i would like to here your opinions.
    Is it "normal" for somebody familiar with mathematics and really interested in maths, and who has studied much, to reach a moment when he hears or thinks of something that appears unimportant or totally understandable-easy, and it suddenly seems not clear as before, and he starts having doubts about it? I mean, is it normal to have constant doubts about your knowledge? I don't know if this is because of my age (18,5) but it happens quite often to me. All of a sudden, while for example solving a problem, I start doubting about the properties of real numbers, of concepts like what is a theorem, a variable, a number etc..
    Anyway, I would just like to know if this happens to you too. One explanation is that I haven't yet understood really well mathematics and their concepts-ideas. But what worries me is that this way of thinking can lead to a continuous search and confirmation of very basic definitions and proofs and hinder my progress into more advanced topics. Can this be a sign that my mind is just not made for mathematics?

    Thanks
     
    Last edited: Mar 3, 2005
  2. jcsd
  3. Mar 3, 2005 #2
    You should read all you can on very basic mathematics. You seem to be the type of person that needs to UNDERSTAND FULLY, not just learn step by step. I am like that as well and it is not a bad thing, for me it helps me understand far more than the average person would. I think its a beautiful (and rare thing) for teens to need that complete understanding of things like math.

    I am a teen in high school. I do take advanced math, but this does not hinder me, instead makes me need to learn more. I hate being told this IS how it IS. I need to know why, and will spend hours finding out why it is that way. I don't consider it a hinderance like I said, I couldn't imagen being different.

    I hope we are on the same page.... If so, I would say to read as much as you can on the simple mechanics of math. Maybe even the history of math.
     
  4. Mar 3, 2005 #3
    im similiar, for instance in my mathmatics classes, and in my personal readings, what i will do is i will look at an example and then find the equation from there, so that in effect i have to continously pick apart the example to find a pattern. of course this can be a completely inefficient way of doing things from large formulas, where then you can start on the opposite and see the equation, and form an example through that so you can work it through that way| so in the end you know the ins and outs of the equation, and often if you work it the first step, you can find several conditional shortcuts, for isntance if the number is an even perfect square, you can do such and such to skip a few steps
     
  5. Mar 5, 2005 #4
    Thanks for your answers. It is good for me to hear that others of my age have a similar way of mathematical thinking. I would also like to hear any opinions from older and more experienced ones. So i ask again: is this because I am young? I mean, a 30-year old mathematician or an older one has such thoughts? Or slowly the mind gets "tired" of constant questioning and starts to accept things without doubting so much?
    Thanks
     
  6. Mar 7, 2005 #5
    I was like that in high school (I'm 21.5 now), doubting concepts and properties of theorems, definitions, etc.....but that made me appreciate mathematics more -- so I decided to minor in math in college. Now, I try to explain everything mathematically. That's why I've decided to go into theoretical/computational chemistry for PhD.
     
  7. Mar 7, 2005 #6
    This may be an odd question, but: If you could sum up math in one sentence what would it be?
     
  8. Mar 7, 2005 #7
    simple in its complexity
     
  9. Mar 18, 2005 #8
    wow interesting question lol I am not big on math, although Ive done well in it and didnt have trouble. I stopped after college trig (Im a college sophomore) Even I had this experience, it just means that youre an independent thinker. Its a good thing.

    As for the one sentance question: My mother is a mathematician, Im gonna have fun asking her. lol
     
  10. Mar 31, 2005 #9

    bfd

    User Avatar

    That's a good question. For me math is one of, if not the most, precise sciences out there.
     
  11. Apr 19, 2005 #10
    I am 51, since you asked for responses from older people. I am uncertain that older is wiser. :-)

    There are excellent reasons to question everything about basic arithmetic and math. For instance, arithmetic contains certain ideas that we all just agree to accept (cardinality, equal distance between integers, etc.). All other math is built upon arithmetic. To a certain extent, all math is, then, based upon general agreement, as opposed to axiomatic reasoning. In general, there are excellent lessons to apply to all of life in this concept: 1) it is ok to be arbitrary sometimes, if a meaningful majority can agree about the arbitrariness. A corollary to 1): Both clear thinking and clear communication in life is important. 2) You can take a guess sometimes, and let later events prove you correct. 3) You've got to start somewhere. You don't have to know everything beforehand to know anything at all.

    My point here is that the study of math may lead to ways of living that are generalized ideas from math. If you are like me, you will eventually turn from the questioning of the basic postulates of math, once you build confidence in the math, to use the underlying reasoning to let you question the rest of life. I will give some examples.

    Statistics is all about deciding if some particular thing happens randomly, or if there is a causal link between two events. You can use this same principle in your life to help decide what is true. 1) That is, you may not know, but you are more certain about one thing than another because the one thing seems to be connected to the next, and it is unlikely to be a random connection. 2) Similarly, if a pattern exists, it is most likely not random (which is scientific investigation in a nutshell).

    Another general application of statistics is that the more you seem to know about a total reality, the more likely it is that your entire understanding (as opposed to your certainty about any one happening in that reality) is wrong. In statistics this is called loss of degrees of freedom, but its real-world interpretation is that the more you guess about things, the more likely that all your guesses together are wrong. And this is because your guesses start being built upon your guesses (your explanations are not independent from one another). 1) So you re-build your own theory of everything constantly, and 2) with an open mind. 3) All people are limited in what they can understand of reality. So you get to question on what basis anybody asserts whatever s/he asserts. You can believe in independent investigation of truth, because we are all equally fallible. Just because your parents believe something, or the majority of people in these forums believe something, does not make it right. You have the pleasure and responsibility of making up your own mind.

    To move into another area of math, the first time I saw the underlying graph for Wilson's Lot Size Formula, or the Economic Order Quantity Model of Inventory Control, I was electrified. It made it so clear, in such a simple way, that absolutely everything in life is a tradeoff between at least two things we want (you can't have it all), and that to make anything 100% certain takes infinite resources (so you make a reasonable expenditure of time and effort and then go with the best you got.) I have never seen anyone else use the graph this way, but it hit me like a ton of brick. In life, I do not make a math model of every decision I must make, but I certainly use the philosophy of the EOQ model in making decisions, and in accepting trade-offs. It also makes me want to make sure I understand all the trade-offs.

    So what I am telling you is that the questioning you are doing is great. Take the time to enjoy your relentless exploration of every fundamental, because you will get to find your own ways of using that questioning and the philosophy of math for the rest of your life. Its great. Its a happy thing. You are only 18. At that age, we think everything should come so much quicker than life really allows it to be provided. We are impatient, because we haven't realized that we can be content with the journey, as opposed to needing to get to the destination. You actually never do get to the destination. So let this part of your journey be a goodness. Rather than being anxious, embrace your questioning with passion. Get a teddy bear and name it Questions and kiss it every day.

    In the quicksand of life, we all need some bit of firm ground on which to stand. If you get the math down, then it will provide one of those bits, not necessarily in its direct application, but in its underlying way of questioning and proving things about life.
     
  12. Apr 19, 2005 #11
    O, as to your question of what is math, it is a silly way of constraining the way we look at things, and a glorious way to unfold the revelation of reality.

    Everything that has an advantage has a disadvantage. Everything is a trade-off somehow. Everything that can help you can hurt you. You choose to make math what it is for you. Math is but one tool, and you are the toolmaker and wielder.
     
  13. Apr 19, 2005 #12
    I've had made myself that question all my short but intense life (14.5). It's until know the hardest think I've come to about mathematics. I have reached a conclusion that I find practical, easy to understand and explenational.

    MATHEMATICS IS THE DEMOSTRATION THAT SOMETHIN EQUALS SOMETHING.

    And that is all, no more problems, look at it, all math enters in the description. Well, at least all math I no and tht I have done (which is limited, as for any other of my age).

    About the first question, well, I do doupt and wonder about many concepts-ideas, and think about them until I completely agree or, for myself, disprove them or neglect them. For example, now I wonder about who was the first person (tipical math question when ou learn something) that thought about multiplying? it is such an amazing thing jsut to be the first one to have the so general idea. Also about who was the first one to count, but that isn't so amazing because is everyday life, (now a days also multiplying is). If anybody know s who was or where the first/s to multiply please tell me.
     
  14. May 4, 2005 #13
    Thanks for your answers.
    I have doubts about it too, that's why I also mentioned something about our mind getting tired.
    So can you ever reach a conclusion?Or you can never be sure of anything, so I think that it's like being in a labyrinth with no exits and trying to get out. This problem seems to be solved partially by religion. But in the way I see things, mathematical reasoning and way of thinking can't co-exist with religion (although I know that there are many examples of scientists,and mathematicians, that believed in God)
    I hope that this is actually pleasant and enjoyable.

    Thanks again for sharing your opinion and experience.
     
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