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Love of Mathematics

  1. Dec 16, 2011 #1

    When I was in elementary school and high school, math class was very fun and easy and I was naturally good at it. But then when I turned sixteen I had to stop going to school and start working. I had no other choice. A devastating head injury on the job made me unable to work. Now, at the age of 25 I have nothing to do, and so I was thinking of starting mathematics again and perhaps one day if I get really good at it, I might be able to discover new theories etc. Who knows.

    I bought the book "Mathematics: From the Birth of Numbers" (by Gullberg) and I will be studying it in 2012.

    Basically, my question is, how difficult is mathematics compared to the math one learns in high school, and also, can almost anyone get really good at it?

  2. jcsd
  3. Dec 17, 2011 #2


    Staff: Mentor

    Basic HS math will cover Algebra, Geometry, Trigonometry, sets, sequences and series, complex numbers and other misc stuff. Everything you need before you can begin to learn Calculus.

    I think the Gulberg book covers these topics pretty well with a lot of historical backstory too. Another book I like that came out recently is Math 1001 by Elwes. It provides paragraph summaries of various math problems that are still unsolved. Its fun to read and ponder even though they are very deep. I was surprised at the variety too,
    Last edited: Dec 17, 2011
  4. Dec 17, 2011 #3
    The main difference is that what you learn during school is mainly skills, higher level mathematics is less about computation and more about proofs. This might not sound like a huge difference but the mindset you need is VERY different.
  5. Dec 17, 2011 #4
    I am a failed graduate student in mathematics.

    At some point everyone gets to a level where they cannot go any further. It is like trying to see out of the back of your head. For some people this level is high enough, for others not.

    Talent makes a huge difference, more than in any other endeavor I know of. Hard work does not fill the gap.

    Success with high school math does not predict success with higher math.

    BUT you could have the potential to be the greatest mathematician in the world, for all I know. But folks like that are generally obsessed, which you are not.

    BUT if you have nothing better to do, give it a shot. Why not? It's better than attempting nothing.
  6. Dec 17, 2011 #5
    I think when you're at school, you can be good at maths without really trying or putting alot of work into it. Some people are just better than others.

    At university it is a lot different, it is more about understanding rather than just solving equations, etc. It requires alot more work and dedication. Certainly if you enjoy mathmatics, then give it a go, it's never to late to learn and there are plenty resources.
  7. Dec 18, 2011 #6
    Unfortunately I may have lost that talent which I had when I was a kid. I remember always being one of two students in the class who finished math tests first. I remember everyone was doing long division while my friend and I discovered short division.

    For years I worked at my uncle's construction company and came home exhausted. The rest of my time was spent drinking two beers (that was the limit!) and watching TV. However, sometimes I would read parts of a novel before bed.

    Now, after I've recovered (for the most part) from the head injury, I feel like changing my life. I no longer have to work because I'm on disability. It would be great if I could somehow get that talent back and build on it etc.

    It's true, I'm not obsessed about math at this stage. Never have been but I did have a talent for it when I was a kid. I'm sure anyone can become obsessed about something (anything really), work hard and make great progress.

    All I have is time right now. I would like to use that time wisely. People can change. The brain is full of mystery.

    I believe I can become a math genius is I choose to do so. Now, I'd like to know what you all think about this. For instance: why can't anyone become a math genius? If everyone has a limit what if we work to surpass that limit? Surely this can be possible? Etc etc.

  8. Dec 18, 2011 #7


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    I think it's great that you want to pick up some maths after all that time. You might have to start at the basics again though, but, why not?

    I don't want to discourage you, but the thing about high level maths is that it's very different to anything you see in high-school. A mathematician friend of mine related it to music - In high school, learning maths is like learning an instrument by only ever being allowed to play scales. What's more, you don't even get to hear a song, just scales, up and down. It's only when you get to university that you start to hear songs, and at the beginning, it's only "chopsticks". Eventually, you may get to hear (and play) a symphony.

    This is why people "hate maths" or think it's "boring". However, it also gives people unrealistic ideas of what maths actually is.

    For me, two years of honours university maths was my limit. I just don't have the intuition - something that is a little bit innate, and a little bit learned. I'm a physicist - I love and use maths all the time, but I think about it in a totally different way to a mathematician.

    The question is then - can the intuition be learned? I tend to think that (pure) mathematics is something that requires some innate talent, again, perhaps, like playing an instrument or being an artist. I also think that you can learn to do maths, like anyone can learn to play the piano.

    That is, I don't know if you can become a productive mathematician - why don't you go find out? Just go in with your eyes open.
  9. Dec 19, 2011 #8
    I think we're all born with certain abilities, of course, but these abilities can be further developed through practice and learning. Take Mozart as an example. It has been said that he was a very talented musical prodigy from an early age, however, from what I understand, his father pushed him, from an early age, to work hard at it and his talents grew and grew. In this way, our brain is like a muscle, it'll just keep getting stronger and better as long as the motivation etc is there.

    So I don't understand how there can be a limit to learning. We just keep getting better and better as long as we work hard at it. If what you're doing isn't working anymore then change it and adapt. You'll see the results sooner or later. I've always believed this.

    In short, I think almost anything is possible and talent is, for the most part, developed. We all have some talent (innate ability) to start with and improve upon.

    Thanks for the replies, by the way.
  10. Dec 19, 2011 #9

    k good luck
  11. Dec 19, 2011 #10
    I'm no expert in neither life, neuroscience, nor psychology....nor mathematics for that matter. That said, I agree wholeheartedly with what you've just written. Furthermore, even if your opinions are wrong, they represent a very healthy self-image: simultaneously confident in your intelligence while staying grounded in work ethic.

    What I really think is that, yes of course some people have a higher innate talent for math. However, I believe the term "innate" is a misrepresentation. It's more a function of the resources available to the developing brain, as you've basically said. While some math genius may pick ideas up quicker and improve at a higher rate, you can always match his level with persistence and dedication. The key is to use your time wisely. Don't let confounding ideas stall you for too long. Move onwards if stuck and return when necessary.

    Now it's debatable that two people working equally hard, one with a more developed brain than the other, will likely not achieve the same things in their lifetime. I guess it all boils down to how much time you have available for catching up.
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