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What research basically is [in mathematics]

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  1. Dec 23, 2015 #1

    faiziqb12

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    I want to pursue a matametical career but all of us know that a good research career or even professorship at good universities needs a good amount of research papers.
    so what basically is research , is it contributing new things or giving depper understanding of a known fact for example a mathametical equation?
    please reply ASAP
    Thanks
     
  2. jcsd
  3. Dec 23, 2015 #2
    'Research' is generally a term used when talking about observational aspects of science.
    Telescopes and test tubes and so on.
    Mathematics doesn't really require research as the whole idea of it is built upon axioms like addition, 1+1=2.
    Would be really hard to do an experiment which either validated or falsified a concept like addition without assuming addition is a valid idea to begin with.
     
  4. Dec 23, 2015 #3

    micromass

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    Wow. Talk about the most wrong thing I've seen all week. Of course there is research in mathematics. You seem to be under the impression that research is only experimental stuff. It's not.
     
  5. Dec 23, 2015 #4

    radium

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    People seem to think theoretical physics and math aren't research since there may be no experimental data (this is not true for many fields of theoretical physics). However, anything that involves thinking about some unanswered question is research. From what I have observed in math (I have a good friend doing his PhD in math), the focus is on proving things as in making something completely rigorous.
     
  6. Dec 23, 2015 #5

    Krylov

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    Post #2 is intolerable not only for the ignorance it displays about the field of mathematics, but mostly because it offends every mathematician on this forum and, indeed, an entire well-established and age old academic discipline.

    Earlier today, I made an attempt to more briefly express my judgement, but that attempt failed.
     
  7. Dec 23, 2015 #6

    faiziqb12

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    fine , guys please forget the wrong of post #2 and start focusing on my original questionn
     
  8. Dec 23, 2015 #7
    I confess to my sin although I think it might have been misconstrued as well.
    I didn't mean to imply that math isn't science, yes that would be truly ridiculous.
    I meant it more in terms of 'research' being generally understood as investigating stuff with instruments.
    My apologies to anyone offended by my misunderstanding of the word.
     
  9. Dec 23, 2015 #8

    micromass

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    Why would anybody understand research as that? I mean sure, a high schooler with no experience in academia might understand research in that terms. But it's clear the OP is not talking about that kind of research.
     
  10. Dec 24, 2015 #9
    Hi,
    I'm from computer science, which in general ways is a branch of math, and as well we have some misconception on What we research (specially on the more theoretical areas).

    In math, so far as I know, you can make research on both "areas", the more practical (applied math) which can be used on computing, engineering, physics and stuff. Other one is the pure math research, which sometimes May seem useless today, but in the future can be used (like number theory, useless some years ago, but now is the base for Cryptography).

    Anyway, you Will be proving equations, and testing some theories. In my university (in Brazil, and we are not famous for math publications) the math researchers public less arcticles than any other departament (I think because of the hard side on proving things in math).

    Again, I'm not from math, my knowledge is from some friends I have in this area and on my own field (which is theoretical computer science ).

    Best redards,
    Leon.
     
  11. Dec 24, 2015 #10

    Krylov

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    The contribution of Brazilian mathematicians to the modern theory of differential equations and dynamical systems is quite substantial, see e.g. Jacob Palis and his students: https://en.wikipedia.org/wiki/Jacob_Palis
     
  12. Dec 24, 2015 #11
    Oh, I meant my university specifically. But I really didn't know about those contributions. Thanks for sharing :)
     
  13. Dec 24, 2015 #12

    faiziqb12

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    everytime somebody asks a good question , nobody gives a good answer , but loves critisizing other peoples answers
     
  14. Dec 24, 2015 #13

    SteamKing

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    Research in mathematics can involve several things.

    Someone earlier mentioned developing proofs of certain theorems, which does involve research.

    At times, prominent mathematicians have made various conjectures about things mathematical. While initially informed speculation, a conjecture needs to be shown to be true or false to determine if it belongs in the body of mathematical work.

    There are various unsolved mathematical problems, the solution to which may or may not have practical applications. Attempting to find these solutions often involves a great deal of research in the mathematical literature, to see what others have tried.

    Some researchers may decide to take their mathematics research into previously unexplored areas. Chaos theory is one such recent example of a new branch of mathematics which developed out of older topics in math, like the solution of certain differential equations.

    This is just a quick discussion off the top of my head. There may be much, much more to uncover, which you should try to do on your own.
     
  15. Dec 25, 2015 #14

    faiziqb12

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    SO , basically research means just investigating mathametics , and does not necesserily require a person to do some new discovery .
    right , sir ?

    and what do you need to do to get a promising research position anywhere , (not asking about being a professor)?

    and does pure mathametics give you anything more than just adjusting you at a professors job?
     
  16. Dec 25, 2015 #15

    micromass

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    Research is basically synonymous with making new discoveries. But you can make a lot of new discoveries. You can of course invent (and prove) new result. Or you can give new proofs and insights to already known results. That is valid research too. But it does have to be new and original.

    Sorry, but unlike physics and engineering, it is almost impossible to do research in pure mathematics outside of academia.

    Probably not.
     
  17. Dec 25, 2015 #16
    One of my professors who is a mathematician, is working with an Alzheimers research group. Before that, years ago, she went to Canada regarding an issue with their maple trees.

    My other professor, found a solution to a differential equation a while back.
     
  18. Dec 25, 2015 #17

    faiziqb12

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    most probably your professor is a applied maths professor.but i think pure is better than applied , even if it doesnt sound like having a value nowadays
     
  19. Dec 25, 2015 #18

    micromass

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    Sorry, but that's a really dumb opinion. It's the kind of things I see from undergrads. Pure mathematicians are seen like geniuses, while people look down on applied mathematicians. This needs to stop. Sure, you can say that you enjoy pure better than applied. Me too. But saying that one is better than the other? That's a poisonous opinion.

    Besides, pure math is nothing without applied math. A lot of pure math only makes sense after you know the applications. This kind of divorce between pure and applied is very much unhealthy. http://pauli.uni-muenster.de/~munsteg/arnold.html Knowing everything about Hilbert space is cool. Knowing also how it is applied in QM, there is where the miracles happen!
     
  20. Dec 25, 2015 #19

    Krylov

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    Yes, yes yes! You stole my post!

    In reality, there is a continuous transition between pure and applied mathematics and I prefer a spot somewhere midway. To me, there is nothing more beautiful than solving concrete problems (from engineering mechanics, for example) using abstract methods, thereby discovering the mathematical structure that such problems may have in common.

    Sometimes, people think that there is a trade-off between applicability and profoundness of a mathematical result. This is very much not true.
     
    Last edited: Dec 25, 2015
  21. Dec 25, 2015 #20

    faiziqb12

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    thats what the thing comes in , i dont really care about applications of pure maths and i solely love maths without being concerned about its applications
     
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