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What is the essential elements of being a mathematician

  1. Aug 20, 2011 #1
    I just want to know, what are the essential elements of being a mathematician? Because I want to decide whether I am better to study physics or mathematics in the University.
    I knew that a lots of people learn mathematic olympiads and got a good result in the competition, but I am not the people who got good result in the competition. I just want to know is result of those kind of competitions represent the future of being a mathematician?
    and are those people always got a better result in exams of university?
  2. jcsd
  3. Aug 20, 2011 #2
    No, olympiads are not necessary to be a good mathematician. Sure, people who do good at an international olympiad will probably also do good at math exams, but it's neither necessary nor sufficient.

    Essential elements of a mathematician is going into details (finding out exactly why something is true), being extremely precise about statements and liking to abstract known ideas.
  4. Aug 20, 2011 #3


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    I met a guy with a PhD in mathematics from Cambridge. He said that he never got higher than a bronze certificate in the UKMT, but other people who worked at the faculty told me that he was an extremely proficient and talented mathematician. I do not think olympiads are the only indicator of mathematical ability and competence.
  5. Aug 20, 2011 #4
    Olympiads are an indicator that one cares enough about a given subject and bothered to go into a competition for it. Or maybe one was just bored. :D
  6. Aug 20, 2011 #5
    but I think olympiads always study into very details, and all way of solving the problem is always abstract. So, could you tell me what exactly is the idea and proposes of olypiad, because some of my teachers said olympliad is a branch of math, and some said it equals to the ability of your mathematics, so who is right and who is wrong? (I could study high level mathematics easily but not MO, why??)
  7. Aug 21, 2011 #6


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    curiosity, creativity, persistence. (I am a mathematician.)
  8. Aug 21, 2011 #7
    1) Being able to look at physical phenomena and translate it into a mathematical equation.
    2) Being able to visual mathematical phenomena
  9. Aug 21, 2011 #8
    Although 1) is often a side effect of doing mathematics, I don't think it is actually necessary, is it? Especially not for mathematics that is pure as the driven snow?

    Also, as per 2): how do you visualize objects in an infinitary logic or a large cardinal, or the least set of axioms that can be used to prove a theorem? I suppose you visualize the syntax, but some areas of mathematics are significantly more syntactic than others, so geometric intuition doesn't really apply.**

    **Though I recall reading about some work being done in the visualization of logics and syntax, loosely based on some of the ideas of C.S. Peirce.
  10. Aug 21, 2011 #9
    I can visualize things like large cardinals... I can't tell you how I visualize it, but I tend to do such things quite easily...
  11. Aug 21, 2011 #10
    So then the question becomes "what are you actually visualizing?" Just so we're clear on terminology (I think we probably are, but it's good to be certain), I'm talking about inaccessible cardinals, not Aleph null or Aleph 1 or other limit cardinals.

    I'm not sure what it even means to "visualize" a cardinal, given that it's an element in an ordering of measures of ordinals. Visualizing computable fragments of a set of some cardinality is standard, we all do that when we think about analytic geometry (all that is needed to visually approximate a smooth surface is a rough computable approximation), but I assume this is not what you mean.

    Whatever your brain is doing is -very probably- computable, so it's working recursively and whatever it's doing is -very probably- not involving any -actual- infinite sets, so there is some sort of trick of intuition at play, using some sort of visualization techniques to facilitate reasoning. Whether or not you can successfully communicate your visualization techniques is another matter, but I would be very interested in your explanation if you would be willing to give one; it can't hurt to have another heuristic! :smile:
  12. Aug 21, 2011 #11
    Olympiads are about problem-solving. That involves creativity and knowledge and speed of thought.

    To do mathematics professionally, these are MAJOR pluses. This is why there are plenty of international olympiad winners who do well at research mathematics.

    However, research also involves continually updating on what's going on in the math world, formulating interesting questions yourself, having the discipline to read all the necessary literature, and more long term creativity.

    Some blend of all of these is necessary. It is not necessary to be very successful at olympiads to do well at math research, because those involve too much of on the spot cleverness, whereas research mathematics is a slower, more arduous process, involving looking things up over a period of a year. HOWEVER, there is so much complexity to it that being able to internalize a lot of stuff swiftly is crucial.
  13. Aug 22, 2011 #12
    You sure post fast, maybe you have some solid thinking powers of your own?
  14. Aug 22, 2011 #13


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  15. Aug 22, 2011 #14
    A thirst for knowledge and a drive to understand!
  16. Aug 22, 2011 #15
    A thirst for knowledge and a drive to understand!
  17. Aug 22, 2011 #16
    So essential it had to be said twice! :)
  18. Aug 22, 2011 #17
    Prove Riemann's hypothesis.

    You have to be smart and creative, must write papers if you want to be successful.
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