In my previous piece, I outlined this pervasive feeling of being <, this mix of imposter syndrome, stereotype threat, and my own insecurities blended together in a, to say mildly, unappetizing concoction.
Since then, I’ve spent the past month interviewing four mathematics and statistics faculty members here at Swarthmore, to see if their experiences as professors would cultivate wisdom and help solve this particularly nasty equation of feeling consistently and constantly inadequate. I spoke to Professors Hsu, Schofield, Talvacchia, and Thornton, at great length and detail, about their experiences, their interests, and of course, their shared love of math. I am grateful to all of them for their time, advice, and encouragement.
Introduction: Welcome to “real” Math!
My first realization during all of these interviews was “Wow, math is significantly more dynamic, new, and diverse than I thought!” That says more about me and my general ignorance, but I was heartened because in a field so varied, there could be a spot for me too.
Professor Hsu “fell into” algebraic number theory, a field Hsu characterizes as “under many different umbrellas … but very loosely, number theory, as you might guess, is the study of numbers, and all sorts of questions that are related to numbers.” Professor Schofield is a psychometrician, someone who uses statistics to measure educational and psychological variables. Professor Talvacchia researches differential geometry and geometric analysis, using “generalized, souped up techniques of calculus to understand the geometry of spaces.” Lastly, Professor Thornton is investigating two fields of statistics: how we should broaden our definitions of categorical variables (categorical variables are qualitative variables such as gender, marital status, etc.) and “new ways to conduct inference, or drawing conclusions about our certainty or uncertainty of different model parameters.”
When Professor Talvacchia mentioned that her research was based on the 2010 work of Oxford Professor Nigel Hitchin, I was stunned. The math I’d been learning came from Newton, who was not from 2010. How new could math be? In hindsight, this is a silly thing to be surprised about — all fields are growing and expanding— but it’s symptomatic of the tunnel vision with which our society views math.
My friend, who is a history major, mentioned that he didn’t even know what mathematicians could study further — everything seemed solved. When I mentioned this to Professor Talvacchia, she referenced “the vertical curriculum.” She further explained, “that is sort of the nature of the beast [math] is that it’s relentlessly vertical in the way that for example, that languages are.” Vertical, in the sense that all things — like grammar and vocab in the case of languages, — accumulate on top of each other.
Math is like building a skyscraper, in the sense that you start underground, in dull arithmetic and times tables. Then you start cracking through the surface with algebra, but it’s a tall journey. Only after building levels and the foundation can you see beautiful stars. Once the sky has visible stars, you can explore “mathematical galaxies.”
It seems that few make it to the skyscraper stage, in which the delicacy of logic and the strength become the aforementioned “beautiful stars,” in part due to the extreme vertical nature, and difficulty, as Professor Talvacchia remarked, of building on top of everything and remembering it.
Because of these challenges, it’s impossible for many outside the field, including myself, to imagine a field that continues to grow, like an actual Tower of Babel, since “everything seems to be solved.” This mindset seems distinctive to math, and it’s likely due to the stigma around being a “math person” or not. This brings me to my first lesson from these professors: resilience.
Professor Hsu: Pick yourself up!
S.T.E.M. attrition is notoriously atrocious, having classes that “weed,” or distinguish through struggle, the students who can do S.T.E.M. and those who can’t. For Professor Hsu during her undergraduate years at Rice, it was her first real analysis class (MATH 063 here) that almost “weeded” her. She describes the experience as “very, very disheartening to me. And I actually thought, at that point, that I had been weeded. … I just thought, It wasn’t meant to be … so onto the … next topic.”
The journey doesn’t end there because “my undergraduate advisor said no, no, no, it’s not over for you in math … I was able to move on in my undergraduate math career.”
The next obstacle was that she only got into one graduate school. It’s true that students only need one graduate acceptance among the horde that people apply to, but rejection is still rejection, and Hsu described this as “a little frustrating.” Although Professor Hsu enjoyed real analysis much more during graduate school, she struggled to pass her comprehensive exam in the same subject that almost “weeded” her in undergraduate study. She told me, “And so the third time I took it, I’ve just never studied so hard for an exam ever.”
When I asked Professor Hsu for advice, the first piece she gave was this: “I think it’s important to hear that you will stumble. … So my first piece of advice is that when you stumble, it’s so important to believe that you will, and that you can pick yourself back up. And that you … can do it. The reason I say it’s important to hear that [is] because throughout my career, I’ve had people in my corner, when I stumbled, to say to me, you can do it, pick yourself up, don’t give up.”
When I was a junior in high school, the same year I felt “weeded” from math, I had to read Angela Duckworth’s Grit, which is a book based on this theory that grit, which is resilience and hard work, is the essential ingredient to success. Reading the transcript of my interview with Professor Hsu, I remembered all the feelings of inadequacy and “failure” (an 83, Alicia??), and I remembered not expecting to struggle. Sometimes I wonder what would’ve happened if I had had someone in my corner to help me be resilient. Resilience sprouts from the inside, but it is greatly encouraged and discouraged by external factors.
Professor Schofield: It Takes a Village…
Professor Schofield’s father was a math major, and when they played board games as a family, Professor Schofield could go farther than her dad because her dad could go as far as the dice added, while Professor Schofield could go as far as the dice multiplied.
She explains further, saying, “Whenever we cooked we would talk a lot about fractions and all of that. … So I really in many ways credit my, I guess my journey as a mathematician to him, because by the time I then reached elementary school, I had a lot of skills already that he had sort of helped develop.” This exposure to math as something interesting and entertaining elicited a positive reaction to math throughout her childhood.
When she went to college, Schofield played field hockey and had a teammate who also was a math major. Schofield elaborates, “And it made me love math more because I had somebody else with whom I could kind of share my love.” This friend also helped to understand confusion, in the sense, “there were all of these different reasons that I could be confused. And having other people around, I think can help both in getting rid of that confusion, but in also helping you realize when it’s about you, and when it’s really not, because a lot of the time, actually, that stuff is not actually about you.”
It takes a village to raise a child, and it takes a community to cultivate a mathematician. It’s the sense that math, as a “vertical” subject, requires understanding the knowledge of your predecessors. On this journey, however, it’s significantly more bearable when you have a community to support you. Did I have that community when I was in high school? Part of me didn’t want to live up to the stereotype of women being worse at math and S.T.E.M. in general, so I refused to seek help. Community isn’t something you only reach for when you’re staggeringly lost; it should be the place where you try to make a map together to prevent getting lost, and when the GPS inevitably breaks down, it’s where you ask for direction. I had an isolationist mindset to math when I was in high school because before calculus, I did not need anyone’s help, so I chose not to help others, and when I needed help, I was too afraid to ask. I didn’t have a community where I felt comfortable enough to fail, and since I wasn’t comfortable with failing, how could I pick myself up?
Professor Talvacchia: The Struggle is Real
I never had to struggle in math until calculus. In my previous article, I mentioned that I wrote poetry during all of precalculus, but I also did not mention that I almost never did homework since it wasn’t graded and I didn’t need it. Yeah … Not super proud of that, but it’s the truth, and it’s a truth borne by the fact I just didn’t care. When I got to calculus and was still struggling, while doing the homework, I didn’t know how to study or what to do. In her story of resilience and struggle, I was deeply touched by Professor Talvacchia’s wisdom and strength.
We begin with a discussion of our backgrounds, and she details this.
“My grandparents, you know, emigrated to this country where they were tailors actually, they dressed beautifully. They made their own clothes. They worked in sweatshops, big factories, but for them, it was the American dream, they made enough money to buy a home and live, you know, stable, comfortable lives here in the United States. But it wasn’t like it was, you know, a family that had access to a lot of education before, but they very much valued it.”
My own grandparents worked in factories in China, and none of them went past high school, but they valued education enough to encourage their children to succeed and eventually go to graduate study in the U.S.
When Professor Talvacchia spoke about graduate school and sexism, I was shocked.
“When I got to graduate school, I realized, it’s not a fair situation for women. There were no women on the faculty. The faculty used to say to us things like, ‘Oh, we would like to hire women, we just can’t find any that are any good.’ Yeah. And all the other women [in] my year quit. So there was only a sprinkling of women in the graduate program.”
She then detailed her determination to finish and be different.
“With that said, [I] wasn’t discouraged by this, I was really aware of it. And I just determined that I was gonna finish and be a mathematician, because I wanted very much to be a mathematician. And coming from a background that was not so privileged, in some ways, I think was a big advantage. Because I wasn’t expecting anything to be given to me. Or I wasn’t expecting really, to be fair, I grew up in a neighborhood where life was unfair for a lot of people. Okay, and you learn how to just try and be persistent with what you want to do. And that’s the way I viewed it. … I mean, it bothered me, I didn’t think it was fair that all the other women dropped out, or the discrimination that I saw, but I just determined, I was going to do my best to finish be as good a mathematician that I could be and that if I came to this career, I would be different. I would encourage students, I would make sure I was not biased, I would try and counter it very proactively that way.”
What struck me as inspirational was Professor Talvacchia’s ability to fight for what she wanted, to achieve her goals in spite of the struggles many women found indomitable.
She further elaborated, saying, “I think life is a difficult journey, right? Privilege or no privilege, there are advantages and disadvantages to whatever circumstance you’re brought into. You just have to deal with it and try and make the best of your life. I agree that sometimes access is problematic for society. But I don’t think anyone gets a free pass.”
To know that life is difficult is sobering, in the sense of cold water splashed on one’s face during a fever, the fever of idealism. To know that one will struggle prepares one for it; it gives one a strength that one has through foreknowledge.
Professor Thornton: Don’t Box Yourself In
Professor Thornton and I had similar religious upbringings, which we briefly spoke about in regards to how they affected our own insecurities. I mentioned how girls’ bodies were policed by the male elders and pastors “to not tempt the boys,” and she mentioned how a boy she knew told her that men were supposed to be leaders, and women were supposed to follow. (As someone who was raised evangelical, this is a legitimate thing people say, actually quite a bit.)
She mentions, “My appreciation of it [math] grew, but also so did my insecurity. Because … I had internalized those messages of I’m not really supposed to be good at this. I’m not supposed to like this. And so yeah, so it really came to be in something that I struggled with a lot was internal and external biases and pressures.”
Professor Thornton, as I documented earlier, has two main research interests, which to me, someone who has little statistics background, seem quite divergent. These different interests (the expansion of categorical variables and new ways of inference) resonated with what I believed was her best piece of advice to me.
“There’s this saying in this phrase by a famous statistician, one of the less problematic ones, I think. But the saying is that you get to play in everybody’s backyard. And so that was also my appeal to statistics. I love learning about anthropology, sociology and psychology and economics, and physics. And like, all of these things are interesting to me. And the one tool they have in common but they all use statistics at some level or another and so that’s kind of why my research is a little bit weirdly split right now is because I’m trying to incorporate some of those other interests of mine into my work.”
She further elaborated, “Your interest[s] will never be easily summarized in one subject, or one field, or one major. You’re a human being with so many different aspects … Picking a major, choosing a major is not the same thing as … defining your identity.”
As someone, like many Swatties, preoccupied with their future, to hear that my identity wasn’t consistently and inexplicably bound up with whatever field or occupation I had was heartening.
It was heartening to know that I am more than my failures and successes in math. I am more than my GPA. As someone who is incredibly grades conscious, it’s something I must tell myself.
After all of these conversations, so full of wispy inspiration and the precipitation of wisdom, I felt a slow change. This slow change was that yes, I am going to struggle and fall. I am going to fail, whatever that even means. But what makes this is a change is that I am getting up, dusting myself off, and finding “the path” again. I am finding community, and something, just a flicker of a candle, within myself to once again feel “good enough” and greater than.
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