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Which is more difficult: pure or applied mathematics?

  1. Jun 29, 2007 #1
    How would you compare applied and pure mathematics? Is one more difficult than the other? What is the general difference? What do you think is the most interesting field of those two? Can someone who is bad at using applied math, be more capable of pure math and vice versa?

    ("Theoretical" mathematics might be a better term instead of "pure" mathetmatics.)
    Last edited: Jun 29, 2007
  2. jcsd
  3. Jun 29, 2007 #2
    Pure mathematics is more like art. Pure mathematicians work on building a foundation for a theory. One nice feature about pure mathematics is that it is free from argument. When a mathematician makes a discovery there is no opposition, as in science. And his theory stands the test of time, unlike science where one law is shown to be wrong in special cases. But once a foundation is build (like complex analysis) applied mathematicians take its result and use it to solve important problems.

    Pure math is much more difficult. Classes in applied math consist of memorizing the steps to solve problems. However, classes in pure math involve proofs, which implies a good understanding of the subject matter is required.

    In pure math you need to justify everything you do. Which can sometimes make a simple argument long and complicated.

    I like algebraic number theory.

    It is easier for someone in pure math to learn applied math rather than someine in applied math to learn pure math.

    What is theoretical mathematics?
  4. Jun 29, 2007 #3


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    Its such a subjective question. If you're asking because you're about to make a decision as to which you'd rather do, then give them both a try and find out for yourself.
  5. Jun 29, 2007 #4
    I forgot to add. Even though I like pure much much more. Applied is also fun.
  6. Jun 29, 2007 #5
    i think maybe you're a little biased because applied math is not memorizing steps, it is applying math, it is taking predictive abilities of math and employing them in solving problems. im sure an applied mathematician does not come out of school having memorized every single problem scenario that they will be faced with in their career.
  7. Jun 29, 2007 #6
    True, applied mathematicians are no biologists!
  8. Jun 30, 2007 #7
  9. Jun 30, 2007 #8


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    But how does one apply a mathematician?
  10. Jun 30, 2007 #9

    matt grime

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    If only that were true. Mathematics is plagued by opinion (predominantly over what is 'good') just as much as the next subject. I know you mean more the 'factual correctness' of a proof, but even those can be disputed and not accepted at the high end where proofs are complicated, long and sometimes not even understood by a single person. E.g. the four colour theorem or the classification of finite simple groups.
  11. Jun 30, 2007 #10

    matt grime

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    Really? Cos the feeling I got from teaching engineering students that being taught every conceivable example and no theory was precisely what they wanted.
  12. Jun 30, 2007 #11
    that is a reflection of poor students, not the mission statement of an engineering school
  13. Jun 30, 2007 #12

    matt grime

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    Since it is the opinions of students that seemt to really matter these days, I don't see your point.
  14. Jun 30, 2007 #13
    what? bad students don't become good engineers, good engineers do not algorithmically solve problems, they are creative. bad engineers design toilet seats and cardboard boxes
  15. Jun 30, 2007 #14


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    I can't understand anything that I don't find to be 100% logical and consistent. That's why I like pure math better.
  16. Jun 30, 2007 #15
    That is why I do not except the 4 color theorem nor the classification of finite simple groups. Though the finite group classification would be nice to have as a tool, I must live without it.
  17. Jun 30, 2007 #16
    I think it's really fascinating, but will I as an average student (maybe even worse) even achieve the slightest success in studies of pure math?
  18. Jun 30, 2007 #17
    Pure mathematicians do not think of themselves as students. I don't know what they are exactly, but definitely not students in the classical sense of the word.
  19. Jun 30, 2007 #18
    Well, let's put it this way: will an average high school student be able to understand pure math?
  20. Jun 30, 2007 #19


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    Sure. Why not?
  21. Jul 1, 2007 #20
    Since pure math is said to be very hard, I thought only the most prominent students were able to learn it.
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