a pro at imperfections, and best friends with her doubt

It's a Friday in May, maybe half past noon. I'm sitting in a lecture hall that holds about sixty students at full capacity, but this is an upper-division mathematics course, and only roughly a third of those seats are taken. As I watch my Advanced Calculus professor lecture on the Cauchy Condensation Test and try to follow the multiple concepts with my red pen, my thoughts are half with the lecture, a fourth with the midterm I'm about to turn in, and another fourth with the linear algebra midterm I have to turn in my 2 p.m. that has a proof on it that I just can't figure out. Oh, what a joy it is at 10:30 in the morning to find out that one of your proofs has a major flaw, and you doubt you'll be able to fix it with two classes in between the 10:30 a.m. and the 2 p.m. deadline. Maybe it doesn't help that I can't get the phrase “infimum of a set” out of my mind, and it's not because I need to figure out what the infimum of any given set actually is. I even had a dream on Wednesday night that Jesus was talking about the infimum of a set in the Gospel of Matthew.
As I'm sitting here, I start wondering at the fact that I'm sitting here at all. This is an upper-division mathematics course. I hated math in middle school, tolerated it in high school, and randomly decided to pursue it as my major when I took trigonometry. At this point, I had never had any logic, I had never seen a fully developed proof except for the ones in my calculus textbook that I didn't understand more than 1% of. Why am I sitting in a lecture hall with a score of other students -- one or two of whom I might classify as genius -- in front of a similarly genius professor, listening to a lecture I don't understand much of and probably won't understand much of for the rest of my undergraduate career? I should be sitting in an English class, because that's obviously where my real talent lies. My coworkers at the tutoring center used to tell me that I'd make a great proof-writer; I am the only person in Learning Support Services who's taken both upper-division mathematics and upper-division English courses. My grades on the recent homework assignments and the fact that I can't keep up with the homework revisions most of the time tell a different story about my proof-writing skills, and having to admit to various people that I'm really struggling in all my classes this quarter doesn't help my self-esteem. For the first 130 credits of my college career, I never got anything other than an A. That included a graduate-level biotechnology course and five college-level mathematics classes. And then the minute I came to Central, my perfect 4.0 GPA was slashed down to a 3.99 by my sophomore-level linear algebra instructor.

After I leave class, I ruminate that day, and the next, on how I should quit this thing they call the math major, how I should drop out of university. I know with a sickening certainty that I failed my junior-level linear algebra midterm, and I don't understand why linear algebra just isn't my thing. I don't understand why I had no trouble getting straight As until I came to Central, and suddenly I'll be lucky if I pull out of Linear Algebra II with a B.

I have trouble sleeping over the weekend because I'm afraid to get my midterm scores back. When my professor hands me my linear algebra midterm, my awful premonition is realized, and I don't know what bothers me more: the fact that my score doesn't even meet C level or the fact that I have trouble feeling anything about it. I don't really have the energy to cry, and all I feel is a weight tugging down all the hopes I had for my career in math.

But I go talk to my professor, even though I don't want to, and leave his office feeling relieved that I finally let someone know the struggle I've been having with every one of my classes all quarter. A couple days after, my instructor is proving that the countable infinity of every irrational number in the set S := [0,1] exceeds the countable infinity of the natural numbers (that is, the counting numbers). Finally, I can see why some infinities are considered larger than others! But then my instructor talks about Cantor -- or maybe it was Hilbert; he can't remember -- and how one of these mathematicians was committed to the insane asylum for the concept behind this proof about countable infinities, because mathematicians didn't want to accept the proof as fact. My instructor inserts into the story, “At one point Hilbert proved something existed by contradiction; that is, he said something could not exist and came upon a contradiction, thereby showing that it must exist. And mathematicians were angry, and said 'That's not math! That's theology.'” And the sheer beauty of logic, of mathematics, of God so overwhelmed me that I wanted to cry, and days like this show me how privileged I was to have stumbled upon the math major to begin with.

The mathematics major is a lonely business, and often an unforgiving one. Mathematics is inexorably precise. Mathematics means sometimes spending ten hours a day working on proofs, three or four days in a row. Mathematics means being wrong, a lot, and sometimes it means looking really stupid. There aren't a lot of people who understand what you're going through or the insecurities and anxieties you face. There aren't many people who understand your sense of humor or your math puns or why you're socially awkward. (I guess the good thing is that I've found a place where being socially awkward is considered socially acceptable.)

But there do exist some people who do understand, because they also have fought and tried to overcome the insecurities and anxieties that curse you. There are some who laugh at your silly math jokes and think your social awkwardness -- that is, the fact that you laugh uncontrollably about absolutely everything -- is charming. They've spent hours writing and refining proofs; they've probably spent a couple of those hours crying over those proofs, too. They're socially awkward. They don't shut up, they never speak, they make weirder noises than you've ever heard, they tell more jokes in sixty seconds than most people hear in a month, they freak out about anime and a cappella and theology and philosophy, they jabber in Elmo's voice, they tease so seriously you'd believe anything they say.

Yeah, the mathematics major is a lonely business, and often an unforgiving one, and no, my linear algebra midterm score probably isn't going to make it past C level (it's a shame my score can't hike). But there are days like today, and there are people like my classmates, and there are gifts God created like laughter and smiles and spring, . . . and when morning rolls around, it is, indeed, another day of sun.


  1. Hannah, I have to say it is so admirable to see you pursue a subject so intricate, complex, and challenging as mathematics. I think you need to keep studying math if only to breech the gap of communication for people like me, people who are inclined to see math as nothing but a string of formulas, proofs, and numbers. Here your English and writing skills put you at an advantage, because not only do you understand these formulas and concepts, but you also know how to communicate them to other people.

    You are going great places, I promise. And while the struggle is so hard and tedious now, the months and years will fly by and before you know it you will be graduated!!

    Much love to you,

    Dani xoxo
    a vapor in the wind

    1. Dani, thank you so much for your encouragement. The last three weeks have been pretty rough on me, and while I don't want to say any of this to complain, I am still learning how beneficial it is to get my feelings out in the open, and I want to have the chance to encourage other young students who feel the same way.

      Really though, the thought of my graduation was one of the few things over the past several days that made me want to stay in the math major. I'm keeping plugging along :-)


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