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Is Mathematics Worth It?

  1. Jun 13, 2014 #1
    I'm going into second year next fall, but even after a whole year of college and after getting exam results I'm not completely sure about what major(s) I should do. I'm 90% sure I will do physics only but I'm afraid of regretting not sticking with pure maths. The reason I'm reluctant to double major is that it will mean less physics, applied maths and programming classes which are all useful to my long-term goals. I don't ever see myself researching maths devoid of direct application, and from what I know the maths necessary for understanding all the physics I will be doing will be taught in the physics classes themselves.

    Additionally, I find pure maths classes to be much more difficult than physics or any other field of application, proofs don't come to me easily as the non-trivial ones generally involve some subtlety. I dislike things I can't have intuition for , i.e. algebra, especially abstract. When there is no intuition to either quantify (like in geometry) or contradict (like in topology/analysis) I don't find things interesting. When things are not interesting, I end up either bored and disillusioned, or I try thinking of applications because that would at least give me some purpose, but the most abstract parts of maths tend to have the fewest applications. I feel I have to memorize all theorems and results when I don't have intuition, while in physics I never feel like I have any rote-learning to do. Also, this intuition thing bothers me because all the real "maths types" I know tend to enjoy things like abstract algebra and number theory the most.

    I know that so far, it seems like I have no case for double majoring, so I'll explain. I will only be forced to do two or three more of the no-intuition classes for the rest of my degree if I double major, which is a minority considering I'd be doing 18 more math classes in total. When it comes to the others I know I will very strongly enjoy them. I really love the rigor of maths theory, in contrast to physics where I often find theory very dry and only start to like it when I'm doing problems. I find analysis exciting; even though results involve infinite and infinitesimally small quantities have surprised me many times, I can still never see the next one coming. Even though I haven't done any yet, Differential Geometry, and non-Euclidean geometry are things I'd really like to study. I've seen some of it in Roger Penrose's book; and manifolds, fiber bundles, etc. all seem very cool.

    So, to the people here who are familiar with advanced maths, does it sound like I should double major or not? I would like to make this decision as soon as possible. Thanks!
  2. jcsd
  3. Jun 13, 2014 #2
    You said you don't like math. Don't study math. Problem solved.
  4. Jun 13, 2014 #3
    I really don't know what to make of your reply. I assume you just scanned through what I wrote and you got the impression that I don't like it. But I never said I don't like math.
  5. Jun 13, 2014 #4
    I'm only an undergradute student myself, and to be honest you've probably taken more math than me, but here's what I have to say:

    Option 1: The Physics Intensive Route
    If you like applying your mathematics, I would definitely switch your major to Physics. At that point, fill up as much of your classwork as you can with Physics. Fill up the rest with mathematics, and you'll probably have enough classes to qualify for a minor.

    Option 2: The "Get a Job" Route
    Switch your major to something more marketable, like ME or EE. From there, minor or double major in physics. Maybe take two minors, in math and physics! Either way, with this route you'll be preparing yourself for industry where you'll get to apply your math every day.

    Option 3: Continue with the Double Major
    Keep your double major in mathematics. Doing so will probably better prepare you for graduate work in EITHER math or physics, so your options are open. Keep in mind, though, that while you are enhancing certain academic prospects for yourself, you are also likely limiting your industry prospects after school. Sadly, this dynamic is often at play when studying things like pure mathematics -- or physics.
  6. Jun 13, 2014 #5
    Who said you can't have intuition for that? Maybe try reading Visual Group Theory by Nathan Carter. You're having a hard time because mathematicians are bad about motivating things, not because the subject is actually that way. Also, learning about math history may help.

    Again, this is because mathematicians are often bad at motivating things. There should be plenty of intuition if people explain things properly, but often, they don't. No-intuition classes are the professor's fault, not the subject's fault. If you talk to them in office hours, though, you might find that they at least have more intuition than they might be letting on in class--but there are no guarantees.

    If you get to research-level math, it becomes very hard not to rely on memorizing lots of big nasty theorems because the proofs are insanely complicated in many cases. Some of these theorems may be basic to the field. I have a sneaky suspicion that, in at least some cases, if you talked to the right person at the right time, they could give you the idea behind the theorem, so that you wouldn't have to waste your time studying a couple books and reading a 300 page paper if you wanted to avoid doing what everyone else does and just take it on faith. But no, that would be too easy. Instead, people just write down their proof and then force you to either reverse-engineer it or come up with your own proof of it from scratch if you want to make any sense of it. Of course, often, people do talk to each other to bypass nasty proofs that conceal the ideas, but it's not always easy to know who to ask, and a lot of times, I think the intuition is just forgotten, but people just keep plugging away with the theorems anyway. It's really a mess. You wouldn't like it. I couldn't take it anymore and quit, myself.

    Needless to say, no matter whose fault it is, it's still going to probably be somewhat painful to study.

    Usually, I think math can be a good double major, but for you, I don't know. With physics as the other major, something more marketable like statistics or computer science might be better. You have to think about jobs at some point. Math goes well with something like engineering, as a double major, in certain cases. It goes really well with physics, too, except that most physics students won't end up doing physics, so that cancels out most of the benefit, except in the rare cases in which physics (and not just some data science job that's sort of like physics and uses some of the skills) actually works out as a career.

    You can always study more math on your own, if need be. I think that's probably what you should do. I have a feeling that you'd like Visual Complex Analysis.
  7. Jun 13, 2014 #6
    Thanks, I'll take a look at Visual Group Theory. Part of the reason I've given up hope that an intuitive understanding is possible is that even the students who are good at that sort of thing don't exude a deep understanding, rather they just tend to be creative when it comes to symbol manipulation.

    I'm aware of how unemployable it is but I'm still naive, and like many science undergrads, I'm only thinking of doing research in the future.

    I think you're right. Thanks for sharing your experience of this problem.
  8. Jun 13, 2014 #7
    The guys that are just good at symbol manipulation will just forget most of what they learned, I bet. Unless, they are always using it. It's pictures that stick in your mind.

    Being "good" at it by the standards of some class isn't any sort of absolute measure of success. Also, appearances can be deceiving. For example, if I think of the concept of a coset of a subgroup, I think of it as "hitting every element of the subgroup" by some element g and seeing all the places where it lands. After I've learned it, you might not see me explicitly invoke that picture all the time, but it will be there. It may just look like I'm moving symbols around, but in the back of my mind, there are pictures that make it a little more than that.
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