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Is pure math useless?

  1. Feb 1, 2013 #1
    I was not too sure what to title this but I just skimmed through a thread with the same title so I just used this. I am not sure whether to go into math or physics. I would prefer math but how will I ever know if I "know" something. This is a troubling thought that discourages me from math. On a side note, that foreign language requirement for math is annoying. Anyways, physics seems safer. Its hard to argue that one does not know how to produce a product if they physically made it. But with math it seems very difficult to "know" that you "know" - I actually do not "believe" in 100% "knowability", which leads to the "belief" chance for any possibilities at any time which leads to the "belief" of "unknowability". It has not been proven that the uncomprehendable is impossible. The perception or reasoning ability of the spectator does not change what is already there, could be there, or is not there. I hope you can see the evidence I provided in the context I wanted it instead of literally what the words say because everything I have said does not agree from the beginning but the "opposite" is unprovable. Regardless of my "belief", I am willing to go along with "2 can only be 2, and no other number at the same time" for now. Does more relativly solid evidence like this come up in pure math? I do not care if math is applicable or not, and I do not care about producing products at all, but I just want to "know" I "know" - and I think something intangible like math seems difficult to "know" I "know" it. One of my main goals is to attempt to "know" as much as I can, and/or spend the rest of my life attempting to maximize an impression of "truth". Another goal of mine is to continuously raise my reasoning skill as high as I can. Heck, I might even do philosophy. I can correct relatively inaccurate statements all day because it is just fun. I get nervous when I communicate because I'm an unconfident person, because of my "beliefs", so I'm not sure how accurate this is. Also, I forgot to include more "things" so ask questions!
  2. jcsd
  3. Feb 1, 2013 #2
    I recommend that you go into philosophy.
  4. Feb 1, 2013 #3


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    Hardy said the more useless it was he felt purer. Or something like it.

    "A Mathematicians Apology"
  5. Feb 1, 2013 #4
    That's Hardy's opinion. Not all mathematicians think that way.
  6. Feb 1, 2013 #5


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    Sure. I didn't say they do.

    OTOH, Hardy was important enough in pure math to give his opinion some weight (IMHO).

    I look forward to contrary quotes from other noteworthy pure mathematicians, if you have any.
  7. Feb 1, 2013 #6
    Wow! You guys are really gonna have this pissing contest on my post? Why.......
  8. Feb 1, 2013 #7

    While an entertaining read, I think that book has done more damage to the social culture of mathematics than other single book I know. There is nothing wrong with Hardy's opinions, just that people take them way too seriously.
  9. Feb 1, 2013 #8
    Just look at the following interview with some Fields medalists: http://www.ams.org/notices/200703/comm-fields-interviews.pdf All seem to be implying that applied mathematics is important one way or another. While they might not particularly care much about applications, they don't seem to be very much adverse to it, unlike Hardy.
  10. Feb 1, 2013 #9


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    Thanks! Great reading.
  11. Feb 1, 2013 #10
    Eh, guess ill give my opinion on something on my post, even though y'all aren't helping. So yeah, the one talking isn't the problem. Problems occur when people take actions, that cause harmful results, based on another persons speech.
  12. Feb 1, 2013 #11
    I think the important thing to remember is that even the parts of math that seem the most "useless" can turn out to be very practical. There is a lot of interplay between various branches of math. For example, stat is a pretty applied branch of math, I think most people will agree. On the other hand, many people might think that algebra is a branch of math that is less "applied" than other areas - and I would agree. Yet, there is an entire area of research known as algebraic statistics where "useless" stuff from algebra is used to do stat stuff. This has the advantage of advancing both statistics and algebra. This kind of thing happens all the time, and I didn't really notice it until I started grad school and began attending seminars and such.
  13. Feb 1, 2013 #12
    K. I'm sure I did said I do not care about applicability. Just about "knowing". I suppose I could learn all the math and then apply it every now and then just to satisfy this "knowing".
  14. Feb 1, 2013 #13
    What do you want to do with your life?

    If you want to do anything other than be a professor who researches, I would strongly discourage a pure math major. I would also discourage an applied math major, since the theory being taught is presented better in engineering courses where you will actually experience countless applications of what you're learning. If you want to teach, most math programs have an education emphasis.

    At one point in my career, I was into pure math. However, after reaching the 700 level in Algebra and finding very few true applications, I totally lost the motivation to learn it.

    Maybe theoretical computer science would be up your alley... but good luck finding a job where you'll be able to do anything other than programming.
  15. Feb 1, 2013 #14


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    I'm curious as to how you people figured out what in god's name post #1 was actually saying.
  16. Feb 1, 2013 #15
    Ima be a teacher ,no matter what I major in(including engineering), to reinforce my knowledge. So if I learn the math in engineering anyway then ima do engineering. I just wanted math/physics for a dramatic understanding so I won't miss anything but if engineering encompasses enough math/physics understanding to be very competent then ill do engineering. And if I can build it then I "know" something. I didn't want to multi phd major anyway because I like to overanalyze and there isn't enough time to overanalyze all these fields.

    Wait but I'm still confused on this. I'm doing ChE, btw. What am I missing from the physics classes that are named "solids" ,and "eletricity and magnetism"? What am I missing from advanced organic chemistry and inorganic chemsitry classes? What am I missing from math classes I am not taking? I am just convinced that all of these upper division and grad school course versions of my foundations of ChE(chem, math, phys) cannot be for nothing. Is there really no reason to further my physics/math/chem education beyond those basic lower division undergrad courses? Will extra classes just be a waste of time? Should I just stick to the ChE classes now? Will I learn everything I need to know and build up my intuition of theoretical possibilities to an optimum level with just that?
    Last edited: Feb 1, 2013
  17. Feb 1, 2013 #16
    I have no idea what the ramblings in post #1 were saying. I guess I was just answering the title of the thread.
  18. Feb 1, 2013 #17
    I know you said you were willing to go along with that, but the only thing I could make sense of in the OP was something along the lines of "how do we prove something like this."

    The short answer is, we don't. Unfortunately, in mathematics, there are a few things we just have to take for granted. For instance, I don't think we can provide an entirely rigorous definition of equality, other than "two numbers are equal if it's obvious they're the same number" and "two numbers are nonequal if it's obvious they're not the same number." Or the fact that 1+1=2, it's difficult to define addition unless we define it with respect to "adding 1," but then we need to define adding 1. And so on.

    If you're confused, don't be surprised. My point is, we can't prove or define anything in maths from scratch, we have to take some things for granted. 2=4 if our number system is based on modulo 2, for example, so it's possible to design systems where almost any axioms break down.
  19. Feb 1, 2013 #18
    First of all this post embarrassed me because I am sitting in a coffee shop on my kindle reading it and trying tohold back the laughs. I actually get what you are saying and I have gone through this same thought process myself (and still do at times), which has caused me a lot of stress and delays in my college career. The best thing to do is to stop worrying about "knowing everything" and just focus on one subject until you can master it, and afterwards continue with another subject if you like. It is impossible for one man (woman) to know "everything " that there is to know. If you try to do this you will become a jack of all trades but a master of none. With regards to the applicability of math classes to engineering / physics, I have found that the physics classes have increased my understanding of what the equations actually represent in the real world, whereas before when I was taking only mathematics I just saw a bunch of variables and differentials and symbols but did not really understand their significance.

    Also, I am not a big fan of pure math myself, but keep in kind that a lot of pure mathematicians do not realize the applicability of their work until they are long dead.

    If you want to be a teacher, I would suggest improving your grammar (ima be a teacher LOL).

  20. Feb 1, 2013 #19


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    The title was cogent. Rest wasn't. :)
  21. Feb 1, 2013 #20


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    Haha fair enough. I saw the title and almost had a heart attack.
  22. Feb 1, 2013 #21


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    No body could! That's why:
    babysnatcher, to answer your questions
    Read the college catalog descriptions or, better, ask professors who have taught them. The content of even the same named course can vary from college to college and even from teacher to teacher. For math, at least, the content of upper level undergrduate and grad courses tends to be the derivations and proofs of the "methods" that you learned in the lower level courses.

    Statements in mathematics are "verbal knowledge". Things are true because they follow from the basic definitions. "2 can only be 2, and no other number at the same time" because "2" is defined to be a specific number. Every statement in mathematics begins (even if it is not explicitely written) "IF (all definitions, axioms, etc. for this particular branch of mathematics) THEN ...". A specific theorem makes no claim that all of those are true, just that if they are true, then ...
    Last edited by a moderator: Feb 1, 2013
  23. Feb 1, 2013 #22
    I think your decision should depend on how much you like theory, some people get into really pure math, with no applications, and find it pointless, others like it best. If you really like your applications, I would stick with applied physics, or engineering. Also, you may be surprised by how much 'pure' math you see in theoretical physics. You should research into each field a little more, look at pure math topics and see if any really interest you.
  24. Feb 2, 2013 #23
    My main response to such questions is to ask in return:

    Is music useless?

    How will I ever know what a symphony means?

    Should everyone become a professional musician? No, of course not. Should people have strong preferences in music? I know I do.
  25. Feb 2, 2013 #24
    You can never know anything "beyond doubt", except (perhaps) that you are a thinking consciousness, even "2 is always 2" might be just a dream you're having, or a malicious idea that some demon has placed in your mind. There is really only "best opinion" as defined by the gatekeepers having that opinion (in maths it's maths professors, in physics, physics professors...) If you like maths more than physics then why is that? If you prefer mathematics to physics because it's a more interesting "game" for you, then do mathematics, don't do it because you are worried about "truth standards", because there is no truth... (if you can't see that, and are really bothered by it, then you better study a lot of philosophy... Socrates said we know nothing, and he's right...) Also don't choose on "usefulness", who's to say what's useful? Do what you like...
  26. Feb 9, 2013 #25
    To all you people with the same issue,

    Solving a thousand 30minute physics problems? No problem.

    Understanding my post? Legendary difficulty.

    I'm glad some of you can automatically connect everything together. Its relevant one way or another.
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