✦ Thursday 09.10.26 ✦
Ok. Hi. It's late and I'm about to try to write about math, of all things, which if you know me is a little bit funny, because I hate math. Or at least I used to think I did. Bear with me. I promise this goes somewhere.
I hate math. I used to say it out loud all the time. Every single person I ever considered a friend in school just assumed, or straight up said to my face, that I was an idiot for not understanding the most basic things in a subject like that. My grades in algebra were the lowest in the class, a shaky C or D through high school and sometimes a very fair, very precise F. I couldn't understand the teachers. I couldn't understand why I was supposed to follow this linear, direct process that was so obvious to everyone else, without asking any of the questions the process kept dodging. I got tangled in doubt. I convinced myself I was, in fact, an idiot, or maybe they just made me feel like one. I convinced myself I couldn't solve a single miserable exercise without feeling failure knocking at the door.
Here's the thing, though. My problem, honestly, is that even though I didn't like math the way it was handed to me - cold numbers on a gray, boring board - I always kind of thought it wasn't really being math. Like the version I was being shown wasn't the actual thing. Numbers are a language, one of thousands humans invented, and this one is the invisible language that keeps building the reality we walk around in. When you sculpt digital worlds as an artist, when you decide to program something even in the tiniest way, when you time an animation so it lands the way your heart wanted it to land - you are speaking that language, whether you know it or not. And what I actually think, deep down, is that math is the bridge between the chaos of the universe and the very human desire to find some order inside it.
I just couldn't say that at fifteen with an F on my report card. Nobody would've listened.
I don't remember exactly how old I was the first time I saw The Theory of Everything. Maybe fifteen? Sixteen? Somewhere in the wreckage. I probably shouldn't admit that a Stephen Hawking biopic with Eddie Redmayne looking soft-focus into a chalkboard is what started to crack me open, but that's what happened, so I'm just going to say it.
There's this scene, and I've thought about it more times than I can count, where young Hawking is trying to explain to Jane, on a date, what he does. He tells her, in the simplest possible way, that he's trying to find one equation that explains everything in the universe. And Jane, sensibly, asks him if he's religious, because that sounds like a religious question. And he sort of laughs and says no, he's a cosmologist. Which is, in his words, a kind of religion for intelligent atheists.
I remember pausing the movie right there. Not dramatically, I just sat with it. Because up until then, I had only ever met math and physics as adversaries - subjects I was supposed to get right, subjects that were going to reject me. And here was this guy saying, without irony, that what he did was the closest thing he had to prayer. And it hit me that maybe I had been introduced to math wrong. That maybe it wasn't a test. Maybe it was a religion for people who couldn't stop asking why the light behaved that way when it hit the surface of the water.
I know a movie is not a book. I know the movie flattens him. Hawking himself, in A Brief History of Time, is drier and more careful than his Eddie Redmayne version, and he specifically doesn't like it when people project theology onto physics. But I was a teenager who needed a door, and the movie was a door, and I walked through it. Whatever.
What was on the other side was quantum mechanics.
Here is the thing about quantum mechanics that nobody tells you when you're twelve and trying not to cry over a variable: the actual foundation of the physical world does not behave the way your teacher's word problems say it does.
At the smallest scales we have ever measured, particles do not have precise positions and precise momenta at the same time. This is not because our instruments are bad. It's because those two properties, mathematically, are what physicists call conjugate variables, and you literally cannot know both of them at the same time to arbitrary precision. This is Heisenberg's Uncertainty Principle, published in 1927. The mathematics say the uncertainty in position, times the uncertainty in momentum, is always greater than or equal to ℏ/2, where ℏ is a very small constant named after Planck. That is not a metaphor. That is a hard theorem.
Let that sit for a second. The teacher who told me an equation had exactly one correct answer, at exactly one point on the number line, was, at the deepest level of physical reality, wrong. The universe doesn't work like that. The universe works in probability clouds. A particle doesn't have a definite location. It has an amplitude - a complex number - that spreads across a wavefunction, and the square of that amplitude gives you the probability of finding it somewhere when you finally look. This is Max Born's rule, 1926. It's still the interpretation that most textbooks use.
What this means is that when you fire a single electron at a barrier with two slits in it, that one electron passes through both slits at once, interferes with itself, and lands on the detector as one dot. Fire many electrons, one at a time, and the dots build up an interference pattern like waves overlapping in a pond. Try to sneak a look at which slit the electron went through, and the pattern collapses. The electron picks a lane the moment it is observed. This is the double-slit experiment. Feynman called it "the only mystery" of quantum mechanics - the phenomenon that, if you understand it, you understand everything, and if you don't, you have to just accept it and move on.
I sat with this for weeks the first time I read about it, and here is what I finally thought: if the universe itself is written in a language where a thing can be in two places until you look at it, then the classroom math I failed at was a caricature of what math actually does. The classroom math was one-answer-per-question. Real math, at the frontier, has been comfortable with plural, superposed, entangled, probabilistic answers for a hundred years now.
The universe was doing quantum mechanics behind my back the whole time my teachers were telling me there was only one right way to move x to the other side of the equal sign.
The mathematical scaffolding of quantum mechanics is really just linear algebra done in an infinite-dimensional complex space called a Hilbert space. That sounds intimidating and it is, a bit, but the core idea is small enough to put in a sentence: every possible state of a quantum system is a vector, and any two states can be added together to make a third valid state. That addition is what we call superposition. It's not magic. It's the vector addition you learned in tenth grade, done in a bigger, weirder room.
The mathematics were mostly figured out between 1925 and 1927 by a handful of people who were all under thirty-five: Werner Heisenberg, matrix mechanics; Erwin Schrödinger, wave mechanics; Paul Dirac, who married the two into a much more elegant operator formalism a few years later; Max Born, the probability interpretation. They fought about it constantly. Einstein hated it and spent decades trying to punch holes in it; he never really succeeded, but he did push the theory to become more precise in the process, which is maybe the greatest gift a doubter can give a science.
Dirac in particular is my favorite of that crowd, because he wrote his 1930 textbook, The Principles of Quantum Mechanics, in a prose so austere that reading it feels like walking into an empty cathedral. He famously said:
"It is more important to have beauty in one's equations than to have them fit experiment." - P. A. M. Dirac, in Scientific American, May 1963
Which, on the face of it, sounds absurd. Physics is supposed to fit experiment. That's the whole point. But Dirac was making a subtler claim: if your equations are ugly, and they fit the current data, they will not survive the next experiment. If your equations are beautiful and they don't quite fit, they might be pointing to a deeper truth that the current experiment is missing. He was right, empirically. His own equation for the electron predicted the existence of antimatter before anyone had ever seen it, purely because the mathematics required it. Positrons showed up in a cloud chamber four years later.
Think about that. A young man sat at a desk, insisted his equation be symmetric in a certain algebraic way, and in doing so predicted a whole other kind of matter that nobody knew existed. The universe, when it was measured, agreed with him. Not because he had guessed. Because the mathematics knew before he did.
This is what I mean when I say I stopped believing math was a series of exercises. Math is what the universe uses to remember what it's allowed to be.
Now let me back up, because I don't want this to become a physics lecture. I want to tell you about Simone Weil, because she changed how I thought about the act of studying itself.
Simone Weil was a French philosopher and mystic in the 1930s and 40s. She died at thirty-four in a sanatorium in Kent, essentially of self-neglect, because she refused to eat more than the rations of the French workers under Nazi occupation. Her brother, André Weil, was one of the greatest mathematicians of the twentieth century - a founding member of Bourbaki, the collective that basically re-founded modern mathematics from scratch. Simone was not a mathematician. But she wrote to her brother constantly, and she read the Greeks obsessively, and she believed that mathematics was originally a spiritual discipline that got severed from its roots somewhere along the way.
In one of her essays, she says:
"L'attention absolument sans mélange est prière."
Attention, unmixed with anything else, is prayer. - Simone Weil, Attente de Dieu, 1950
And elsewhere, in her Cahiers: "Attention is the rarest and purest form of generosity."
The first time I read that, I understood something about myself in the fourth grade. When I sat in class, chewing on my pencil, trying to figure out why on earth you would move a number to the other side of the equal sign, I was paying attention to the wrong question, and I was paying attention to it fully. The teacher wanted me to do the mechanical step. I wanted to know what the mechanical step said about the nature of equality itself. And nobody could have that conversation with me because I was ten and my questions weren't in the curriculum.
Simone told me, from across seventy years, that my slowness was not stupidity. My slowness was a form of taking the problem seriously. It was, in her language, generous. It was almost sacred. I was giving my full attention to a thing that was designed to be answered in thirty seconds. Of course I was struggling. I was doing something else entirely.
I sometimes wonder what would have happened if a single teacher had said to me: Skye, you don't have to keep up with them. Keep asking. Come back to me when you've figured out an answer that makes sense to you, even if it takes a week. A different life, maybe. But I don't want to dwell on that. Simone Weil starved herself for the French working class. I can survive my algebra grade.
Ok, back to the big stuff. Let me tell you about the moment I fell in love with mathematics for real, on my own time, without a report card in sight. It was when I learned that infinity comes in different sizes.
This sounds like nonsense. Isn't infinity just, well, infinity? Isn't it the maximum? What could be bigger than something with no end?
A German mathematician named Georg Cantor, working in the 1870s and 80s, proved that the answer is yes, some infinities are bigger than others, and here's a proof so short you can write it on a napkin.
His proof, called the diagonal argument, goes like this. Imagine someone hands you an infinite list that they claim contains every real number between 0 and 1. Each number in the list is written as an infinite decimal. Cantor says: I will construct a new number, not on your list, in one move. I do it by walking down the diagonal of your list - the first digit of the first number, the second digit of the second number, the third digit of the third - and I change each digit slightly. Say I add one, wrapping around if needed. The number I just built differs from your first number in the first decimal place, from your second number in the second, from the nth number in the nth. It differs from every number on your list. So your list was incomplete. So no list, no matter how long, can contain all the real numbers.
The real numbers are uncountably infinite. The natural numbers - 1, 2, 3, forever - are only countably infinite. Both are infinite, but the first is bigger. Provably bigger. In the same way that seven is bigger than four, but scaled up to infinity.
Cantor found more sizes above that. He called them alephs, after the first letter of the Hebrew alphabet. Aleph-null is the size of the natural numbers. The reals are at least aleph-one, maybe bigger, depending on which axioms you adopt - this is called the continuum hypothesis, and it turned out to be independent of the standard axioms of set theory, meaning you can consistently believe it or its negation and no math will contradict you. Gödel showed one direction, Cohen showed the other, decades apart. Choose your infinity.
Cantor was also, unsurprisingly, in and out of psychiatric hospitals for most of his adult life. He believed, sincerely, that his alephs were a glimpse into the mind of God. He wrote letters to cardinals about it. His colleagues mocked him. Henri Poincaré called his theory "a disease from which mathematics will have to recover." Kronecker, his old mentor, tried to keep his papers from being published. Cantor answered all of them with what is, to me, one of the bravest sentences ever written by a mathematician:
"Das Wesen der Mathematik liegt gerade in ihrer Freiheit."
The essence of mathematics lies precisely in its freedom. - Georg Cantor, Grundlagen einer allgemeinen Mannigfaltigkeitslehre, 1883
Math, he was saying, is not obligated to describe what already exists. Math is allowed to invent. And when it does, sometimes the world turns out to be wearing exactly the shape of that invention.
Cantor's alephs are baked into modern set theory. Modern set theory is baked into everything. And Jorge Luis Borges, who never studied mathematics formally but had a nose for infinity like a hound for game, wrote The Aleph in 1949 as a short story about a small sphere on a basement staircase where every point of the universe is visible without overlap. It is, to my mind, one of the best pieces of literary criticism of set theory ever written, by someone who didn't know he was writing literary criticism of set theory.
Alright, story time. This is one of my favorites.
In 1913, a British mathematician named G. H. Hardy received a letter from India. The letter was from a self-taught clerk in Madras named Srinivasa Ramanujan, then twenty-five years old, and it contained roughly nine pages of dense mathematical claims that Ramanujan had made up more or less on his own, without formal training, with a couple of textbooks he'd borrowed and re-derived from scratch.
Some of the claims were things Hardy already knew. Some were wrong. But some were new, and clearly deep, and Hardy could see he had no idea where they came from. One of Hardy's colleagues, J. E. Littlewood, said the formulas had to be true, because "no one would have the imagination to invent them." Hardy invited Ramanujan to Cambridge.
Ramanujan came, worked with Hardy for a few brief years, produced formulas that mathematicians are still, a full century later, mining for insight, and then died of tuberculosis at thirty-two. When Hardy asked him where the formulas came from, Ramanujan would sometimes just shrug and say that the goddess Namagiri - the family deity from his hometown - whispered them to him in his sleep. This is documented. He believed it. Hardy, a self-declared atheist and empiricist, apparently found it charming and left it alone.
Hardy wrote a small book toward the end of his life, A Mathematician's Apology, which is short enough to read in one sitting and honest enough to break your heart. He argues, among other things:
"Beauty is the first test: there is no permanent place in the world for ugly mathematics." - G. H. Hardy, A Mathematician's Apology, 1940
Hardy is not being fluffy. He's making a technical claim. He's saying that ugly proofs, even correct ones, do not survive, because they don't propagate - nobody remembers them, nobody teaches them, nobody uses them for the next thing. Only elegant proofs survive long enough to become part of the language mathematicians speak with each other.
I think about this a lot when I make things. Whether I'm drawing or writing or coding, I have the same instinct: if it isn't beautiful, it won't survive me. Even if it's technically correct. Turns out that instinct was already in the water supply of pure math a hundred years before I got there.
The mathematician I love most, the one I would probably not have understood a single word of but whose life story shapes how I think about intellectual work, is Alexander Grothendieck.
Stateless refugee, son of anarchists, orphaned by the Nazis, he taught himself algebraic geometry after the war and in about twenty years rebuilt the whole field. His ideas - schemes, sheaves, topoi, motives - are big enough that current mathematicians talk about them as if they were geographies, whole countries they can visit. He got the Fields Medal in 1966 and refused to travel to Moscow to accept it, because he objected to Soviet policies. He got the Crafoord Prize in 1988 and refused to accept it at all, because he objected to what he saw as the corruption of scientific ethics in the modern research economy.
In 1970 he walked away from the Institut des Hautes Études Scientifiques when he discovered it was partially funded by the French military. In 1991, he moved into a small stone house in a village in the Pyrenees, alone, and for the rest of his life he wrote - mostly by hand - a text called Récoltes et Semailles ("Harvests and Sowings"), thousands of pages of memoir and mathematics and grief and philosophy, only fully published after his death in 2014.
He wrote something in there, about how discovery works, that I want to share:
"L'inconnu à connaître se présente à nos yeux comme une chose totalement indistincte, insaisissable - et pourtant elle est là. […] Il faut se pénétrer patiemment de cette masse informe qui semble un mystère."
The unknown thing we're trying to know appears to us as something completely indistinct, ungraspable - and yet it's there. […] You have to steep yourself patiently in this shapeless mass that looks like a mystery. - Alexander Grothendieck, Récoltes et Semailles, part I
Steep yourself patiently. That's the phrase. Steep, like a tea bag in hot water. You don't attack the unknown, you sit in it until you're the same temperature as it. This is exactly the opposite of what a classroom asks of you. A classroom asks for velocity. Grothendieck asks for infusion.
He also wrote, more quietly, that he was never the smartest mathematician in the room. What he had, he said, was patience. He was willing to sit with an idea for months, turning it, letting it show him its shape. Everyone else was running ahead. He was steeping. And that patience, over decades, produced continents.
I think about this every time I hate myself for taking too long to understand something. Grothendieck says: the world belongs to those who wait.
A brief detour to the seventeenth century, because I can't help myself.
Blaise Pascal was, before he was anything else, a mathematical prodigy. He invented mechanical calculation, he corresponded with Fermat about probability and effectively co-founded the field, he did serious work on projective geometry as a teenager. And then, in his thirties, he had some kind of mystical experience one November night - he wrote it down on a scrap of paper he sewed into the lining of his coat and carried until he died - and after that he spent most of his energy on theology.
He never finished the book he wanted to write. What we have is a pile of fragments called the Pensées. And in one of them, this line, which I would like tattooed inside my ribcage:
"Le silence éternel de ces espaces infinis m'effraie."
The eternal silence of these infinite spaces terrifies me. - Pascal, Pensées, fragment 201 (Lafuma edition)
Pascal was one of the first educated Europeans to fully absorb what the new astronomy was saying. If the universe was infinite, if Earth was not the center, if the stars went on forever with no purpose we could name - then the mathematics that had helped uncover all of this had, by the same act, exposed us. We were alone in a very big room. And that room was mostly quiet.
He didn't respond by giving up on mathematics. He responded by folding mathematics into a bigger meditation on how a small, temporary, thinking being can live in a universe that is vastly indifferent to it. His famous wager - the argument that, given uncertainty about God's existence, it is rational to bet on God - is quite literally a piece of decision theory. Pascal was doing expected-value calculations about salvation. He was applying the same tool he had helped invent for gambling problems to the problem of being alive.
I love Pascal because he shows that the fear of the infinite and the mathematics of the infinite are not opposites. They are, in the same person, two sides of the same wound. He gave the fear its name and then he tried to compute his way through it.
There is a French philosopher of science who almost nobody outside France reads, called Gaston Bachelard. He was extraordinary. He wrote two parallel bodies of work - one on the history of scientific concepts (La Formation de l'Esprit Scientifique, 1938) and one on the imagination of poetic objects (La Poétique de l'Espace, 1957) - as if science and poetry were the same act performed with different tools.
He argued that to learn a new scientific concept, you first have to break the everyday intuition you had before. He called these obstructions épistémological obstacles. The reason people can't understand relativity, he said, is not that relativity is too hard, it's that they still have a small Newton living inside them, whispering that space and time are absolute. You have to evict the small Newton before Einstein can move in.
I read this in high school and I recognized my own struggle with algebra in it. The teacher wanted me to move x to the other side. My small Newton was screaming: but x doesn't exist yet, you haven't told me what it is, how am I supposed to move something you haven't given me? Nobody was helping me evict my small Newton. Nobody was showing me that the letter x, in that expression, was a placeholder for an unknown that was being defined through the very equation I was solving. I was doing the problem wrong because I was refusing, correctly, to treat a symbol as a thing before it was declared.
Bachelard would have loved me. Bachelard would have said: the child is not wrong, the child is standing at the boundary between arithmetic and algebra and refusing to cross without a proper introduction to the new territory.
The twentieth century, mathematically, gave us one of the strangest gifts a science has ever given: the discovery that order and chaos are not opposites. They generate each other.
Ilya Prigogine, a Belgian chemist, won the Nobel in 1977 for showing that certain physical systems, when they are pushed far from equilibrium, spontaneously develop order out of pure noise. Convection cells in heated fluids. Chemical reactions that oscillate between colors. Living things. His book with Isabelle Stengers, La Nouvelle Alliance (in English, Order Out of Chaos, 1984), is one of the most beautiful pieces of popular science ever written. It argues that the old Newtonian picture - a clockwork universe of deterministic laws grinding away forever - was wrong. The real universe is full of systems that evolve, self-organize, and cannot be predicted in detail even though they obey local rules.
Benoit Mandelbrot, at IBM in the 60s and 70s, discovered fractals. Ask how long the coastline of Britain is, and the answer depends on how small your ruler is - the smaller the ruler, the more inlets and coves you can measure, the longer the answer, and in the limit, the answer is infinite. He noticed the same property in ferns, lungs, lightning, neurons, cauliflower, the distribution of galaxies. Nature, at every scale, has more detail. He gave us the word fractal and the whole geometry of self-similarity.
Then Edward Lorenz, trying to model the weather in 1963, ran the same simulation twice with the initial conditions rounded slightly differently in the second run. The weather forecasts diverged wildly. He had just discovered sensitive dependence on initial conditions, the technical name for the butterfly effect. His paper called Deterministic Nonperiodic Flow is short, unshowy, and permanently changed our idea of what "prediction" means.
What all of this is saying, together, is this: our lives are not a badly-formulated problem. They are a chaotic system. We cannot predict them because the initial conditions - the childhood, the neighborhood, the teacher who sighed, the friend who called us stupid, the movie we happened to see at fifteen - compound and amplify in ways that no calculation can trace. And yet, in the chaos, patterns emerge. Fractals of our own biography. I have been drawing certain lines, without knowing it, for over a decade. You have been repeating certain sentences, in different rooms, without knowing it, for years. That is not weakness. That is what a system out of equilibrium does. It finds its own order, from the inside.
The math of the last century gave us permission to be complicated. That's the gift.
Ok, this is where I have to fess up. I use math constantly. I just never call it that. Nobody who codes, or draws digitally, or animates, or designs a website, can avoid it, and I've been quietly doing it for years while telling everyone I hate math.
When I write an easing function for an animation - cubic-bezier(0.22, 1, 0.36, 1), my favorite, the one that feels the softest when a menu slides in - I am picking two control points on a cubic curve and asking the browser to interpolate between two states along that curve. That's a parametric equation. Bézier curves come from a French engineer named Pierre Bézier who worked at Renault in the 1960s and needed a mathematically clean way to describe car body panels. They are polynomials. Every soft animation on the modern internet is, mathematically, a polynomial.
When I set up a gradient with radial-gradient(circle at 30% 25%, …), I am specifying a scalar field over the plane. When I write a media query, I am doing case analysis on a piecewise function. When I space chip pills evenly along a row with flexbox, I am asking the browser to solve a small optimization problem for me every time the window is resized. When I animate a clock hand rotating around its pivot with transform-origin, I am setting the axis of a two-dimensional rotation matrix. When I set up the timing of a sound with a small delay before playing - if (now - lastSfxAt < SFX_COOLDOWN_MS) return; - I am implementing a rate limiter, which is a discrete-time control system.
The clock in the journal, the one that shows you time as morning-noon-dusk-night on a circle, uses hourToAngle, which is literally a mapping from a modular group (the 24-hour clock) onto a circle (the 360° dial). That is elementary group theory, the same subject that unlocks Galois theory and modern cryptography.
Digital art is math wearing a costume. Shaders are systems of equations run per pixel. When I made a starfield background, I had a probability distribution and a sampling function and a per-frame update rule; I just called it "sparkles" because it sounded nicer. Every artist who touches a screen is doing computational geometry. Every animator is doing calculus (the derivative of position is velocity, the derivative of velocity is acceleration - that's the difference between a boring linear tween and one that feels alive). And every one of us is, on some level, taking the abstract objects that mathematicians built for their own reasons and using them to make something small and lovely.
The math was there the whole time. I was speaking it fluently and refusing to call it by its name.
There's a story Richard Feynman used to tell, and it's been repeated so many times it's almost worn out, but let me repeat it once more because it belongs here.
He said he had a friend who was a painter, and one day the painter picked up a flower and said something like, look, I as an artist can see how beautiful this is, but you as a scientist take it all apart and it becomes a dull thing. And Feynman answered - I'm paraphrasing - you see the beauty of the flower and I see it too. But I also see the cells, and the color of the pigments produced by those cells, and the fact that the color exists to attract insects, and the evolution that shaped that attraction over millions of years, and the fluorescence of certain molecules, and the way the plant transports water through capillary action against gravity. Knowledge doesn't take away the beauty. It adds more beauty. It only takes away from beauty if you were counting on ignorance to keep the magic alive.
I keep this in my back pocket for the days I meet someone who tells me they don't want to know how things work because it'll ruin them. It won't ruin them. It's the other way around. The people who love physics the most love flowers more than most people, not less.
Hey, kid.
I know you're going to fail the algebra test on Thursday. I know your teacher is going to sigh when you raise your hand for the third time. I know that girl in the second row is going to whisper something to her friend and they're both going to look at you.
Here's the thing: you were not stupid. You were slow the way people who take a subject seriously are slow. You were asking why the letter x has the right to be in the equation, and the technically correct answer is a small chapter on the foundations of algebra, and it was never going to fit in the six minutes between the bell and the next class. The problem was not you. The problem was that a real math conversation and a school math conversation are two different things, and they were only offering you one of them.
You are going to grow up and read Simone Weil, and Pascal, and Grothendieck, and Cantor, and Hardy, and Ramanujan, and Bachelard, and Prigogine, and Dirac. You are going to fall in love with quantum mechanics without ever having to solve a Schrödinger equation, because what you actually love is the philosophical shape the equations make when you stand back and look at them. You are going to write JavaScript that uses probability, and CSS that uses interpolation, and you are going to make animations that use easings named after a French car engineer. You are going to build a little clock on a website that maps a modular group to a circle, and you are going to think of it as a cute design detail, and it is that, but it is also elementary abstract algebra doing its job while you make it pretty.
Nobody told you that being slow was a way of being generous. Simone Weil is going to tell you, from 1943. You will believe her, because you will already know it in your body.
You are not the F on the report card. You are the questions that didn't fit inside the test. Nobody at that school knew where to put them, so they marked them wrong.
It's ok. You forgive them. It's not a burden anymore. You just want to write a long thing about it and put it on the internet, because there is another kid out there, in another town, and she also does not fit her algebra test, and if she stumbles onto this at 2am, she should know that she is in extraordinarily good company.
I want to end on Rilke, because he says it better than I can.
"Have patience with everything that remains unsolved in your heart. Try to love the questions themselves, like locked rooms and like books written in a very foreign language. Do not now look for the answers. They cannot now be given to you because you could not live them. It is a question of experiencing everything. At present you need to live the question." - Rainer Maria Rilke, Letters to a Young Poet, letter IV, 1903
Real mathematics is patient. A theorem can wait three centuries for its proof. Fermat scribbled at the margin of a book that he had a marvelous demonstration that didn't fit in the space, and humanity spent 358 years trying to find it. Andrew Wiles finally proved it in 1994 by reformulating the whole problem as a statement about elliptic curves and modular forms. Three and a half centuries of open question, and then one man in an attic in Princeton with a dream in his head. That is the actual tempo of the discipline. Not the 40-minute test with 20 kids crying at 8am.
I am not a mathematician. I never will be. But I have stopped being afraid of numbers, and more than that, I have started to feel affection for them. On nights when I can't sleep, I sit at the window and I think about the planets moving, and the ferns unfolding, and the stars quietly turning into other elements before they die, and my own small life bending into its own private fractals. I think about all of it - the whole trembling apparatus - and I know it can be written down. I know it is being written down. Not by me. By other people, with more patience and more gift than I have, in a language I only half-understand. But sometimes, when I write something like this, I feel like I am adding a tiny sentence to the long, long letter our species has been writing to itself for centuries, trying to explain the silence.
That is enough. That was always enough.
✦ with love and a lot of questions still open,
skye
Hola. Si llegaste hasta aquí sin leer todo el ensayo en inglés arriba, va este resumen: es lindo y suficiente por sí solo.
Odié las matemáticas durante toda la escuela. Sacaba C, D, y F en álgebra, y todos mis compañeros me llamaban tonta con esa naturalidad de la infancia que duele porque parece verdad. No podía entender a los maestros. No podía hacer un proceso "directo y lineal" sin detenerme a preguntarme por qué se puede pasar un número al otro lado del signo igual. Nadie tenía tiempo para contestarme. Con los años me convencí de que era, sencillamente, incapaz de números.
Ese diagnóstico era falso. No era tonta. Era una niña que le prestaba demasiada atención al problema. La filósofa francesa Simone Weil escribió que la atención pura es una forma de oración. Yo estaba rezando cada vez que abría el cuaderno, sin saberlo, y me estaban castigando por rezar demasiado lento.
Lo que me abrió los ojos, más allá del aula, fue una película: La Teoría del Todo. Ver a Stephen Hawking decir, sin ironía, que la cosmología era una religión para supuestos ateos inteligentes, me hizo entender que las matemáticas y la física no son un examen. Son la manera en que la especie humana se atreve a nombrar lo que no cabe en el lenguaje ordinario. Cuando Werner Heisenberg publicó su principio de incertidumbre en 1927, mostró - con matemáticas duras - que no se puede conocer al mismo tiempo la posición y el momento de una partícula. La realidad, en su base, no funciona como una respuesta única. Funciona como una nube de probabilidad. Todos los profesores que me dijeron que había una sola respuesta correcta estaban, en el fondo, equivocados sobre la naturaleza del universo.
Descubrí a Georg Cantor, que probó que el infinito viene en varios tamaños. A Srinivasa Ramanujan, un empleado indio que decía que la diosa Namagiri le dictaba fórmulas mientras dormía y que produjo teoremas que un siglo después seguimos sin entender del todo. A Alexander Grothendieck, matemático refugiado que reescribió la geometría algebraica entera antes de irse a vivir solo a un pueblo de los Pirineos a escribir sobre por qué había amado tanto lo que amaba. A Blaise Pascal, matemático adolescente prodigio que escribió una frase que llevo tatuada por dentro: "el silencio eterno de estos espacios infinitos me asusta". Ese miedo y esas matemáticas eran, para él, la misma persona.
Descubrí también algo que me hubiera consolado a los quince: uso matemáticas todo el tiempo. Cuando programo una animación con un easing suave, estoy usando polinomios de Bézier. Cuando escribo el reloj de este diario, estoy mapeando un grupo modular sobre un círculo. Cuando dibujo digitalmente, estoy haciendo geometría computacional sin llamarla por su nombre. El arte digital son matemáticas puestas un vestido bonito. Yo hablaba ese idioma con fluidez y me negaba a admitirlo.
Las matemáticas del siglo XX me enseñaron otra cosa: el orden y el caos no son opuestos. Ilya Prigogine ganó el Nobel por demostrar que ciertos sistemas físicos generan orden espontáneamente a partir del ruido. Benoit Mandelbrot descubrió los fractales, esas figuras que tienen infinito detalle dentro de un contorno finito, presentes en helechos, costas, pulmones y galaxias. Nuestra propia vida es un sistema caótico, y aun así - dentro del caos - se dibujan patrones que uno reconoce después, años después, al mirar hacia atrás.
Lo que quiero decir con todo esto, más allá de las citas: no era tonta. Preguntaba demasiado. Prestaba demasiada atención. Las matemáticas de verdad, no las del salón de las 8 de la mañana con veinte niños llorando, son la disciplina más paciente que existe. Fermat escribió un teorema al margen de un libro y a la humanidad le tomó 358 años probarlo. Ese es el tempo real. No el de un examen a contrarreloj.
Si eres una niña o un niño que no entiende álgebra, y tu maestro suspira cuando levantas la mano, y tus compañeros creen que eres tonta: no lo eres. Estás en compañía extraordinaria. Estás con Cantor, con Ramanujan, con Grothendieck, con Pascal. Ellos también preguntaron demasiado. Ellos también fueron llamados locos. Y sin embargo, sus preguntas construyeron el mundo.
Rilke escribió, en 1903, algo que quiero dejarte antes de cerrar: ten paciencia con todo lo que en tu corazón no está resuelto. Trata de amar las preguntas mismas, como cuartos cerrados y como libros escritos en una lengua muy extraña. No busques ahora las respuestas… vive las preguntas.
Yo no soy matemática. Nunca lo seré. Pero he dejado de tenerles miedo a los números. Y a veces, cuando escribo algo así, siento que estoy sumando una línea diminuta a la carta larga que la especie humana lleva siglos escribiéndose a sí misma para explicarse el silencio.
✦ con cariño y con muchas preguntas aún sin resolver,
skye