Why doesn't math make sense anymore?
December 4, 2008 5:35 PM   Subscribe

I've got math anxiety but not the traditional kind. I'm graduating with a math degree but I feel very insecure pursuing higher math. How did something this beautiful turn into a bugbear?

I've gone to a good undergraduate institution (Fields Medalists in the faculty) and I've taken higher math classes on functional analysis, algebraic topology in addition to foundational stuff (real analysis, topology, algebra). So I'm happy with the training I got and material I've been exposed to.
My problems are:
1) Self-worth: I don't feel creative or original. An English major isn't expected to be an author, but in Math you're expected to produce. I studied math because it was beautiful but the thought of making it a job has made me second guess my first love.
2) Abstractness: I never feel like I really know what's going on. I can pass the classes/tests but I feel like I'm faking it, as if I'm just parroting proofs. I've considered applied math but there's this really macho posturing between pure and applied and applied is seen as "dirty" or for the guys who couldn't hack it.
3) Intelligence: I used to breeze through lower division classes and would be the go to guy for a problem but in these upper division classes I feel like I don't get things as fast as my peers. They can follow a conversation on harmonic analysis while I have to scramble to write down notes and take several hours after class to understand. Some of my friends have papers published with professors and I feel like I'm behind the game.
4) Socialization: I don't feel like I can connect with my professors on a personal level. I'm fairly socialized and have hobbies like music but my professors are either genetically blessed or work non-stop and think about math all the time. I don't know if I can commit to that level of intensity.

I don't know if I should go to graduate school. I feel like I've put in so much time thinking about this stuff that it would be a waste to stop now but at the same time I don't know if I want to continue the abusive inferiority complex. I'm considering teaching high school math but I feel like I've failed relative to some of my friends going off to prestigious universities for doctoral studies.

Please help me think about this stuff.
posted by anonymous to Education (20 answers total) 20 users marked this as a favorite
As an undergrad math major, I was advised by a professor (of applied math) to go to grad school in anything but math, which he described as "stuffy." I don't know how true that is, but having the same kind of math anxiety you describe after four years of abstract math, it offered me a great "out."

I'm terrible at biology, chemistry and physics, so I picked computer science, and it was a great choice. I think economics would have been a good fit for me too. The job market for PhD's in the sciences is pretty bad right now, so you may want to consider that, but just because you go to grad school doesn't mean it has to be math grad school -- it doesn't even have to be anything in which you have any real background! (I had two programming classes in college, and that was it.) Consider a field where you can use your math abilities at a less abstract level while solving more applied problems where you can get your hands dirty.
posted by transona5 at 5:59 PM on December 4, 2008 [1 favorite]

"How did something this beautiful turn into a bugbear?"

Simple. You formalised its role in your life by studying it and assigning an enormous amount of importance to it beyond mere enjoyment. It can happen to anything.

Hell, you could be the biggest Star Wars fan in the world, but if you were to suddenly start studying it so that you could write essays that needed to be in by a certain date to ensure you earned enough passing grades to allow you to study the next set of subjects in the following term, and then devoted three or four or more years of your life to it, repeating the process every one of those years for however many years... I guarantee you that you'd hate Star Wars, and not just because you're sick of listening to Jar Jar.

The only solace I can give you is that once you leave the structured world of University and enter into the adult world of working and using what you've learned to earn you money, you'll find a certain amount of joy returning to you.
posted by Effigy2000 at 6:01 PM on December 4, 2008 [1 favorite]

That time you spent thinking about math can be put to use in any number of academic subjects--computer science, physics, chemistry, biology, or economics to name just a few. Or you could go further afield and use your skills in abstract thinking and problem-solving in business. Or you can give your brain a break and travel around the world for a year, maybe take up painting or creative writing. No matter what you want to do, you will very likely find a way to apply your training to it. I encourage you not to rush into the decision.

Don't go to graduate school if it's not what you want to do, and especially don't go into a field you're not going to enjoy. And especially especially don't study something just because of macho posturing. A friend of mine told me that the way to pick a subject of study in graduate school is to figure out something you really like doing, then come up with a course of study that lets you do a lot of that. This is how I picked my graduate program, and although I've just started it's looking good so far.
posted by fermion at 6:03 PM on December 4, 2008

There is a strong distinction between love of a subject and the subject as a profession. My opinion is that success in a profession is often as much personality traits (obsessive, extroverted...) as talent or love.

Another opinion: many mathematicians are not well-socialized and don't connect well on a personal level.

By this time there are probably a couple of professors you respect. Ask them their thoughts.

Your possibilities are not so limited. Math is a fine precursor to many subjects - my father started in engineering school, and ended up as a chaired professor of sociology.

Teaching can be extremely gratifying.

So: what will you find yourself happy with. What can you live with, and what can't you live without?
posted by dragonsi55 at 6:10 PM on December 4, 2008

There is no shame in realizing that you aren't the smartest person in your major at a prestigious university. Also, as someone who has run the grad school gauntlet (though not in math), some of the feelings you describe are pretty much endemic in any person with an ability to realistically assess themselves. When I was in grad school the "macho posturing" you describe was palpable. When I decided that I needed my interests and hobbies outside my discipline (i.e. a life outside the ivory tower), and started pursuing jobs at regional state colleges, all the bigwig professors in the department wrote me off. And you know what? Screw them. Do I publish in my discipline's flagship journals? No. Do I have groupies that follow me around at academic conferences? No. Does my research light the world on fire? No. But I'm an excellent teacher, I publish regularly, and I enjoy turning my earnest but average middle-class students on to the ideas that matter to me. I also have smart, well-rounded colleagues that I respect and who respect me. You don't need to be gold plated from Harvard to have a rewarding career as a mathematician if that is what you desire. There is a graduate program out there for you if that's what you want to pursue. You should consider yourself blessed to have abilities in a subject that is so important to our society that exceed those of all but the very most gifted.
posted by Crotalus at 6:16 PM on December 4, 2008 [11 favorites]

2) Abstractness: I never feel like I really know what's going on. I can pass the classes/tests but I feel like I'm faking it, as if I'm just parroting proofs.

You never really know a topic until you teach it.

3) Intelligence: I used to breeze through lower division classes and would be the go to guy for a problem but in these upper division classes I feel like I don't get things as fast as my peers.

The most horrible two years of my life were when I hit the point that I could no longer breeze through school. Bored through high school, bored through freshman year of college, and then WHAMMO. For the first time in my life I had to learn how to learn things, a trick that my less gifted peers had picked up years ago.

It sounds like your gifts have taken you much further than mine did, and congratulations on that. But now you're in the same boat as everyone else: your raw intelligence will serve you well, but now you'll have to learn the discipline and develop the tenacity that is demanded by higher education.

Or go off and do something else. That's always a good option too.
posted by tkolar at 6:36 PM on December 4, 2008 [1 favorite]

There are lots of options between teaching high school math and going off to prestigious universities for doctoral studies.

My sister graduated a couple years ago with honours in pure maths, and is working at a hedge fund creating models of the stock market to predict its behaviour. While that particular job is perhaps not a great option today, it definitely uses all her maths background, and there must be other jobs like that available.
posted by jacalata at 7:00 PM on December 4, 2008

There are lots of options between teaching high school math and going off to prestigious universities for doctoral studies.

In fact, there's an old askmefi question about that exact thing, for what it's worth.
posted by inigo2 at 7:06 PM on December 4, 2008 [1 favorite]

By this time, you may have heard of the infamous Impostor Syndrome within grad students. As someone who suffers from a sickening dose of that, let me tell you that most people seem like they know more than they actually do. Don't let that bother you. Deep inside, everyone is worried about the same thing.

I once had a very similar question on metafilter, and the wise told me something in the lines of, "you may not be the best chess player out there, but that doesn't stop you from playing. You play because you love the game". My only advice is that if you like math, do math. Don't do grad school as means to an end (i.e getting a better job), because you can get equally good jobs with an undergrad degree. Grad school can be a en end to itself. If you like learning and enjoy the stuff, then this place is for you, even if you're not the next Andrew Wiles. Just remember that nothing good comes easy. If you don't want to end up at a mind-numbing job at a desk 5-9, you have to put effort, even if that means you're not staying at school.

Good luck!
posted by shamble at 7:17 PM on December 4, 2008

Maybe look into an MBA with a focus on finance? While there may not be gold plated jobs waiting on wall street, there are always opportunities in business for people who can run the numbers. CFOs and the like.
posted by T.D. Strange at 7:20 PM on December 4, 2008

but in these upper division classes I feel like I don't get things as fast as my peers. They can follow a conversation on harmonic analysis while I have to scramble to write down notes and take several hours after class to understand.

One more thing: different people learn differently. If that's how you learn, then that's best for you, who cares how others do it? I personally always have to take notes too, and study them afterward.

In any case, I'm sure your other peers also have to spend hours learning the material, upper level math is no joke. Knowing how to talk like you know your stuff when you don't is just a skill. It doesn't mean anything. Don't let it bother you.
posted by shamble at 7:28 PM on December 4, 2008

Feelings of self-doubt and inadequacy are extremely common amongst math graduate students, math Post Docs, and new math faculty. (They may also be common in other fields, but I'm in math myself, so I happen to be a little more well-informed here than I am elsewhere.) While some of them might actually be inadequate, many are not. When the feelings aren't accurate, this is sometimes referred to as "impostor syndrome". (I mention this not because I feel it needs psychiatric help, but to illustrate how common and well-known the phenomenon is.) The upshot of this is that you should probably find some other way of deciding whether this is for you than your gut feeling, which is probably going to tell you that you're nowhere near smart enough regardless of how true it is. Ask your professors if they think you've got what it takes. Don't ask them what they think is a good career path in general (well you can, but that should be a separate question). If you're doing well on exams, you probably are doing just fine.

If your plan B is teaching high school math, then I highly recommend starting grad school even if you're not completely sure about research as plan A. The nice thing about many math PhD programs is that they're designed so that 2-3 years in, if you decide that this isn't for you (maybe you hate research, or you can't pass your qualifying exams, or you just don't want to do it anyway), you can get out with a Masters degree. By then, you'll probably have a little teaching experience. Depending on the school (and your mastery of English, if you're in the US), you may end up teaching your own sections of low-level math courses or just running a recitation section, but you'll probably pick up something. From there, depending on the state, it's usually not hard to get a high school teaching certificate. Having the Masters gets you an automatic pay boost for teaching high school too.

I was not 100% sure what I wanted to do when I got my BS in math, but I liked tutoring/assisting and figured that I would like teaching. I also thought that I might like research. So I went to grad school in math. I've got a Masters and I'm working on my PhD right now. I've only just started genuine research, which has been great so far, but I haven't done anything I'm proud of yet. I didn't start getting serious doubts about my own adequacy until my second year of grad school, but they hit pretty strongly. Almost every other grad student I know gets them too. I still don't know if I'll do fantastic research, but I'm pretty sure I'm going to finish out my PhD. If I hate it, or I'm bad at it, I'll look for a job in a department that focuses on teaching instead of research. If I take to it, I'll look for one where I can do both. I know at least a dozen other math grad students who didn't take to it and got out with a Masters to go into teaching or some other field. Unless you decide to take a complete left turn and do something totally unrelated, the Masters degree will not be useless.

Another thing to keep in mind is that the classes will get very hard. If math didn't get hard, nobody would pay you for it. You will have to learn to ask your professor for help, to stay up all night trying to comprehend something that seems like it should be trivial (often it will be!), and to work with friends in study groups. People who have always struggled with math have probably had to do this all their lives in order to succeed, but if math was always easy for you, they may be new concepts. Measure theory will probably kick your ass. I had to take it twice. I've never met anyone who got through an algebraic topology class with a firm grasp on the material on the first try (unless they already had some background on the subject). The more advanced you get, the average mathematical aptitude of your classmates will rise. This can result in a really nasty sensation that you're quickly being passed up by them, especially if you're used to being so far ahead of the game that you don't have to put much effort into things. Also, math grad students are very good at hiding how much they grasp during a lecture. We do it instinctively, motivated by a subconscious desire to keep the lecturer happy. The result of this is that your fellow students are not nearly as good at this as they seem. Of course, there will be some who are way ahead of you, and you'll probably notice them because of this fact. The ones behind you will probably disappear into the haze and not contribute to the sense you have of where you are in the scheme of things.

Also, it's a very rare mathematician that thinks about math as often as much as they seem to. The talking-about-work phenomenon (which occurs when any group of people whose only true reason for knowing each other is that they have the same job) has a tendency to make it seem like math professors don't talk about anything but math. If you get to know most of them, you'll eventually find that they're not quite as obsessed as they seem. Granted, for an occupation that's primarily about stringing abstract concepts together, "obsessed" is a relative term.
posted by ErWenn at 7:30 PM on December 4, 2008 [4 favorites]

I am a math professor who runs graduate admissions at a top-20, but not top-5, Ph.D. program. I won't presume to tell you whether or not you should go to graduate school. But I will say that your misgivings are pretty common, and you really might have fun getting a Ph.D. I think you ought to try it. Math is unlike many other fields: you won't pay tuition in a Ph.D. program, and in fact will get a reasonable stipend; and if you leave with a master's degree, you're more employable than you were before, not less. So you're not taking a giant life risk by entering the field.

A few things about your specific concerns.

1. "there's this really macho posturing between pure and applied and applied is seen as "dirty" or for the guys who couldn't hack it.... I feel like I don't get things as fast as my peers... Some of my friends have papers published with professors and I feel like I'm behind the game."

Macho posturing is one of the worst things about undergraduate studies in mathematics. In math, there's always somebody who's better, faster, more technically powerful than you; and I promise you, that applies to your peers and to your professors, even the ones with Fields Medals. Mathematics is a basically cumulative and cooperative subject; it only works because thousands of people are pounding away at it every day, and if everyone who wasn't "the best" quit, it would come to a stop.

2. "I'm fairly socialized and have hobbies like music but my professors are either genetically blessed or work non-stop and think about math all the time. I don't know if I can commit to that level of intensity."

This is almost certainly false. You're comparing the part of their life you can see (the math part) to your entire life.

It comes down to this. You should keep studying math if you still like it. Forget about the inferiority complex; that'll pass. On the other hand, if you find the classes are less fun for you as they get more abstract, it's probably a sign that pure math isn't to your taste. In which case, I think applying for a graduate program with a big, active applied math faculty (like mine!) is a terrific idea. Nobody in the real world, including pure mathematicians, thinks that applied math is for people who "can't hack it" -- a lot of the most exciting (and well-funded) action in math is on the applied side, in mathematical biology (both genomic stuff and neuroscience), in climate modeling, in fluid dynamics, in large-scale data analysis.... if you're mathematically minded and skilled, and like tackling real-world problems more than proofs, this is something to think hard about.

Feel free to contact me, by MeFi mail or regular e-mail, if you have more questions.
posted by escabeche at 7:30 PM on December 4, 2008 [8 favorites]

Ah, one last thing. When I was an undergrad, I had a vague sensation that applied math was somehow viewed as "dirty" or inferior. After I got to grad school, that feeling slowly seemed to disappear. Now, I'd be totally weirded out to hear a pure mathematician say something bad about applied math. If you want to dip into applied math, don't let anything stop you. You probably won't even have to decide before you go to grad school (although it may influence your decision about which schools to apply to).
posted by ErWenn at 7:33 PM on December 4, 2008

Abstractness: I never feel like I really know what's going on. I can pass the classes/tests but I feel like I'm faking it, as if I'm just parroting proofs.

That's actually a good thing because you are aware that taking a few classes does not an expert make. To truly get conversant enough in anything to be innovative you need to spend a lot of time working with it in different ways- student, teacher, applied projects etc.

As long as you're uncomfortable faking it, you're good to go because you won't ever settle for sliding by.
posted by fshgrl at 8:03 PM on December 4, 2008

About a year and a half ago I was in your exact position. I had the same mathematical background and passion, but also the same fears about whether this was "enough" -- specifically, I worried that I wouldn't be smart enough to make it in graduate school, that I wouldn't be able to connect with my professors, that I wasn't quite good enough to do this thing that I love.

I decided to apply anyways, and I'm now in the middle of my first year in graduate school: while it's a lot of work, it's also a hell of a lot of fun. If you love math -- not "if you are a mathematical savant," but rather if it's something you really enjoy doing, and will be OK with taking up ~60-70 hours of your life a week -- apply, and go.

I'm really thankful that I did.
posted by Chionophilia at 8:32 PM on December 4, 2008

A pure math background is not a waste. I went through / am going through something similar: I started off university in pure math because I was good at and enjoyed math. A couple of years and many math courses later I found that some of this stuff is really kind of hard, that I'm not enthralled by most of the material, and that even if I think it's a beautiful subject, I probably don't actually want to do it full time. Somewhere around this point I looked a bit more seriously at the psychology courses I was taking for fun, and decided to make a (second) major of it. I'll be doing grad school in some kind of neuroscience. No regrets here — I think a math background will come in handy: an ability to understand statistics is superior to an ability to simply use it, models are mathematical, mathematical thinking is useful for issues of research design, etc. But most importantly, mathematics trains your mind for whatever you may wish to apply it to.

I suspect the ratio of insight available in a class to the amount of work necessary to obtain it decreases as you take more math classes: you end up with more esoteric techniques in more abstract areas that often don't really change your perspective as much as the early classes do. So you may have simply lost interest in math of certain levels. There's nothing wrong with that, and if you are passionate about math anyway, teaching seems like a great thing to do.
posted by parudox at 10:05 PM on December 4, 2008

I don't know if I should go to graduate school.

You haven't listed any good reasons to go to graduate school.

If you really, really wanted to go to graduate school because you know you'd love it but you're a bit worried about being able to cut it, I'd probably say give it a try. But the only reasons you list for wanting to go are "it would be a waste to stop now," wanting to avoid feeling like a failure, and competition with your classmates going to prestigious universities. Those reasons will not carry you through the more difficult times in your graduate course.

Do something else. Being a high school math teacher would not be failure at all. We need good high school math teachers who actually understand math, as many don't.
posted by grouse at 11:10 PM on December 4, 2008

You sound like me about ten years ago. I was a senior, just about to graduate with a couple degrees and not much motivation or direction.

Thinking about grad school was a nightmare. My dad was pushing me into it. I had few research contacts and experience, no papers, and no desire to continue in a field (electron microscopy) that didn't really have my full mental focus, the way that my friends were focused on their med school plans, from working in research labs. I had spent most of my free time in my junior and senior years running a movie theatre. I really didn't know what else to do with my life. I was a nervous wreck.

I had recommendations for my grad school applications but skipped out on the essays, instead visiting old friends in Germany for a few months. I came back and did something entirely else I loved for seven years, before finally going back to grad school.

Going back was a difficult change in my life, and there was one very rough patch at the end, but I know I got more out of the classes I took and I definitely put the effort in, in a way that I never really did in my undergraduate program. Towards the end, without the level of self-motivation I had, I would not have finished.

I can't tell you what to do, but in my own experience, if I'm not totally into something, I've learned to do something else until I am ready to commit myself fully. Perhaps being a teacher is for you is a "next step", in the same way.
posted by Blazecock Pileon at 11:34 PM on December 4, 2008

I went to several years of Ivy League intending to be a pure-math major. That "macho posturing" was horrible... but the worst part was when I believed it. In looking back, I completely agree with that professor's earlier post: applied math is not inferior, if you're not enjoying pure-math look into your options, and there are a lot of average-people cogs in the pure-math machine. It took me a while to figure out what I actually wanted to do (industrial design), as opposed to what everyone told me I should do, or what in which my ego insisted I prove myself.

Give yourself a minute to think about what you truly enjoy/want to do. Do some preliminary research on what those things entail. Talk with professors or mentors. If you love pure-math (and I agree, that stuff can be beautiful), do it! If you really enjoy something, it will give you a better boost than that macho junk.
posted by vaguelyweird at 6:13 AM on December 5, 2008

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