Perceptions of Mathematical Success
By Sandra Nair
When people in various social gatherings ask me what I do, and I tell them that I am pursuing a Ph.D. in mathematics, the most frequent response is “Oh wow, you must be brilliant! I sucked at math in school.”, followed by a complete turn in the conversation. I used to have very mixed feelings about such a response. On the one hand, it feels so refreshing and motivating to be seen as smart for once. After all, imposter syndrome has its clutches on me every day while I’m working in my department, exacerbated by my intersectional identity. Don’t I have a right to feel good about myself for a change? However, when I return to my usual academic life outside the social gathering, I recall those words not with a sense of satisfaction, but the opposite - if I was so smart, why am I not a good enough mathematician? No matter how much I suffer toward my end goals, will I ever be treated with the same level of admiration as my more successful peers within the math community? Instead of inspiring me to better myself, this “praise” gets added to a festering mix of jealousy, resentment, and guilt.
Let me begin with some background. I am an international student from a developing nation. I identify as a queer woman of color, with a native language that is a disappearing minority even within my own country. A (male) teacher once told me that I wasn’t meant to pursue math, as it required “real talent and intelligence”. I did my best to put this behind me upon starting college, as a double major in math and physics. My undergraduate institution, though an R1 public university in the US, is not considered to have a top-ranking math department. Even so, I recall my time there with a lot of fondness, and will always be grateful for the opportunity to learn math in an encouraging environment. I did very well in all the advanced classes offered there.
In 2020, I joined a “prestigious” Ph.D. program. It felt like vindication at first, but it came with an unexpected downside: suddenly, I was supposed to be in the same league as those who went to Ivy League programs with the top math departments in the US. My peers cleared all their qualifying exams on the first attempt, while I had to retake them multiple times. I felt that I had no choice but to play catch up to my peers, who came in with a level of background that I couldn’t even comprehend. By the spring of 2022, I was diagnosed with depression. I got stress-induced migraines and nosebleeds three times every week and consumed a daily dose of 700 mg of ibuprofen, just to get through the day. I had no faculty looking out for me, and no hope for my career beyond the Ph.D., save for the brand value of my institution.
My worst nightmare was being told that I wasn’t good enough to be in the program, and then get asked to leave. This is precisely what happened, about a week after I had arrived at the decision myself, for the sake of my mental and physical health.
I hated myself for “failing” my family. I was forced to reflect upon what I truly wanted out of life. It wasn’t fame or prestige, though that would be a great bonus. It wasn’t payback either, because I would spend my whole life chasing the approval of those determined to underestimate me. It wasn’t competitive success compared to my peers, because there will always be folks with more credentials and accomplishments than me. I went halfway around the world chasing curiosity and knowledge. Mathematics itself gave me joy, with no other attachments around it. It required a lot of sacrifice and discipline, but it had always been worth it. And math can be done everywhere, provided I have the right mindset to approach it.
I was under a fixed mindset on who I was as a person. My core identity was that of a “disciplined student”, and nothing more. I was supposed to be someone who did not fail because failure is indicative of insufficient preparation, and that was not something acceptable to a disciplined student. The moment I was declared inept in mathematics in high school, my fixed mindset reacted by internalizing the message of “stay away from math, or you’ll fail”. It took 5 years of subconscious effort for me to change that message. This is also why I took failure so hard in grad school - it was a blind response of my mind to protect its fixed state. I was so afraid of confronting my lack of knowledge that I kept repeating the same mistakes.
In a study published by Maass et al. in 2008 in the European Journal of Social Psychology, then replicated several times by other research groups, a link was discovered between chess performance and gender stereotypes. A group of female chess players were assigned an anonymous online competitor. When the gender of the opponent was not revealed, the participants won 50% of the matches. When the opponent was said to be a woman, the participants still won 50% of the matches. However, when the opponent was said to be a man, the participants lost many more matches than the previous occasions. The truth was, it was the same opponent throughout. The conclusion was that the idea of men being better at chess than women was so deeply ingrained in the psyche, that it led to the underperformance of women participants when they subconsciously believed their opponent to be better than them.
The stereotype being perpetuated here, namely that of women being worse at a given intellectual activity than men, directly harmed the participants’ performance because they had absorbed it into the “fixed” aspect of their mindsets. “I am a woman, and that cannot be changed. A man is better than a woman in chess. Ergo, I am not going to win this match” sums up the subconscious mental activity that lay in the back of the players’ minds. We have several such stereotypes in math about gender, race, ethnicity, nationality, sexual orientation, etc. to name a few. While we cannot control the stereotypes being thrown at us as we grow up (and should actively work towards dismantling them at all levels of academia and society), we can still proactively attempt to protect ourselves from serious harm.
This is where the growth mindset comes into play. Part of it involves the acceptance of the following concept: talent of any kind, along with knowledge and skills, is something mutable, which can grow or shrink depending on how frequently one polishes and uses it. It means taking statements like “You’re not good enough to be in our program” to not be a reflection of one’s identity but as an impassive statement about needing to improve the current skill level and knowledge base. It also means taking statements like “Oh wow, you must be brilliant to be doing math!” with a pinch of salt - this is just as inaccurate of a statement about one’s ability to excel in a field as the statement of not being good enough. The only thing determining one’s ability is the current actions.
I decided to practice the attitude of a growth mindset when I reapplied for graduate programs, having left my first Ph.D. program with an MS degree. This entailed treating failure and success with equanimity while understanding that failure is an opportunity to learn, yet another way to satisfy mathematical curiosity. It meant dissociating myself from the sole purpose of being a student, and learning that there is much more to life than academic progress. It made me accept that there have been many missed opportunities and successes in my journey and that my peers not making those mistakes does not make them worthier than me. It told me that what I did or did not do in my past does not permanently decide my future.
I realized that I could improve not only my current level of mathematical knowledge and abilities but also the characteristics associated with “innate talent”, which I had previously used to justify the ease with which my peers mastered a topic that I struggled with. I stopped taking to heart various forms of microaggressions around my intersectional identity. For instance, at a prestigious conference that I recently had the privilege to attend, an old white male mathematician that I was talking to about research randomly interrupted me with the following remark: given that I’m a woman of color, I “just need a Ph.D.” to land a job in academia, as I have all the features of a good diversity hire. In the past, I would have likely spent the night crying, convinced that any success I have is due to the alms handed out to me by the system, not because I earned it. This time, I simply reflected on three points: 1) The only thing I can control is doing my best. Everything else, including my gender and race, is out of my control. Nor should it be a matter of concern when dealing with mathematical creativity. 2) This person does not get to decide my worth or my academic future. I do. 3) My life and success do not require the approval of every person on the planet.
I started ascribing to the philosophical thought of “action detached from the outcome”. It motivates me to take on challenges that my past self deemed unlikely to succeed in, and therefore would not even have tried. I have become more ambitious than before because I am not held back as much by the fear of failure. I no longer resent my peers’ for their success. I have begun to see it as fortunate that I know folks who navigated certain waters I had trouble with and could learn from. I purposefully chose to go to a program that was far less prestigious than my first, but which had a supportive department, and a brilliant, kind advisor who saw my worth. I stopped measuring the amount of work put into a subject by the amount of suffering involved; and instead decided to change strategies of learning the moment suffering started registering in my mind.
To summarize, the perception of mathematical talent and success can be detrimental if taken too seriously, both in the sense of having it and not having it. One way to navigate this is by asking yourself what you want from your life. Adopting an attitude that allows you to evolve upon facing challenges can help you not only survive but thrive. That might mean letting go of certain parts of your academic and emotional sense of self, in a way that doesn’t sacrifice your unique personality. I’m rooting for all of us in this beautiful journey of mathematical discovery.
Sandra Nair is a Ph.D. student at Colorado State University, advised by Prof Rachel Pries. Her research is on arithmetic geometry. She enjoys reading and writing fiction in her spare time.