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Few questions for mathematicians

  1. Dec 10, 2007 #1
    Hello there

    I have few questions for mathematicians

    1- When you was in High school and college, did you solve all problems or you run over some math problems that you couldn't solve? how did you feel when you could not solve something?

    2- Is being mathematician means that I have to be able to solve everything?

    3- What is your best advice to someone who wants to study math on his own?

    Last edited: Dec 10, 2007
  2. jcsd
  3. Dec 10, 2007 #2
    1.) I'm still in high school. I run over some problems that I can't solve, but go back to it later or after a few days. I feel a litle frustrated and the same time challenged if I can't solve it. And the last option is to ask some help.

    2.) No you don't. For me, being a mathematician is to understand how the math works, and how to derive the math (not the usual memorize, memorize, memorize...). You should learn how to do things from the start, not from where someone gave you a start and continue from it.

    3.) My best advice: Enjoy the math, don't think of it as a duty, but as a hobby.
  4. Dec 10, 2007 #3
    You are aware that there are some unsolved problems, right? I don't think they're unsolved because nobody's tried to solve them.
  5. Dec 10, 2007 #4
    As you learn more math, you find more ways to come up with problems no one can solve or prove, and the more possible exceptions you can come up with for things that once seemed simple.
  6. Dec 10, 2007 #5

    I'm not a professional mathematician, but hey I manage to keep a near flawless GPA in my Math courses during college.

    Let's say

    1-hehe...of course not. I'll be damn if I would be able to solve all problems in a section. It's huge task, and to be honest, i felt there were better things to do than simply do all those problems that seem rather formulaic. However, if there were problems I couldn't solve but wanted too, I would leave it alone, come back to it, work on it, couldn't get it ask someone to help me.

    2-Of course not. You should have an idea how to solve most things in your book though, but it does not mean all problems you see should be trivia to you. Give me a problem regarding elementary number theory and i'll flap around like a fish out of water.

    3-Work hard, talk to other people with your interest, and above all, enjoy working in mathematics.
  7. Dec 10, 2007 #6
    1.) Everyone runs into problems that can't solve. What is really important is that you figure it out eventually. Personally when I can't solve a problem I just leave it alone and come back later, most of the time I just need to look at the problem form a different angle and clearing my mind for a little bit usually helps

    2.) Being a good mathematician means knowing how to apply what you know to solve other problems. Even today there are many unsolved problems. Here's a starting list: http://mathworld.wolfram.com/UnsolvedProblems.html

    3.) Read as many books on a subject as you can, it'll help you get a better and a wider understanding for the subject.
  8. Dec 10, 2007 #7
    If you are not the bookish or bookworm type, try learning from someone you know is great at the subject :D
  9. Dec 10, 2007 #8
    1. You will always be run over by math problems.

    2. No

    3. Here are some great "High School" level books:

    a. The Shape of Space (solve all the problems!!)

    b. Journey Through Genius

    c. How to Prove It (Do the proofs and check them on Physicsforums -- be sure to mention that you are a High Schooler working on your own)

    d. Who is Fourier?

    All the books above are challenging, but all you need is HS Geometry and Trig.

    And remember we are here to help you for Free and free is a very good price.
  10. Dec 10, 2007 #9
    In my opinion:
    Do it for the love of it. I think there is only one person in my math classes who does consistantly better than me (I'm not bragging I go to a very small school). She hates math(!) because from day one she was obsessed with her grades and because of this she stopped caring about the material and only cared about her GPA. That is not to say you shouldn't think about them at all but *I think* in the long run, it will be better for you to care deeply about what you study more. She's an absolutly miserable person and every semester she's worse to be around which is really unfortunate.
    There is already a rediculous amount of pressure on students to do well so don't add any to yourself. Study what interest you. Do your best and ENJOY it.
  11. Dec 11, 2007 #10
    Thanks for the encouraging and inspiring sentences.
  12. Dec 11, 2007 #11
    I am not a mathematician; however, I assure you that you will have a massive burnout if you let the problems you cannot solve get to you too much. Get back to them later, read, ask for help.
  13. Dec 12, 2007 #12


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    Back when... I found the difference between high school maths and university maths so great that the two seemed unconnected.

    I would settle for nothing less than 100% up to the age of 18, then I started doing some real pure maths...

    A lot of people dropped out because they thought they could carry on through university just solving problems.

    My advice would be to work at a steady rate and to keep you grades the best they can be without putting too much pressure on yourself. Enjoy your maths but, more importantly, enjoy life!
  14. Dec 12, 2007 #13


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    Staff Emeritus
    Science Advisor

    How very true! I took modules in my a levels called "pure mathematics n" (I think n ran up to 6, but I only took 1 to 3) which were just calculus: differentiation, integration, diff eqns. It was quite a shock getting to university to find that what I thought was pure maths was really applied, and that real pure maths was completely different! I know that a level exam boards have since changed the names of modules to "core mathematics"
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