Note: This essay was inspired by Weike Wang’s piece “Notes on Work”, which was published in the New Yorker.
Books I’ve read on the subject: David Graeber’s Bullshit Jobs; Cal Newport’s Deep Work; Jenny Odell’s How to Do Nothing: Resisting the Attention Economy. Ling Ma’s Severance and Raven Leilani’s Luster probably fit in here too also, especially the first one. Mark Fisher’s Capitalist Realism, though I didn’t finish it. I remember more distinctly reading his Wikipedia page, which in its tragedy and clinical style I felt stated more to me than his books. A lot of thinkpieces. A lot of Byung-chul Han quotes about the "achievement-subject”. And yet I still feel like there is a dearth of literature about working, and why we work, and what it’s supposed to mean. I am still looking for a book that will articulate the message I want to hear.
I mean, to be clear: there is a lot of talk about work, especially in the past two years, especially about overwork. Burnout is the word of the moment. People urging each other, and by each other I mean other upper-middle-class white collar professionals, to take a step away from work and remember that companies don’t really care about you. They’ll hire you and forget you, capitalism is morally corrupt, etc. etc. Of course I agree with this. Of course I am aware of burgeoning economic inequality, and the way that an ethos about work is, essentially, politically and economically convenient for a moneyed set of elites. But what can I say? I found Digital Minimalism depressing. I don’t really find it very inspiring to work less as a way of making myself feel more pleasure. Talking about working less when the only end is self-gratification, optimization - is this the best we can do?
Of course my work is of a particular kind. I edit materials for students; this is one job I do, and it’s the one that pays. Typically I do it in the summers, when my time is free. I like writing to teach, to educate (vulgarising, as we say in French), and I like writing carefully. I used to work in journalism, which satisfied the same itch. The other work I do, the one I considered my life’s focus, is learning math. This is uncompensated work, work that theoretically never ends. It’s also work that I’m not very good at.
The issue probably amounts to the way I thought math was supposed to be approached. Growing up, I was good at math, meaning I could solve many problems quickly, without that much instruction. Useful, but no one needs an abacus, and the attitude it left me with cripples me to this day. Even now, knowing better, I find myself getting competitive while learning math. Reading some notes on category theory, I feel itchy and bewildered. All I want to understand is quickly, and now. This is not necessarily compatible with math at the university level, where why is as important as that. One invents novel objects, formulates precise definitions. Sometimes, a proof hinges on a single clever observation or some random inequality. Rarely do things come immediately, transparently.
Like, what even is an adjunction? According to page 108 of the notes I’m reading, by Paolo Perrone, it’s the following:
Does that make sense? Of course, reading this, I know what a category is, and I know the precise mathematical definition of a category, and a functor, and a bijection, and naturality. Yet I won’t know the definition of an adjunction for a while, probably not until I’ve read 20 more pages in these notes, at which point I will understand page 108, but not page 128. And so on and so on.
It’s not really pleasing for me to learn math, most of the time. Actually, it’s an exercise in confusion and frustration. Sometimes, I have flashes of insight. And there are pieces I find beautiful. The most trivial results in set theory and analysis—the existence of non-analytic sets, the uncountability of the reals—somehow have ended up things that I think about quite often. They’re like punchlines to a joke I never asked for. Surprising, bewildering, maybe even profound. In this sense, mathematics to me can be a kind of Holy Fool, nonsensical, a deep pool of still water.
My favourite results are those wrapped in simple language. A branching process dies if µ is not greater than 1. Simple random walk is null recurrent. There exist non-determined infinite games.
But most of math is not like this. For each beautiful theorem, there is a litany of abstruse definitions and theorems that precedes it: the definition of a branching process, a random variable, a Markov chain, µ itself. A game - what’s a game? (A tree, a set of choices with a payoff set, a set of infinite sequences.) An infinite game - what kind? (Two-player, with perfect information.) So much language, language that can feel arcane, with a novel but in some sense useless reward. The most fundamental theorem in category theory, the Yoneda embedding theorem, took me about 2 weeks to even understand the statement.
If I wanted to pursue self-pleasure, why study math at all? If I get burned out on math and competitive about it, and I do, should I just put it aside entirely? On the other hand, should I be as competitive about math as possible, as ruthless? I’m not sure. I vacillate between these two approaches. I rarely feel satisfied with either.
The reasons why I study math are banal. Some of them are even bad. I study math because: my father was a category theorist, and my great-aunt into torsion theory. Because I find other subjects non-rigorous. Because now I have a very particular epistemic taste, not even that mentally well-argued, which makes me unable to take the humanities and certain ways of knowledge creation that seriously. Because I resent the social sciences for their diluted quasi-empiricism. Because I’m too chicken for the real empirical fields, like biology and physics. Because I want to seem smart. Because I’m deeply invested in my 4.0 GPA and so learning math is, sometimes, somewhat a byproduct of my own bizarre expectations. Because I want to grasp something totally unknown, because math gives me a beauty that I don’t think I can could access in any other way, even if I can barely access it all. Something like reading a very difficult novel, badly translated from German, which requires you to solve multiple Sudoku puzzles to even understand it. And then you understand it, and you’re like: oh.
As Byung-Chul Han writes in Saving Beauty: “Beauty is a hideout. […] Opacity is inherent to it.” The Torah, for example, is described as veiled: ‘through a light veil she speaks allegorical words’. Another way of putting it: the channel is noisy, the information is dense. My math textbooks, though secular, are similarly compact. I pore through a paragraph. I repeat the action. A single sentence can answer a question, can turn like a key, if only I read it enough times.
To love something, even when you don’t love the work of it, even when the work of it is mentally grueling. To pursue something for abstract reasons, even meaningless reasons. Out of habit and convenience. Out of rigidity, even. And anyways, no matter how bad it is, at least it’s something to do.
It’s like, well, Why write? A banal question, for sure, and one that unfortunately spawns all sorts of narcissistic articles about the artist’s place in society, and the important political significance of a Sally Rooney novel, etc. Why write (or do math, or teach, etc.)? I think Zadie Smith’s answer is still best, from her short book of essays Intimations:
[T]he surest motivation I know, the one I feel deepest within myself, and which, when all is said, done, stripped away – as it is at the moment – seems to be at the truth of the matter for a lot of people, to wit: it’s something to do. I used to stand at podiums or in front of my own students and have that answer on the tip of my tongue, but knew if I said it aloud it would be mistaken for a joke or fake humility or perhaps plain stupidity … Now I am gratified to find this most honest of phrases in everybody’s mouths all of a sudden, and in answer to almost every question. Why did you bake that banana bread? It was something to do. Why did you make a fort in your living room? Well, it’s something to do. Why dress the dog as a cat? It’s something to do, isn’t it? Fills the time.
Yesterday I read this article in Quanta about June Huh, one of the 2022 recipients of the Fields Medal, a prestigious prize awarded to mathematicians under 40. I read it a couple times. Huh works about 3 hours a day. He dropped out of high school in order to become a poet. He was rejected from every master’s program he applied to except one, in recognition of his terrible university grades. After proving some results related to Rota’s conjecture in about 50 pages with two other co-authors, he decided the proof could be done more cleanly. At Huh’s urging, rather than publishing, the group took another two years to craft a deeper argument.
Huh speaks slowly, pausing often and choosing his words carefully, and carries himself in a calm, peaceful manner that borders on meditative. “He doesn’t get so easily excited,” said Botong Wang, a mathematician at the University of Wisconsin, Madison who has collaborated with Huh on a number of important recent results.
He proceeds just as deliberately when doing mathematics. Wang was shocked when he first witnessed it. “I have this math competition experience, that as a mathematician you have to be clever, you have to be fast,” he said. “But June is the opposite. … If you talk to him for five minutes about some calculus problem, you’d think this guy wouldn’t pass a qualifying exam. He’s very slow.” So slow, in fact, that at first Wang thought they were wasting a lot of time on easy problems they already understood. But then he realized that Huh was learning even seemingly simple concepts in a much deeper way — and in precisely the way that would later prove useful.
It reminded me of another Fields medalist, the late Maryam Mirzakhani. She described herself as a “slow” mathematician; to do math, she would doodle on large sheets of paper, formulas scrawled on the periphery. Her daughter called her work “painting”. Reading her Wikipedia page once, I teared up. I wondered if I could think of work, and in particular the work of math, as she seemed to.
“I don’t have any particular recipe [for developing new proofs]. … It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.”
I tend to think of math as a mental activity. But aren’t all activities, ultimately, embodied ones? I like the act of carefully writing down definitions and theorems in different coloured pens. I tend to favour blues and greens, also electric pinks. I feel my work is more real in that sense, externalized, physically available. With category theory I tend to draw lots of diagrams, over and over, mostly incorrectly, but sometimes correctly. Indeed I measure my progress not by what I’ve learned but by how many pages I’ve filled up. Sometimes what we call thinking is just movement, repetitive motion, as the poet Mary Ruefle references in this interview:
I write by hand because that is how I began, and I love it. Moving the wrist, the marks the pencil or pen leave on the paper – like the trail of a snail – well, it is like drawing, no, it is drawing, and I am so enamoured of this activity that sometimes I write continuously without actually forming real words, I call it ‘fake handwriting’, and it’s just as much fun as actually ‘writing’. By fun I mean it’s just as much a mystery. This whole wrist-moving action is why I write in the first place. I don’t like tennis, or knitting, I like writing with my hands.
I am not sure I know the right way to work, or the healthy one. A couple of thoughts: there should be more literature in the philosophy of work. Also: we can’t break down every human experience into the language of illness, especially a domain as variegated and expressive as work. I think the word burnout can be useful, but I also worry it has a flattening effect, folding all sorts of complex mental experiences into the umbrella of trauma. I don’t know how to motivate myself most days. I feel slightly better writing than not writing, and doing math than not doing math. I still spend maybe 40% of my non-compensated days laying on my bed with my phone, feeling mostly miserable. I want to figure out how to do less of this without also embracing exhaustion, competition, guilt, self-incrimination. In other words, I want to learn how to do math.
What does man gain from all his labor at which he toils under the sun?
Generations come and generations go, but the earth remains forever.
The sun rises and the sun sets, and hurries back to where it rises.
The wind blows to the south and turns to the north; round and round it goes, ever returning on its course.
All streams flow into the sea, yet the sea is never full. To the place the streams come from, there they return again.
All things are wearisome, more than one can say. The eye never has enough of seeing, nor the ear its fill of hearing.
What has been will be again, what has been done will be done again; there is nothing new under the sun.
Is there anything of which one can say, "Look! This is something new"? It was here already, long ago; it was here before our time.
There is no remembrance of men of old, and even those who are yet to come will not be remembered by those who follow.
I, the Teacher, was king over Israel in Jerusalem.
I devoted myself to study and to explore by wisdom all that is done under heaven. What a heavy burden God has laid on men!
Ecclesiastes, 1:4-13.