My Mathematical Journey

This is a writing assignment that I was given in my Combinatorics class this semester, which is at Swarthmore College. I was only asked to write 1-2 pages, but I wrote more because I wanted to write out my story. There are definitely important experiences that I did not mention in this essay, including my frustrations with Kumon (which my parents enrolled me in for enrichment after I complained about 7th grade maths being too easy) and my teaching fellowship this past summer in which I taught Algebra 2. I will likely write about these and other neglected topics in the future, when the time is right for me.

The essay is largely untouched from when I submitted it, except for a small grammatical correction and a few clarifications for people not in the Tri-Co (i.e. Haverford, Swarthmore, or Bryn Mawr College)

Note: Though I generally use American English, I like to shorten “mathematics” as “maths” to suggest the multifaceted nature of a subject that many people wrongly believe is about getting “the” right answer.  There are many types of mathematics, and not all are true at once.

One of my best and most formative experiences with mathematics was a program in my elementary school called Math Enrichment.  It was offered from 4th to 6th grade as a program that pulled out advanced students from regular maths class 2 days a week.  The program focused on developing problem-solving skills rather than on learning particular mathematical “content,” though we were exposed to many topics beyond the normal curriculum.  I loved Math Enrichment, especially because the teacher was super creative and playful and thus showed me that maths could be the same.  (She loved frogs and had many (fake) frogs around the room, which led me to be obsessed with frogs at one point too.)

In middle and high school, however, school maths was a disappointment.  Firstly, even though in my last year of elementary school (6th grade), I sometimes brought a small algebra book to class and studied it, no one told me that I could test out of Pre-Algebra, the usual Honors maths course for a mathematically strong 7th grader; I only learned of this because several of my classmates with educationally savvier parents tested out.  So I was determined to test out of Algebra 1 the next year, but when it came time to do so, my father forced me not to because he thought there would be too much homework or that I would have no friends.  Only the following year, after finding all of middle school maths to be very boring, was I finally able to test out of a maths course, and the year after that (10th grade) I skipped a course again in order to take AP Calculus BC.  None of the courses I took, however, had the excitement of Math Enrichment.  At least in middle school I had MathCounts, but the high school Mathletes club was bland and not well-run.  I knew about Art of Problem Solving and wished I could take their courses, but my parents did not want me to.  (I have frequently butted heads with my parents on a lot of matters, educational and other.)  And after AP Calc, my school didn’t offer any more advanced maths courses, so in 11th and 12th grades I took first a computer science course my school offered and then an online multivariable calculus course from CTY, the former of which was really fun, the latter of which not so much (mostly because it often did not go into the “why” of concepts; because of that, I taught myself a little real analysis from an online textbook to try to understand the underpinnings of calculus).  

Yet my frustration with my mathematics education and with schooling in general played an important role in my developing a strong interest in thinking about how education should be in general as well as how mathematics specifically should be taught.  I frequently wrote articles for my high school newspaper exploring educational issues and even critiquing the school system, advocating for student voice in school and self-directed learning in students’ own lives.  I devoted a three-part series to mathematics education in particular, arguing for more creative and engaging pedagogy such as what Jo Boaler has written about and for people to be able to find joy and relevance in maths in their own ways.  As I attended a traditional public school, I thought a lot about how public school could be reformed and transformed, but I also semi-secretly longed for more radical and alternative approaches to education, wishing that my parents would allow me to homeschool/unschool or join an alternative learning community.

The summer before 12th grade, I attended MathILy (serious Mathematics Infused with Levity), a five-week summer maths program in discrete maths at Bryn Mawr.  I chose to attend because it seemed reminiscent of the fun, creative vibes of Math Enrichment, and my parents were finally allowing me to do such a program.  It was much more challenging than I expected, not just academically, but also emotionally.  I struggled with much imposter syndrome, crying in class by the end of the first week and multiple times thereafter.  I had grown up always being one of the top students in the class, if not by grades then by obvious intellectual passion, and I had become too accustomed to that.  In MathILy, I was surrounded by students who had a lot more problem-solving experience than I did and who often thought more quickly than I did as well, and it was even more intimidating that most of them were younger than me.  I cognitively knew that maths was not about speed and that my struggle was not an indicator that I did not belong in maths – after all, this was what I passionately preached to others – but emotionally I seemed unable to grasp this.  What I was particularly good at, however, was proof-writing and finding logical holes in other students’ arguments, and I tried to remind myself of this strength when I became frustrated.  There were times, however, when I did find a lot of joy in maths at MathILy, and I am still connected with some classmates and instructors from the program.  

Since attending MathILy, I have realized that one of the biggest difficulties I can have when learning mathematics is when I am first introduced to a concept and its notation, and I must keep the definition and notation in my memory while solving my first problems using that concept.  This was a lot of the difficulty that I faced at MathILy, when it seemed like everyone else quickly developed facility with new concepts.  As I need to have a certain intuitive feeling for a concept in order to understand it well, and that intuition needs time to develop and can be easily hindered by notation that packs so much meaning into an arrangement of symbols that too often looks like the same mysterious jumble of letters and parentheses and such that are overused everywhere in maths, I can struggle a lot in these initial stages of learning and get frustrated if instruction moves too fast.  I need to repeatedly remind myself of what new notation means and be patient if I keep forgetting or fail to connect pieces of various new definitions together.  

At the start of college, I was perhaps 80% confident that I wanted to major in music and maths, and the professors I had for maths confirmed my desire to study the subject.  I saw both maths and music as my tools for creating social change, and I also longed for more enriching classroom experiences in them, since so much of my learning in both subjects was self-taught.  I did well in my maths courses up through fall semester of sophomore year, although taking Differential Geometry in first-year spring was more of a challenge, especially since I was the only first-year and since it was the start of the pandemic.  I particularly enjoyed collaborating inside and outside of class with my friend Alex in Analysis 1; the first time we collaborated in our flipped-classroom class, we ended up excitedly yelling across the room as we generated ideas together.  

When winter break came in my sophomore year, I soon fell into a depressive state, which began a period of struggle with not-easily-definable mental illness/Madness, identity crisis, and the troubling of the buoyant boldness that had carried me through the beginning of college.  The spring semester was very much a mess: I struggled to keep up with all my classes, and I ended up in a psych hospital towards the end.  My struggles continued to the next semester (last fall), but I had a new CAPS (Haverford Counseling and Psychological Services) therapist who was really helpful for me, so even though I was hospitalized again in the middle of the semester, things were getting better and I finished that semester stronger than the previous.  (Why didn’t I just take a semester off?  Because home was emotionally suffocating, and my support system was at college.)  

That fall, however, I had much trouble with my maths course, Topology.  I had taken multiple courses with that professor (Tarik) previously and liked his approach, but for this course he attempted to use the Moore Method, which the usual Topology professor (Josh), who was on sabbatical, used for the course.  Although from what I could tell, people liked Josh’s Topology course, copying Josh’s method backfired for Tarik: many of the students, including me, disliked the limited scope of collaboration allowed beyond the correcting of proofs and much preferred Tarik’s engaging lecture style.  By around fall break, due to this feedback from students, Tarik switched back to his usual pedagogy.  

Yet the way that my mental and emotional wellbeing (or lack of it) interacted with the Moore method drastically affected my ability to engage in the course that semester.  Since we were forbidden from collaborating on problems before they were presented in class, I had to face challenging material on my own, and self-doubt quickly arose.  Soon, I fell into a crisis over my studies: why had I chosen to major in maths?  No one had forced me to — my parents actually were against it, saying that you needed to be a “genius” or that it was not “practical.”  I had decided this, and I now questioned my decision.  Was I simply not interested in maths anymore?  The self-doubts happened so often that I became unable to complete homeworks and fell behind in class.  By the time Tarik switched the format of the course, I dropped it because I felt that I could no longer catch up.  

When it came time to preregister for the spring, I chose to wait on deciding whether to keep or drop the maths major.  Instead, I decided to try applied maths, thinking that it might interest me more.  I took Scientific Computing as well as Information and Coding Theory.  Although the courses were interesting, I found myself really missing the fun of theoretical maths.  (Even though Information and Coding Theory was theory, the course felt directed towards computer science students not as interested in playing with maths as much as using it for computer science.)  That semester, I got to collaborate with Alex again in the first annual TriCERATOPS contest (an informal team maths problem-solving contest for students in the Tri-Co), and it reconnected me with the joy I have in solving problems with other people.  Now, I have realized that that social element is essential for me, whether it is through learning together with peers or through teaching.  

I want to note that though it is important that I have recognized in myself the particular joy I have in learning theoretical maths, I feel that I also still need to challenge my bias towards “pure” maths and familiarize myself with the applications of mathematical concepts I learn.  I do not believe in academic siloing, and I think that it is such siloing that has led to way too much research being done without consideration of real-life ethical consequences.  Often I catch myself feeling particularly defensive about theoretical maths, valuing it more highly because of its perceived beauty or difficulty, and I realize that this has resulted in part from society’s worship of mathematical “genius,” but also from my own battle to have the agency to learn what I want to learn.  

So this year, especially as I am tackling two senior thesis projects, one in music and one in maths, I want to take maths classes for joy.  Sure, I’m fulfilling my last two maths elective requirements, but I want to focus on having fun through learning and playing with mathematical concepts with other people.  I will still get frustrated and even perhaps very distressed at times, but it is worth it for the joy I experience at other times.  

Until just a few months ago, I had vaguely entertained ideas about going to maths grad school, but I no longer consider that a satisfying option for me.  It is not that I would not like studying more maths or learning to do research, but that I cannot do so in the way that a grad school would have me do it.  In many ways, I feel that much of academia is a research mill, and even more so in “STEM” (how much I hate the acronym which wrongly separates “technical” work from “human” work!), and although I know I can challenge what I disagree with from the inside, I prefer to simply refuse.  The work I must do with maths is different: I need the space to think about philosophy and ethics, learn about ethnomathematics and maths from different cultures, engage in maths freely with other people and create spaces for community-building through play.  I would pursue this work in parallel with my equally serious interest in the performing arts, in a way that pragmatically sustains me, but also that gives me the freedom to plant my own path.  It is scary to think about — can I really do this? — but I must.  It is what I’ve been longing for since childhood.  

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A point of passage, told through tarot

Earlier this month, I bought myself a tarot card deck, as I had been long intrigued by intuitive practices of magic, revelation, and healing. There are very many tarot decks available, some of them perhaps more “faddish” than others, but as I follow adrienne maree brown on Instagram (@adriennemareebrown) and read some of her tarot card posts and found that a particular set of cards spoke to me especially, I chose the Next World Tarot deck illustrated by Cristy C. Road. The narratives of the deck are decolonial, transfeminist, anti-racist, centering radical healing and dreaming and rooted ancestral magic — very much what my soul thirsts for in this wretched year when the callousness and brutality of racial capitalism has left far too many people to die from the pandemic, from police and prisons, from the profiteering of the uber-rich…

At first I did a few three-card spreads roughly of the format past-present-future, and one of those readings helped to guide me during a tough finals week. Then, on Wednesday, I decided to do a Celtic Cross — or rather, the version of the Cross that Cristy C. Road describes in the deck’s instruction/inspiration book. I was stunned by the results. So stunned, that I was thoroughly unwilling to shuffle the cards back into the deck afterwards and have since reviewed several times the spread and the narrative it gave me. I recorded in my journal this narrative that the cards told, and now I share it here.

The Celtic Cross spread. Ten cards are laid upon carpet, with six of them on the left in the shape of a cross (two cards are overlaid in the center of the cross) and four on the right in a vertical line.

The fall semester was absurdly intense for me — there was, of course, the thrilling and at times distressful experience of a student strike from the end of October to the middle of November, which I passionately participated in, led by Black women demanding that Haverford be actively and concretely anti-racist and fully meet the needs of BIPOC students — but that was only one part of my wacky and anxiety-ridden semester, in which poor physical and mental health seemed to feed into each other and gradually wore me down. Electrified with new self-understandings and activist visions, I engaged with concepts of identity and justice so enthusiastically even in September that I forgot to care for myself, to be gentle to myself in the difficult processes of unlearning oppression and developing into the person I want to be (and figuring out what that person is!).

So, as winter break has begun — though I still have work for one course that I got an extension for — and a new year daunts me especially as I still struggle to process the introspectively intense happenings of this current year, I asked the cards, how do I get through this difficult passage? Where am I going? What will help me to live, to survive?

For each card I have identified the meaning given by its position in the spread, according to the interpretation offered by Cristy C. Road, and from the often lengthy descriptions of the cards themselves I have summarized what most strongly spoke to me. The cards comprise a coherent narrative that feels extremely personal to me — a beautiful synchronicity that nourishes me with energy to live. Notably, these are not simple happy endings which the cards foretell, but rather more difficult journeys ahead, yet still lit by even a small flame of hope and purpose warming the dark.

The 8 of Cups. Abandon, Saturn in Pisces.

Current Reality: I have abandoned the complacency and conformity that suburban schooling tried to teach me (and only partly succeeded) for a new life, in search of liberation and new, more affirming and empowering self-narratives.

The Hermit. Earth, Virgo, 9, Mercury.

What’s crossing, affecting, or challenging this reality: My flight from the cramped comforts of the old has set me on a journey of frequent, essential solitude. I must care for my own survival.

The 2 of Wands. Dominion, Mars in Aries.

Where I am now in this: I bask in my accomplishments, the growth and discoveries I have made so far in my quest for liberation, and I acknowledge the traumas that these discoveries have freshly unearthed. Though I frequently feel insecure, I am beginning to define and declare my dominion, my realm of strength and of healing.

The 7 of Cups. Imagination, Venus in Scorpio.

What brought me here: I have imagined wildly, envisioning new worlds of justice and revolution, exploring new, resonant ways of expressing and naming myself.

The 8 of Pentacles. Creation, Sun in Virgo.

Projected Outcome: From deep knowledge of my truth, embodying Philosopher, Artist, Awakener, I shall create powerfully, rooted in justice, anti-oppression, and sacred partnership.

The 5 of Pentacles. Turmoil, Mercury in Taurus.

Result of this Cycle: I will face instability, loss, turmoil, but I will stay strong and resilient. Even when my spirit has lost its former home, even when I feel stranded in a world of destruction, there is hope.

The Lovers. Air, Gemini, 6, Mercury.

I as I see myself: There are contrasts of energies within me, queer and archetypal, that I strive to hold compassionately, lovingly. Self-care is especially important when my intensities turn into doubt and self-criticism; I must remember there is a difference between being “broken” — which I never am truly despite what capitalism tells me — and being vulnerable, which I am and which it is okay to be.

The 4 of Pentacles. Arsenal, Sun in Capricorn.

My environment, community, and my relationship to it — or its influence on me: My arsenal of survival includes the friends and mentors in my support network and the magic of sounds, images, words, multi-sensory arts in which I immerse myself. It also draws from my heritage, from ancient Chinese wisdom. Though my suburban home is stifling, my connection with my ancestors is sacred, creative strength that can inspire me.

Justice. Air, Libra, 11, Venus.

Top Secret overlooked guidance: I must hold myself accountable for when I have hurt others or perpetuated injustices, becoming more aware of my privileges and how to navigate them in service of justice. Yet I also must recognize and validate my vulnerabilities, my needs, my identities, my unapologetic body, for self-love is foundational for the Revolution.

The 9 of Swords. Despair, Mars in Gemini.

Final Outcome: In despair is strength; darkness is power in vulnerability. Things will continue to be hard, but that shall not stop me. I shall feel the sadness, the anger, the fear, the pain — and let these powerful emotions drive me to fight for Liberation for all.

If this resonated with you in some way, feel free to comment below! I highly encourage you check out Cristy C. Road’s website which showcases her art and music — and consider supporting her work by purchasing this tarot deck and/or powerfully evocative prints and zines from her store!

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Lieber Beethoven: The Revolution is On

2020 is the 250th anniversary of the birth of Ludwig van Beethoven. All over the world, and especially in Germany and Austria, huge plans were made for momentous performances of that esteemed composer’s works as well as other commemorative events this year. Then the coronavirus pandemic turned everything upside down, and events had to be cancelled, postponed, or reimagined in virtual form. Though digital performances are enjoyable and many concerts are being rescheduled for 2021 or even 2022, devotees of the quintessential musical revolutionary still may naturally feel disappointment at the unfortunate stroke of fate that has posthumously fallen upon a man so inimically assailed by Fate in life.

Well, for those who lament, this is my response: Beethoven was not just a revolutionary in music. He was brazenly political, despising the smugness of the aristocracy and rejecting the system of patronage that had sustained his teacher Joseph Haydn and pretty much all of his contemporaries, for whom music was primarily a means for bread. He avidly followed the French Revolution until Napoleon, at first a promising insurgent, declared himself Emperor and effectively a tyrant fashioning fetters anew. Increasing deafness sent Beethoven into deep despair that might have ended his life, if not for his deep-felt conviction that he still had music to write for the world – powerful music, music that broke aristocrat-defined boundaries and that insisted upon paradigm-shattering meaning – a philosophy of living as striving, as fighting for life – and liberation.

I’m currently learning Beethoven’s last piano sonata, which consists of two movements of very different character: as my piano teacher described to me, the first is an anthem upon “No!”, and the second is a surrender into death, which would come to the composer just a few years after writing this work. It just happens that my teacher was learning the sonata as a college student herself when the 9/11 attacks happened; she has a flashbulb memory of practicing the resolutely militant first movement while watching the TV to follow the tragic course of events. I am learning it during a time of multilayered crisis, of protests unsettling old orders, of instability stirring up newfound spirit and vigor for profound, visionary change.

Some things we cling upon romantically, foolishly, precariously must be destroyed – must be pushed against incessantly, aggressively, uncompromisingly even when the powers that be – and the complacency of the not as individually powerful but still materially and socially privileged – seem so intransigently to fortify the castle of capitalism that from its very design was foundationally rotten. Some strands of our narratives of self and society must sizzle and die, feeding the ashes from which new verdant tapestries will weave and grow.

There will be grief, there will be growing pains, and there will be greatness yet unrealized in this new story of human that we forge from the flames. In these times of retreat is our moment to imagine, to break free, to create – for we are all composers of life, inscribing meaning to motive and enacting symphonies in the epic of our personal battles and of the heroic fight for freedom, justice, and compassion in our ailing world.

So, lieber Beethoven, mein Kämpfer, happy 250th anniversary. Your life is not forgotten; your fight is not in vain. I shall fight in your memory, shall speak and write and compose and act and live boldly as you did, shall summon up the German Geist and strive fearlessly for my ideals – shall be an artist and activist for the people and among the people in solidarity, integrity, and moral clarity.

Lieber Beethoven, the revolution that you foretold in your music is starting to become.


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