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How can one be naturally good at maths?

  1. Jul 11, 2012 #1
    Maths is a tool made by us to understand the nature( or whatever reason). Then how can one be naturally good at it? You have to study the subject, practice it and then become a master of it. But i have heard of prodigies who have done miracles at a very low age.
    Is there a part of the brain dealing with maths(which is human-made)?
     
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  3. Jul 11, 2012 #2

    chiro

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    Re: How can one by naturally good at maths?

    I think like any language, one has to see beyond syntax, structure, and formalism to really understand what mathematics actually is and what it really corresponds to.

    Mathematics to me is like the epitomy of language in that it provides a language that regardless of cultural, social, or any other class or division, everyone can agree on. This to me is the real power of mathematics.

    The properties about it being consistent, logical, rigorous, and so on are definitely great properties, but they simply re-inforce the characteristics of why math is the best candidate so far for a global language.

    But like any language, what representation corresponds to, even with mathematics doesn't always have a clear meaning and that's the real challenge of knowing what something actually corresponds to.

    Sure we know how to define numbers, sets, functions, algebra and so on, but these things in a purely symbolic context really have no deep understanding. If you don't believe me, ask many of the people who have constant difficulties in mathematics who struggle because of the primary fact that the symbols and the systems employed do more to confuse people than to enlighten them.

    Intuition in any language is built up through time, and commonly when one is introduced to any language what happens is that a kind of bridge is used to take a person from a language of great familiarity to one of no familiarity when they are starting.

    Once the intuition has been built up, the concepts become a lot easy to grasp at high levels just like the person is able to craft sentences and even entire reports, novels, essays, and so on with ease.

    But to have the real understanding, you have to leave the symbols behind and look for a way to take those symbols, concepts, and so on and put it in your own language.

    But language is really the bread and butter of analysis and information is everywhere. Information is present when you look out at the world and isn't just available in the symbols, flow-charts, diagrams, proofs, and definitions and restricting yourself to just one language means you miss out on all the opportunities to create otherwise valuable connections to all the other components that are a lot more natural.

    People also like things they can relate to and initially if you teach people mathematics in a way that they can not relate to in a meaningful way, they will lose interest or even end up hating something.

    The way mathematics is taught, is done in a way that there is no meaningful relation. Looking at right-angled triangles, corresponding angles, and rules of algebra is not in any way useful if it has no relation to something meaningful. Unfortunately what happens is that when people don't see the meaning and don't get what's going on, some think they are stupid, and others think that if this is what mathematics is about, then it is completely devoid of any kind of meaning, creativity, or any practical use whether purely intellectual, purely technical and applied, or a mix of the two.

    The other thing that mathematics does is it meets two very important needs: the first is that it is specific which is something that the best of languages aspire to be, and the second thing is that it is also broad.

    These two sound contradictory but they are not, and mathematics shows how this is done. The specificity comes in the attributes associated with unambiguity, consistency, and logic. The broadness comes in with variability.

    The variability itself gives the power known as the abstract nature of mathematics. Mathematics is, in a nutshell, the study of variability. The variation occurs in every known sub-topic and thereof of mathematics including analysis, algebra, and topology. Without variation, there would be no need for mathematics whatsoever.

    Also to become a master at something, you have to seek true understanding and sometimes that means coming in contact with situations that may not seem what you think they seem. It means that you have to accept always the possibility that what you thought might have something that is not complete, and this means having an open mind. This is a lot harder to do when you are older than it is when you are younger.

    The other important thing is to observe and look at what other people are thinking and doing. Just like everything else, communities naturally tend to form when common interests emerge, and like everything else they tend to become a lot more organized with regards to how they operate and how they communicate. This is true of every endeavor and really shows a small glimpse into the amazing capacity of this thing we call reality.

    So always listen to what other people are saying, and offer your own viewpoint whether it's right or wrong. Usually, things are a bit of both and it's going to be better in the long run to get a reference point for your own thinking which other sources provide: the more reference points (and the greater the actual diversity of the points regardless of what they are), then the better you have to grow in your own conclusions.

    Finally I'll leave you with the thought of considering the circumstances of the different people in all aspects. Think of the upbringing, the people that they came in contact to throughout their lives and what these had in terms of impacting their own visions, philosophies, and directions and also on the activities and the connection of all of these on the work of these mathematicians (or any other master). These are often not mentioned, but they are the most important thing to consider.

    For example most people don't know that Gauss had to calculate values of logarithms frequently so the idea of the prime number theorem happening merely without relativeness or context is not true at all, and I think you'll find that this kind of thing without putting it into context is also misleading to say the least.
     
  4. Jul 11, 2012 #3
    Re: How can one by naturally good at maths?

    I've always thought that abstraction is a very important quality to have. In order to be good at math, you have to be able to take concrete examples and abstract them into oblivion.
     
  5. Jul 11, 2012 #4
    Re: How can one by naturally good at maths?

    Actually, no one is naturally good at maths. But in the land of the blind, the one eyed man is king.
     
  6. Jul 11, 2012 #5
    Re: How can one by naturally good at maths?

    There are also other prodigies in other activities that can be considered "man made": art and music for example. The fact of prodigies is really what needs to be explained, not just math prodigies.
     
  7. Jul 11, 2012 #6
    Re: How can one by naturally good at maths?

    In high school I showed no signs at being any good whatsoever in math. However when I got to college I turned out to be special in math. I was a whizz at it so I double majoerd in physics and math, since the former requires a lot of the later. I think that by the time I got to college, which was after a stint in the military, I wanted to become an electrical engineer. I was scared stiff of all the math I had to take. But when it came to learning it I had already had a preview of its applications from life experience so I absolutely loved it, especially since I lovede the topic. I couldn't get enough of it. It was hard socially though to be so good. Other students rejected me because I made the rest of the class look bad. It was a traumatic time in my life. But I do understand this kind of thing to a very small extent.
     
  8. Jul 11, 2012 #7
    Re: How can one by naturally good at maths?

    Why do people around here pluralize math by adding an s? Isn't math the plural of math?
     
  9. Jul 11, 2012 #8

    Dembadon

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    Re: How can one by naturally good at maths?

    It's a U.K. / Australian thing, I believe. They love adding superfluous letters to words. :devil::biggrin:
     
  10. Jul 11, 2012 #9

    StatGuy2000

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    Re: How can one by naturally good at maths?

    The people who pluralize math by adding an "s" are applying the British spelling convention (and hence are likely from either the UK or from former British colonies e.g. Australia, New Zealand, South Africa, etc.).
     
  11. Jul 11, 2012 #10
    Re: How can one by naturally good at maths?

    *shrugs* It appears to be just another way of saying mathemathics
     
  12. Jul 11, 2012 #11
    Re: How can one by naturally good at maths?

    I've always assumed they think in terms of each kind of math, arithmetic, algebra, geometry, calculus, etc. being a separate math, and that referring to more than one requires the use of a plural. In other words, these people never evolved to the level of developing the concept of a singular collective noun in the arena of math.

    They also say "aluminium", which is a waste of syllables.
     
  13. Jul 11, 2012 #12
    Re: How can one by naturally good at maths?

    From my personal experiences, the inaccessibility to math for me has always been notation created by someone else with minimum or no explanation, and assumptions made by teachers or books that either omits critical ideas or information or includes too much unimportant information that hides the concepts. Also, when the information makes leaps from one idea to another, or tries to organize the information that might seem logical from a classification standpoint of someone who already knows the material, but not from a relation based learning perspective, it can really make things more confusing if not impossible since the running dialog in my mind as I'm learning will put up barriers that I don't want to just walk around.

    Once I get over what someone else is trying to tell me, and understand it in the way that my brain thinks, I can quickly adapt and understand things and suddenly what seemed so cold and untouchable is very familiar and even easy at times. I have found that real math, involving proofs and facts about relationships, is much more fascinating and interesting than "work math" where you are taught how to do things mechanically with minimum explanation. The real math is almost like learning a story or learning nature, but work math (the kind I was taught almost exclusively) is like learning how to read and spell.

    I could go on about textbooks and the way instructors choose to present material, but then I would already get more verbose than I already have been. I think the learn by discovery method has severely crippled math education though; I get severely annoyed when an author leaves an example or proof for the reader to solve alone with no hint or end result to compare to, and portrays great delight at the solution as if to encourage the reader to figure it out.
     
    Last edited: Jul 11, 2012
  14. Jul 11, 2012 #13
    Re: How can one by naturally good at maths?

    Pah, it's not half as bad as all you English-speaking people messing up what should be 'Natrium' and 'Kalium'. :biggrin: I mean, seriously, Na = Sodium? K = Potassium? What kind of irrational being thought that'd be a good idea? :wink:

    Back on topic: what kind of 'math' are we talking about? Most people would consider arithmetic some form of mathematics, yet the skills required are totally different from those required to do mathematical proofs.
     
  15. Jul 11, 2012 #14

    BobG

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    Re: How can one by naturally good at maths?

    You know what they say. Those that can calculate cube roots in their head become engineers, while those that can't add 2 plus 2 become mathematicians.

    I guess one can be naturally good at math (or at least with numbers) the same way some people are just naturally good at sprinting. The only real difference is that mental skills are invisible, while you can look at person with certain physical skills and understand why they're better at what they do than anyone else.
     
  16. Jul 11, 2012 #15
    Re: How can one by naturally good at maths?

    I've always thought that IQ tests - while they may not be perfect for testing intelligence per se - may be a good test of this kind of mental power.
     
  17. Jul 11, 2012 #16

    AlephZero

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    You can be naturally good at math the same way as you can be naturally good at anything else. Just choose your parents very, very carefully :smile:

    "How can your improve your math ability" is a different question, of course.
     
  18. Jul 11, 2012 #17
    Re: How can one by naturally good at maths?

    I don't hold much value for IQ tests. One has to be very cautious about using them. Im highschool they gave us IQ tests but they never told us they were giving tghem to us nor did they tell us the results. My IO tested at 100. A few years later when I was in college I took an IO test which came out to 130. I find it hard to believe that my IQ could change that fast. I probably didn't care about the hs test since they didn't tell us that it affected our grades so I probably didn't do as good as I could have it they'd have told me I was taking it.
     
  19. Jul 11, 2012 #18
    Re: How can one by naturally good at maths?

    Were both tests administrated by a qualified psychologist? If so, these results were significant. If not, well, I'm not surprised - there are a lot of bad or incomplete 'IQ' tests. (And, of course, IQ tests don't measure everything, but they're reasonably at measuring mental 'processing power'.)
     
  20. Jul 11, 2012 #19

    BobG

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    Or, more likely, the test wasn't an IQ test at all, but had some estimated correlation to IQ added on based on the percentile ranking of your results (which would explain why they didn't tell you you were taking an IQ test). If you're in the middle percentile, you probably have an average IQ, if your results were in the top 10% you probably have a higher IQ, if you were in the top 1% an even higher IQ and so on. This is a fairly common thing to do for some tests, while some tests absolutely refuse to correlate their results to IQ (even though they do give you a percentile ranking that someone else could correlate to IQ).
     
  21. Jul 11, 2012 #20

    AlephZero

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    Re: How can one by naturally good at maths?

    So I guess that's why Americans write and say titanum, magnesum, etc. Not to mention uranum, plutonum ... oops, I forgot, you just say "nucular". But even that has more syllables than "nuclear" :confused:
     
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