On the Acquisition of a Math Degree

Various ponderings of a mathematics student looking to understand both her brain and geometric graph theory when time permits

[mentalknot]

A brief (kinda) hello

Welcome! My name is Selin, and I'm a junior mathematics student who's followed somewhat of an unconventional educational path.

After discovering my passion for math four years ago in high school, I've quite literally fast-tracked my aspirations of becoming a mathematician. Additionally, I was lucky enough to work with an outstanding mentor during the summer of 2024 on my first research project. The experience was nothing short of lifechanging... and also where I first noticed some of the variance in my academic approach.

I'm autistic, been diagnosed since 14, and recently with ADHD as well. I thought medication would "quiet" my mind, the mind that's constantly brimming with ideas that I simply can't put words to, that I seldom try to explain because they are likely dumb and baseless.

However, I let myself explore this "graph" at the start of October, and eventually got the point where I wrote an algorithm to depict it, and then a formal mathematical definition. People started joking about when I might "release a pre-print," or suggested I "save the project to receive credit for an independent study." As someone who's struggled with severe anxiety and depression since I was around ten years old, I've become extremely comfortable questioning my every move, believing that I am fundamentally dumb, annoying, delusional, and "one-notch away from loosing my mind." They tell me this brain is a "gift," but I fear risk of grandeur in accepting that. I fear that I'm somehow lying to everyone... why is it that I can "see" novel mathematical objects in my mind, and why do I fixate so strongly on these ideas... One of my mentors recently pointed out that a mathematician must learn to trust their work without the validation from others, and I realize that regardless of my skill (or lack thereof) in proof writing, I must accept my brain to continue. I will use this page as a way to empty some of the constant noise (void of trauma dumping) in my mind, and do my best to describe what it feels like. I hope to find people who relate, as I believe it's the only way to convince myself that I'm not going crazy.

[mentalknot]

Combinatorialists

When people inquire into my early specialization as an undergraduate student, I find no difficulty in producing a response. Often, I feel verbal descriptions fail to adequately convey the warmth I feel looking across the dinner table of smiling mathematicians.

The algebraic combinatorics community has always welcomed students and colleagues with open arms. Mentorship is baked deep into our culture, and boisterous tidbits of history weave their way through every lecture and talk.

I recall walking by my future mentor's side as a starry-eyed forlorn freshman, listening to him share tidbits from his well-regarded books and short tales from past conferences. I ate my first conference dinner surrounded by his students and their friends -- being an undergrad mattered little, save for the initial moment of surprise.

Years later, I run up to the same mathematicians with an eager wave at conferences. We catch up on our research, discuss problems the other might take a stab at, and eventually scurry off the next talk. Gatherings that once felt novel and foreboding melt into friendly reunions. Often, the only alarm is that my mentor continued taking students... one that I often laughingly share in -- he is known by all in the field for his kindness and generosity.

As I grew older, my mentor's students offered countless foundational lessons in our field. I stumbled my way through ideas in Coxeter combinatorics, cluster algebras, topological combinatorics, and recent work on vertex models. They dusted me off when I fell flat on my face during countless presentations, pushing me forward with kind yet intentional words of encouragement.

At times, I questioned if others only talked to me because of my mentor, but age and practice gradually aided my emerging voice in the area. My conjectures became more interesting, and I felt no fear sharing opinions among the group. I had friends I could talk math with at length -- my whole world became beautifully entangled with their community.

Specialization came without question -- I finally had a community that supported both my mathematical and personal success. Ideas from areas of math can be picked up over a lifetime, but a found-family is far more rare.

As I prepare for my final undergraduate summer, surrounded by the mathematicians I've now known for years, I cannot help but bask in the history of my field. I adore reading how kindness runs deep through previous senior mathematicians, how a young field tapped into so many different areas in the large expanse of mathematics.

I only hope I can go on to make their efforts and kindness worthwhile. For now, I write.

(I also recognize this post might make me recognizable to those who know me in real life... although I doubt any of them are here, if they are... hi lol)

[mentalknot]

When research gets so good you start rapid-fire explaining niche combinatorial topics to your humanities major friends bc they made the mistake of being “curious about your work.”

Please keep being curious ☝️

[mentalknot]

Mentor’s Return

The group informed me of your itinerary weeks prior. Yet when I saw your kind expression down the hall, I couldn’t help but break out into a shocked grin.

I spent months pondering how you might have observed my progress from a far, how much they told you about my failures, my successes… for know some of them talk.

The project you offered blossomed into a creature I could hardly tame, but adored nonetheless. As I observed the curious behaviors of countless results before me, learned to conjecture on my own... to trust my frame of reasoning.

I met your friend in January — she mentioned you had a student… she called me your student. Another offered me housing — you know her well, as we all shall be neighbors this summer. Her and I frequently discussed why you would take another student during retirement, much less an undergraduate who could barely keep her life afloat when you met her.

Your name alone gave my life premature importance — people offer me more second chances than I deserve. I don’t know what you saw in me, but others trust your judgement like law.

“You know, ______ only works with the best”

“______ students have a reputation for a reason, they all go on to have wonderful careers.”

I often harped on the informality of our mentorship agreement, so not to tarnish your name when I inevitably fell on my face… but then you told your friend I was your student. From her account, the exchange was matter-of-fact… deliberate.

“I do have one student, she’s an undergraduate.”

I thought that I’d see your face and exchange a kind nod, an update quickly so you could leave and join the senior members of the group — the interesting mathematicians.

Instead, you waited for me with a kind inquisitive smile. Chuckling as you asked,

“busy semester?”

I couldn’t help but blurt out a million ideas on those two minutes. We found a chalkboard and you drew up a figure from a MathOverflow post that caught your attention… my post. Though neither of us put words to the thought, our eyes acknowledged that a year of learning from your students’ instruction had done wonders for my background.

Even as we walked towards the classroom for the afternoon’s talk, you stayed by my side, sharing stories of your early days in the department. Life felt… so peaceful.

“Let me know if you want to meet, I’m around.”

The coming weeks will be filled with research, with joy, with community. I will finally have a mind healthy enough to think. I owe that to the loving community you built.

All to think that two years ago, I stood nervously on that sidewalk, questioning what I would possibly say to the acclaimed mathematician walking beside me to the conference banquet.

“Hey, you do work in combinatorics… right?”

[mentalknot]

Clarity

I was never crazy... I was never overreacting.

We reported them, my former boss. The person who pushed me to run from my own department. I always considered myself the problem -- the disgusting vindictive young woman who couldn't complete a task to save her life. Even after I left the job with all the professional tact I could muster, she gossiped about my whereabouts to other students, suppressed my voice until I lost the ability to speak.

So I ran to the combinatorialists; they took me in without question. At the time, I had no inclination of my subconscious self-exile... but everything sits far too clearly before my mind today.

When I came forward with my story, the department chair stared across the table with shocked and solemn eyes...

"This is why you didn't feel comfortable for all those years? Your department is supposed to be your home... I'm so sorry..."

With one year remaining for my bachelors degree, little remains to be realistically repaired -- my loyalties now stand firmly with a cohort to which I have no formal affiliation. They fed me when I was hungry, pushed against my urges to surrender hopes of mathematical success, and even offered to house me for the upcoming summer. However, I cannot help but feel inexplicable joy walking through my own department halls these days. I get one more year with them, one year of clarity -- I ought to make each second count.

Sometimes I long for the conventional undergrad experience that my professors described -- puzzling over undergraduate problem sets with friends my own age... going out on the weekends without a second care, without worrying how my newfound "reputation among academic elites" would fare.

However, such fantasies will never come to pass. For now, I have justice -- they know the full story. i must be satisfied by the emotional closure alone.

[mentalknot]

Mother (TW: Family Dynamics)

The harshest collateral to familial estrangement was the relationship with my mother. She’s my inspiration — one of the strongest and kindest people I know. Her behavior was never perfect, but she makes consistent effort to acknowledge differences in opinion and work on herself. To a degree, I can decipher which responses are seeded by our own disagreements, and which stem from foul treatment by my father.

A sense of “survivors guilt” washes over me when I catch sight of her worrying someone will scream at the sight of her tears. From an outsiders perspective, her continued marriage with my father is a flexible choice… but personal decisions are seldom cut-and-dry. Knowing her history, I can empathize with her decision to stay.

She never understood why I chose to run from my childhood home, to give up a security net and fall headfirst into financial destitution. For years, I tried to explain how the strings of his net wrapped around my neck and ankles, catching me only for the purpose of display… so that society would continue to view my father as a well-to-do-man.

I keep in as close contact with her, when possible; I cannot live in the house with my father, but call and visit her in other locations. At times, her misunderstandings of my choices kept me at a distance.

“You know, your father loves you… in his own way.”

“I respect your opinion, but his form of love is one I cannot accept as a standard for my future relationships”

However, recent family extended dynamics seem to have shifted her understanding. I hate that she had to experience the same pain I felt when leaving my father… and it has brought us closer.

“I still love the version of them from my childhood, but I don’t recognize this new person — my loved one is gone… and I cannot help but feel the grief of loss.”

I finally told her about the night before I left that house for good — how I presented my father with one last attempt to try out repair our relationship…

“I will always work on myself, and accept any criticism. Even if you’re not in a place to do the same right now, it would mean the world to even hear that fact acknowledged — I need something to continue with you…”

My father didn’t even look up from his computer. Responding in an even and nonchalant tone.

“Ok, I guess we won’t have a relationship then.”

I felt as if the wind had been ripped from my chest, stumbling downstairs in an uncomfortable stream of tears — my father, the man I grew up loving… was gone, if he ever existed at all. In my haze of grief, I eventually heard his footsteps across the room.

“Hey, can you keep it down… I’m trying to get work done.”

My mother went silent — I had asked her multiple times if she was sure that she wanted to hear this story, with understanding if she declines… I knew it would be hard to hear, but for the first time she heard me…

Even if there is no hope for my father and I in the near future, I will stand by my mother from the necessary distance… for she deserves so much better than the people she’s surrounded by.

The combinatorialists, my partner, my college friends, gave me a form of compassion that I long believed to be the product of fiction… I only hope she can one day discover a cohort who supplies the same. For now, I will do my best to offer a sanity check — a reminder that pure kindness exists in this increasingly twisted world.

[mentalknot]

Hired

I got a job… I’m not going to be broke again this summer.

I’ll be able to afford housing, food, medical care… this is wild. I’m so happy… I can’t believe it!!

It’s related to math, and gives me tons of time to work on research.

Maybe there is a light at the end of the tunnel…

[mentalknot]

When you reunite with one of your mathematician friends for the first time in (nearly) a year… and they ask “how is that graph theory project going.”

OH BOY… we gotta catch up on some things 😭

[mentalknot]

the six hour research meeting felt like what I imagine ecstasy feels like… perhaps I chose the right specialty

[mentalknot]

Pollen Season

Something about my region’s annual bout of pollen-induced muzzling fuels my compulsion to write once more. Perhaps failing to speak without a scratching pain in my throat is fine for some time, as I seldom succeed to translate any grace from the pen to my verbal communications.

Illness makes one starkly aware of their own mortality, and perhaps I was overdue for such a treatment. Another research funding source fell through, and despite the fact that I am surrounded by caring mentors, colleagues, and friends… I cannot shake the fear that another summer of financial destitution awaits me.

I speak with honesty when claiming an optimistic attitude towards being broke again, for I know that I can get myself through on precedent.

Yet as the summer draws closer, I fail to ward memories of walking into a grocery store with voracious eyes… scanning all the food I cannot afford. The labels become twice as bright and alluring when the content of their package is unattainable.

Rides on public busses are paid for in dignity when your card declines at a $1.70 charge.

Professionalism dissolves when you must admit your desperation for a meal mid research meeting.

You watch others your age running carefree through the streets of your vibrant college town, enjoying dinner with friends, dancing until the sun wakes from brief slumber. The inconsequential lifestyle of a dumb college student, the one you dreamed of while living in that chaotic childhood home, will never be yours…. Yet there is no time to lament, as another delivery order quickly pops onto your screen for pickup.

Research moves smoothly, for a good collection of results and subsequent publications could pull you out of this rut forever… or at least that’s what you’ve forced yourself to believe.

This summer, I am most terrified by my mental rigidity… for if I fall into destitution, the blame will be my own. I have no courage to ask for support, and far too much pride in my hyper-independent grit. Dependency on others makes my skin crawl, and unless I can change such habits, I am doomed to fall right back to the darkness I’ve spent a year running from.

[mentalknot]

Memory

The young woman glances across the room with exhaustion draped across her eyes. I watch her hand desperately grasp the purple marker, covering the page with scribbled for her algebra problem set. The oversized blue hospital gown makes no effort to embrace her, drawing her into the collectivist nature of the facility.

How can a student develop an adequate grasp of cycle notation when she can’t even stop the viscous cycle of her mind? How can she spend hours pouring over a research paper when she has lost the autonomy to hold a mere graphite pencil?

I long to place my hand on her shoulder, to walk her kindly through the examples I lectured to my class just a couple months ago.

I want to tell her that her world will look much different a couple years from now, that the symmetric group will feel like an old friend… a very important tool for her future work.

She will wait for hours to receive her intake meeting… four months to recover her sanity, and many more to finally trust it. Nonetheless, notions of comfort will not remain as impossibilities.

As watch her from afar, exactly two years later… the woman gestures a strained grin.

I’ll get us out, no matter what it takes — I’ll take us to safety. For recovery and peace… are no longer distant dreams.

[mentalknot]

Responsibility

Why must I always stumble straight into the grasp of great opportunity. Why am I given such academic privilege when so many capable friends are left to tread the waters of their degree alone?

For I am a woman who’s prone to self sabotage, who froths at the mouth when presented with the notion of “slipping through the cracks.”

There’s and intoxicating intimacy to loneliness, the sense that no one cares to see the outcome of your story.

However, despite my anti-efforts, I find my recent life filled with fortune — I am told unconditional love exists and ought to be trusted.

While my mind screams to run, my legs carry me forward in defiance, forward to the ivory towers of historic math departments, towards the papers I really ought to write.

“we won’t let you be destitute this summer Selin”

I fear that comfort will make me lazy, forgetting who I owe my successes to, and failure seldom has quiet consequences under a spotlight.

However, when the fog clears I see that the quiet exit has piled steep with stones. Despite my misguided protest of success, I am deep within this academic world — a community that I grew to love for all its beauty and imperfections.

Failure would be loud, and self sabotage is no longer a luxury I get to enjoy.

My life is public, and I have a responsibility to my future mentees — I need to give my soul to this work. I must not let their efforts be in vain.

[mentalknot]

Two Years

(tw: mental health)

In just under a week, I will be two years clean — one step closer to freedom from the illness that consumed my childhood years, freedom from the event that struck my mind with ptsd and derailed my sanity for six months.

For the next few days, my mind will naturally fall into a more active state. Memories will predictably flow with more intensity, more frequency, more burning clarity, than before.

Nonetheless, I do my best to remain from fear — today, I walk among the memories with considerable control. I say just long enough to process those bed-ridden mornings, to recall how fortunate I am for the life I have now, snapping to attention before I fall inescapably into the one-sided world of my mind.

As I watch her sleeping upon the upright cot, I cannot help but feel envious of the freshman her actions have just laid to rest, for she will never emerge with the same glimmer of innocence and belief in the world.

I stare as she wakes to clutch a wire-bound notebook, scribbling down Gallian’s passage on direct sums for her algebra course… only to find a nurse snatching away her work, as the pliable metal spine poses a medical risk of it’s own.

She smiles and nods without argument, as loosing one’s autonomy feels softer with compliance.

I leave to walk the halls that she couldn’t visit unsupervised, carried by legs that lack tremors in their strides. Although I am permitted all she dreamed of: independence, a breath of fresh air, a graphite pencil, part of me wonders if I am truly free.

She knew the journey would be long, but no coaching would prepare her for the bare checking balance she’d soon return to, the dissolving of a family she had given her last burst of energy to repair, the overnight fear of all friends she once held close.

There would be bursts of light too: a found-family of mathematicians, a partner to love, a purpose in her eventual research. She would never find those who provide unconditional support, as such responsibilities are relegated to blood… but such a deficit would hold her socially accountable.

Leaving the hospital, I walk out from the confines of my mind, reminding myself that the reality I had just seen was the past — a past which could no longer touch the life I’d built in recent months.

Finding comfort in distress is an uncanny and illogical practice — the embrace extends from the arms of familiarity, rather than the pain itself.

Yet, I must slowly wean myself of such escapes. My new friends grew up in starkly different dispositions — mental illness is no longer a point of relatability, and I thus social conformity inches me away from the drug I once adored.

I yearn for the day that follows that faithful anniversary, where my mind will sit clear and resupplied with hope for the world. I recall how sections of proofs dripped easily from once clogged lips — falling upon conventions with considerable order and accuracy.

As years pass, this period will grow easier, and I’ll possibly loose contact with that young woman in a cot. When I do, I only hope the woman, whom she removed from her misery, remains proud.

[vacuously-true]

🧮 𝟚𝟘𝟚𝟞 𝕄𝔸𝕋ℍ𝔹𝕃ℝ ℝ𝕆𝕃𝕃 ℂ𝔸𝕃𝕃 🧮

Behold! My approximately annual (depending on my executive function) mathblr roll call! Reblog/reply if you are mathblr or adjacent. And tag the other (at least semi active) mathblrs & adjacents you know of!

"What counts as mathblr?" Math shitposters! Math academia aesthetic blogs! Math studyblrs! Math related gimmick blogs! Unthemed blogs owned by people who happen to be math fans! CS, stats, physics, and other math-adjacent folks are welcome too! I'll even accept engineers if they behave! "Do I count?" If you want to!

Bonus: LCM- Least Common Mathblr discord server. Come hang out!

Check out the Least Common Mathblr (LCM) community on Discord - hang out with 682 other members and enjoy free voice and text chat.

[vacuously-true]

@admiral-crow-is-watching @piles-of-numbers @gay-victorian-astronomer @mathsuggestions @lilith-hazel-mathematics @fencesandfrogs @weaponized-mathematics @thatfunsizednerd @coffee-math-chamomile @seeking-knowledge @insert-math-username @mathematics-official @asstraightasau-turn @bootleghellokitty16 @regina-mathematicae @avatar-of-the-vast @capybaraonabicycle @natural-blogarithm @algebraic-dumbass @deaths-accountant @anonymous-leemur @generally-proven @lilacandladybugs @musical-engineer @question-why-not @fluxion-fluent @sqrt-73 @krasnoarmeyets @sevenfactorial @bleanor @zerenta-mrraow @bayesic-bitch @wuwojiti @bellaswansong @primedetector @tarilaran @rainbow-sloth @rainstormyday @twocubes @3s-are-green @math-is-fake @adjoint-law @yoneda-emma @ann-decart @chongoblog @mathhombre @mentalknot @giantimp1 @mathsbian @kubleeka

[mentalknot]

They told me to get outside more, but neglected to notice that I’m peacefully studying field extensions and finding roots every day… my connections to natural things are quite sound…

[mentalknot]

Seminar Visitors

My partner recently noted that few undergraduate students attend the research seminars I frequent.

They asked me to name other “math regulars,” and I stumbled for a moment — few remain for the long-haul, but common crowds exist in pleasant flickers of memory.

The young woman from a large city, who traveled a great distance to attend a handful of talks. We laughed in a car after dinner, frolicked the streets of the college town, and even enjoyed a short conference (per her birthday wishes).

She hasn’t reappeared since.

The young pair of local students, whom I met late into an autumn night. They were filled with fruitful research ideas and passionate in tone, meshing into the group’s conversation with ease.

They haven’t returned.

The handful of students whom I’ve introduced to the talks, varying generously in mathematical maturity. Some were alarmed by the pace, and others left with a rose-colored impression of the community — as I’d intended.

They disappeared quickly.

Of course, one cannot forget the postdocs who’ve cycled through, the graduate students who’ve recently graduated and moved onto the next stage of life, those left for job talks seeking similar clarity, and the myriad professors who visited on account of nostalgia and fruitful collaboration.

Those characters are recurrent, enthusiastically welcome…

The undergraduates are seldom acknowledged or remembered, always treated with kindness… but regarded as inexperienced.

Why do they keep me around?

When might the next undergrad remain, like myself? I am not special — others are just as capable of grasping these talks.

Why do they treat me as one of their own?

I failed to produce a satisfactory response for my partner that night.

[mentalknot]

On “Academic Families”

Omitting blood-relation, you satisfy all remaining conditions of our general definition.

When I fall into strife, you provide a soft cushion for my landing — a home to reside in, both in the physical and emotional realms.

When I find myself saddled with an exciting update, you’re the first to know, the first to cheer for my success… in every regard.

We share meals that extend hours into the night, where minutes feel like seconds, and social fears melt with ease.

We keep a careful eye on each other, regardless of “seniority” in our group, regardless prior life circumstance.

I fell for my research group, as a form of “family,” after only a few short meetings, quickly relinquishing any desire for reciprocation — remaining welcome in the community was enough.

Their acceptance alone is still enough.

But recently, I told them — I called them my family.

They wrapped me in a warm embrace of smiles, a nudge of the shoulder, a collection of playful retorts…

“Took you long enough to say it.”

Perhaps the notion of academic families was never restricted to a playful classificatory phrase.