Math Autobiography

I’m reading through Tracy Zager’s wonderful book Becoming the Math Teacher You Wish You’d Had. This text is powerful because it focuses on the roles that culture, identity, and relationships play in learning and teaching math. I find this perspective incredibly important, but rarely see it at the center of discussions about education.

Identity is the subject of the first chapter, where Tracy shares her mother’s dramatic math journey. In the book forums, readers have been sharing their math autobiographies. Each one is an incredible read, laying bare the trauma, insecurity — and happily — the catharsis and joy that people have experienced on their journeys to becoming “math people”. I appreciate the vulnerability and honesty it took to share these intimate thoughts.

Growing up, I had a very easy time with math. My mom was a computer science teacher at the local university, and she filled my childhood with activities and games (there are embarrassing math-themed birthday party tapes out there). As the saying goes in Russia, I picked up my math lessons “from a half a breath”. After moving to the US (entering 8th grade), I sped through high-school math offerings, finishing calculus sophomore year and taking two years of online classes (linear algebra, multivariable calculus) following that.

I got into a prestigious college, and took the accelerated path though the math program there as well, compressing my sophomore year math offerings to a 6-week bootcamp called “summer math”. At about this time, things started to get out of hand. The quantity of work I had to do made me hate the process, but I forced myself through with the help of procrastination, caffeine, missed sleep, junk food and alcohol.

I continued earning A’s, but towards the end of college I was burnt out. I came close to changing majors to psychology, and seriously considered going down that career path after graduating. I ended up being able to finish my degree. Having no mental or emotional energy left, I applied to graduate school very much on inertia. Somehow I got into a Computer Science PhD program at a top university.

In grad school I had a revelation — I didn’t actually know math particularly well. Machine Learning and Computer Vision blend many branches of mathematics — probability, statistics, linear algebra, differential equations, Fourier analysis. I knew that I had studied these things. I had earned good grades in all of these classes, but nothing remained in my head. I had a faint memory about how to compute the determinant, and that it could tell you whether a matrix was invertible, but I had no idea where it came from or what else it could be used for; I only had a superficial knowledge of the normal distribution — in that I knew it was used all the time, but I really didn’t know why; I knew the number e was often the base of a logarithm, and had something to do with compound interest, but that’s about it — I certainly didn’t get why raising it to an imaginary power corresponded to rotation along the unit circle on the complex plane. Upon reading research papers and seeing the applications of these concepts I grew to understand that there was a deeper meaning to each of these ideas. The authors were drawing on this deep understanding, and I had to admit to myself that this was something I didn’t have.

At this point my research took a back seat — I certainly didn’t have the will to keep brute-forcing my way through as I had towards the end of college. Instead, I started teaching myself the mathematics I felt I was lacking. I read math books, listened to video lectures, searched through syllabuses and followed online classes. I learned a lot of things about myself and my relationship with math during that time.

In the beginning, I felt ashamed. I was convinced that everyone else had a deeper understanding to get into this top-tier graduate program, and I had ‘faked’ my way in. After studying math on my own, I realized that I wasn’t that different from everyone else. Many of my peers sat through lectures with glazed-over eyes. In research meetings and interactions with our professors, they would do their best to contribute, but in private conversations they would admit that they didn’t really understand this topic or another.

I still feel a bit angry about all the time and stress that my slapdash race through math required, and especially for all of the beautiful things I missed along the way. I think back to my high school calculus class, wherein infinite sums, limits and the fundamental theorem were given a cursory and disjointed glance, and the bulk of the time was spent memorizing and drilling the various rules for performing the process of differentiation and integration. Or my college calculus class, where we did the same but with epsilon-delta proofs. Seeing a visual illustration of the rules of differentiation (of which 3blue1brown does a fantastic job) makes me fume— “how could I go through all of those years of math without ever seeing this?!”

I realize now that knowingly or unknowingly, everyone participates in a value system of math. Unfortunately, this system is often one that praises gifted students who martyr their way through ever more elite (and ever more demanding of sacrifice) tiers of material. In this system, drilling for the AP calculus test takes precedence over all else.

I know that most of the people who pushed me to race through the subject meant the best for me. Alas, I discovered that I don’t have the same value system. In my personal exploration of math I found joy in revisiting ideas from different angles; in building mental pictures and intuitions. I found that digging into the most basic topics would often turn up connections to the most abstract, much to my delight.

I found that being miserable isn’t a prerequisite for being good at math. Naturally I struggled with the material at times, but my mental dialogue changed from “oh no, I don’t get it” to “oh, that’s interesting”. I met people who truly understand mathematics, and found that they engage in the subject because it brings them joy and satisfies their curiosity.

Disillusioned with the PhD degree I was attempting, I ended up leaving with a masters in Machine Learning and going into the tech industry in San Francisco. After spending a bit over a year working on search at Yelp, I started looking for work in edtech. I found companies that were at best clueless in their approach to education, and at worst thriving on exactly the toxic culture that I had given up. Thankfully, the stars aligned and by complete chance I stumbled upon a place with like-minded people.

That place is Desmos, and I feel incredibly lucky to work here. I get to participate in the amazing math teacher community, and to interact with inspiring people. I get to apply my skills as a software engineer to help teachers probe deep mathematical understandings with their students. I get to work on something I truly believe is meaningful, and that is something I value a great deal.

One day, I may become a math teacher (that I wish I’d had). That day I will try and get my students to slow down and feel through their relationship with the subject. Do they see mathematics as a series of flaming hoops to jump through? Can they find their sense of joy and curiosity, and tap into those as they look for beauty and understanding?