I sat cross-legged at the small wooden table in my room, staring at the parchment before me with the reverence usually reserved for divine scriptures or the last dumpling in a communal meal.

  This was, without exaggeration, one of the most important pages ever written in human history.

  Not this specific page, of course. This page was just my own poor attempt at scribbling down what little I remembered. The real page had been written by évariste Galois, the tragic hero of mathematics.

  The man, the myth, the mathematician.

  I tapped my brush against the inkstone and exhaled slowly. This was, in some ways, a nice break from the training. It wasn’t directly about qi. I wasn’t attempting to control or channel anything. I wasn’t falling slightly wrong down a brachistochrone curve or tracing circuits in the dirt like some deranged monk.

  No, this was just mathematics.

  Or, more precisely, it was me attempting to reconstruct a genius’ insights from memory, which was not unlike trying to rebuild a legendary sword using a single blurry painting of it and some deeply unfounded optimism.

  I dipped the brush into the ink and carefully wrote the words at the top of the parchment:

  Galois Theory.

  It looked very profound. It felt important.

  I had absolutely no idea where to start.

  I ran a hand down my face, sighing. Where had I first heard about Galois? Some half-remembered video? A book I’d flipped through but never studied properly? A lecture displayed on the schedule of the math department I passed on my way to work that I hadn’t taken but now desperately wished I had?

  I leaned back and closed my eyes.

  Galois was the perfect xianxia protagonist.

  A peerless genius, undisputed in his ability, so far ahead of his time that not even his elders and sect masters could comprehend his insights.

  A hotheaded youth, brash and unyielding, refusing to bow to the rigid, outdated structures of academia.

  A romantic revolutionary, passionate in both his ideals and his emotions, entangled in political turmoil and personal feuds.

  A defiant rebel, one who scorned the established order, wrote letters denouncing his so-called teachers, and was expelled from the mathematical sects of his day for speaking too freely.

  And, of course, as all great xianxia protagonists do, he met an untimely end in a fateful duel against a nameless schmuck at the age of 21.

  I paused.

  Actually, that wasn’t how it was supposed to go in a xianxia world.

  In a proper cultivation novel, Galois would have survived the duel by some stroke of heaven-defying luck, stumbled upon a hidden manual of divine algebraic arts, spent a few years cultivating in seclusion, then returned to the mathematical sects with a vengeance. He would have crushed the smug elders underfoot with his newfound mastery, ascended to a higher realm where mathematical truth was directly woven into the fabric of reality, and eventually become the Supreme Dao Lord of Algebra.

  Instead, he died of gunshot-induced peritonitis in some random hospital, desperately scribbling his final insights onto paper by candlelight the night before, as if trying to outrun death itself.

  That kind of unfairness wouldn’t have happened in a cultivation world. But in reality? It happened all the time.

  I opened my eyes and looked down at the parchment.

  Symmetry.

  That was the heart of it, wasn’t it? Galois’ great insight — one that nobody had appreciated at the time — was that the behavior of polynomial equations wasn’t just about their roots, but about the hidden structures that linked those roots together.

  Polynomials had symmetries, just like physical systems did. Just like groups of warriors, formations on a battlefield, configurations of energy in a cultivation technique.

  The rules that governed them weren’t just arbitrary formulas — they were deep, woven into the structure of algebra itself.

  It was strange, really. Every time I had thought about symmetry before, I had thought about physical symmetry. Bilateral symmetry in organisms, rotational symmetry in molecules, the kind of things that made sense in a biological framework.

  But this?

  This was structural symmetry, not of physical things, but of relationships between things.

  I tapped my brush against the table again.

  It was almost like a cultivation technique.

  In martial arts, if you were fighting an opponent, you could analyse how they moved, how they struck, what their patterns were. That was the level of direct observation.

  But if you knew the fundamental structure behind their techniques, then you could see what must be true.

  You wouldn’t need to see every movement. You wouldn’t even need to see the whole battle.

  If you understood the underlying group structure, you could infer the rest.

  I sat up a little straighter, frowning.

  That was… an interesting thought.

  I picked up my brush again, smoothing out the parchment.

  Perhaps my problem so far had been that I had been trying to force my qi into mathematical truths instead of recognising the structures it already had.

  Instead of demanding that it obey functions I imposed, maybe I needed to observe what symmetries it naturally possessed.

  If Galois had been a cultivator, he wouldn’t have tried to brute-force a technique.

  He would have analyzed the constraints, studied the transformation groups, and then — and only then — used those constraints to find what was possible.

  I exhaled slowly, staring down at the ink drying on the page.

  Maybe this wasn’t just about equations.

  Maybe I needed to stop telling my qi what it was supposed to be.

  And instead, I needed to start listening.

  -x-x-x-

  The night air was crisp and cool as I strolled through the quiet streets of Qinghe Town, the packed dirt roads dappled with the pale glow of paper lanterns swaying lazily in the evening breeze. It was a welcome escape from the oppressive stillness of my rented room, where my latest mathematical inquiries had reached the stage of ‘staring at a blank page in existential dread.’

  I needed a walk. Needed to clear my mind.

  Needed to figure out what the hell ‘listening to my qi’ even meant.

  This had been the grand insight of my recent studies: I had never actually listened to my qi.

  To be fair, I hadn’t thought it had anything to say. It wasn’t sentient. It wasn’t some ancient sage whispering esoteric truths into my mind. It was energy. A force. A thing to be shaped and directed, or at least, that was how cultivation stories framed it.

  But I had no dantian. No vessel. No core. So why was I still trying to impose rules onto something that had none?

  I’d spent months stubbornly trying to tell my qi how it should work. Trying to define it. Trying to impose mathematical structure on it like an overzealous engineer attempting to fit an elephant into a spherical approximation for ease of calculations.

  And yet, the only times it had ever manifested — ever done anything — was when I wasn’t trying at all.

  The creeping influence that seemed to settle into my students’ minds, filling their innocent thoughts with infinities and paradoxes.

  The moment I’d stumbled on the brachistochrone curve — not forcing my qi into it, but simply aligning myself with the inevitability of its truth.

  The Knight’s Tour, where I had given up on brute-forcing my qi and simply moved as my heart desired.

  It was subtle, frustratingly so — so much that I wasn’t entirely convinced those oddities I noticed were some mystical power at all — but I could not ignore the pattern.

  I had spent months attempting to enforce equations upon my qi in various ways, demanding that it fit within structures of my own making.

  Had I ever considered that perhaps it had its own structure? That maybe it had already spoken to me?

  And that I — like the worst kind of obtuse researcher ignoring experimental data that didn’t fit his convenient hypothesis — had simply refused to listen?

  I sighed and rubbed my temples, feeling the weight of my own ignorance settle over me like an unwelcome blanket.

  The walk had been meant to help, but now I was just getting lost in circles of my own thoughts.

  At least the night was peaceful.

  The streets were nearly empty at this hour, the town beginning to settle in for the evening. The only movement came from the occasional flicker of lantern light in the windows, the faint sound of merchants packing up their stalls, and the rhythmic clink of metal from the direction of the forge.

  Wait.

  The forge?

  I squinted ahead.

  A small figure trudged down the road, carrying a bundle wrapped in cloth over one shoulder. Even in the dim light, I recognized the distinct gait. Zhao Qiang.

  I approached, and he noticed me immediately, pausing with a small nod of acknowledgment.

  “Teacher,” he said, bowing low, voice steady as ever.

  I almost sighed. It had become increasingly apparent over the past months that the students I met during my study breaks had simply decided I was a hidden expert.

  None of them ever said it outright, of course. But the way they spoke to me had changed. They bowed just a little lower when greeting me; seeming almost to hang on to every word that I said.

  I had done nothing to deserve this.

  I had, in fact, done everything possible to avoid this.

  And yet, here was Zhao Qiang, standing before me like a student before a grandmaster, patiently awaiting my words of wisdom.

  I cleared my throat. “Out late, Zhao Qiang?”

  He held up the wrapped bundle. “Delivering something to my father.”

  I nodded, falling into step beside him. “And how are your studies going?”

  There was a pause. Then, in his usual blunt manner, he said, “Not as fun without you.”

  Unauthorized duplication: this tale has been taken without consent. Report sightings.

  I blinked.

  Well. That was… unexpectedly straightforward.

  “Ah,” I said, caught slightly off guard. “Headmaster Song is still teaching the lessons, isn’t he?”

  He nodded. “But it’s not the same.”

  I glanced at him. “Why’s that?”

  Another pause.

  Then, in the most deadpan voice imaginable, he said, “No one else makes our heads hurt like you do.”

  I let out a strangled cough.

  “That’s… not usually something people say as a compliment.”

  “It is,” he said, very seriously.

  I squinted at him. “Is it.”

  He nodded.

  I sighed. “I’m not sure how I feel about that.”

  Zhao Qiang shrugged, shifting the bundle on his shoulder. “It was better before,” he said simply.

  Before.

  I found myself unexpectedly struck by that. I had assumed that after a few months, the students would have adjusted. I wasn’t some legendary scholar, after all. I wasn’t a proper teacher. I had expected them to forget me. Or at least, to move on to a more structured education under Headmaster Song.

  But apparently, I had underestimated just how deeply I had inflicted mathematical trauma upon them.

  “You’re saying the lessons are boring now?”

  Zhao Qiang nodded without hesitation. “Yes.”

  I sighed. “I’m sure Headmaster Song is a fine teacher.”

  Another nod. “He is.”

  I squinted at him. “But?”

  “But he doesn’t talk about infinity,” Zhao Qiang said. “Or paradoxes. Or numbers that don’t behave. Or why some things are impossible, but if you twist them sideways, they aren’t anymore.”

  I stopped walking.

  That was… a surprisingly good summary of what I had been doing.

  Zhao Qiang looked at me expectantly, as if I were supposed to provide some kind of answer. And perhaps I should have, but instead, I just stared at him, my mind spiraling into yet another self-inflicted crisis.

  Because he wasn’t wrong.

  That was what I had been teaching them. Not just numbers or calculations, but concepts that felt wrong until they felt inevitable.

  That was what had made my students so unnervingly good at accepting paradoxes. It was why they had taken to discussing infinities like they were actual quantities instead of vague, incomprehensible abstractions. They had learned to think about numbers not as simple tools, but as things with their own strange properties.

  I had, in a way, been shaping their perception of reality.

  And that — more than anything — was what my qi had responded to. If manifested because I made them think.

  I swallowed.

  It had spoken.

  I had never listened.

  I rubbed the back of my neck, feeling an odd weight settle over me. “You… actually enjoy all that nonsense, huh?”

  Zhao Qiang nodded.

  I frowned. “Even the paradoxes?”

  He nodded again.

  “The headaches?”

  “Mm.”

  I gave him a long look. “You’re not just saying that because you think I’ll smite you with hidden cultivation powers, are you?”

  Zhao Qiang tilted his head, considering for a moment. “No.”

  I exhaled slowly.

  Alright.

  Fine.

  This was a conversation I would need to unpack later. Much later. At the same time that I considered what it spoke about me that my students had developed some sort of Stockholm syndrome centered on me tossing infinities into their mind like some eldritch Lovecraftian horror.

  For now, I examined what I already suspected, and now was more or less confirmed by Zhao Qiang. If my students had changed because of my teachings, then my qi had been influencing them.

  Not through direct intention. Not through conscious will.

  But through conceptual resonance.

  I wasn’t controlling it. I was warping reality around me simply by believing in something strongly enough.

  And wasn’t that… how all cultivation techniques worked?

  A sword cultivator believed the sword was an extension of their soul. So it became true.

  A body cultivator believed their flesh could become as strong as steel. So it did.

  A scholar believed that the heavens could be defied. And so, inevitably, someone proved it.

  I had spent the better part of two months trying to force my qi into obedience.

  But what if that wasn’t how it worked? What if I had to treat it like a student?

  What if I needed to stop trying to command it?

  “Maybe I’ve been thinking about this the wrong way,” I muttered.

  Zhao Qiang was still looking at me, waiting patiently for whatever wisdom I was supposed to impart.

  Instead, I just sighed. “Alright, alright. I get it. You miss me.”

  He shrugged. “Lessons were more fun when you were there.”

  Something about that made me pause.

  I had spent most of my life regretting that I had never properly pursued mathematics. Wishing I had been braver. Smarter. More disciplined. And yet, despite all that, despite my own inadequacies…

  I had made it fun for them.

  I had made math fun.

  That thought lingered as I watched Zhao Qiang continue on his way, disappearing into the dim glow of the forge.

  Maybe I couldn’t control my qi the way a cultivator did.

  But maybe — just maybe — I could teach it to behave.

  And wasn’t that, in the end, what teaching was? Taking something unstructured, chaotic, and slowly, carefully, guiding it toward something more?

  I exhaled and turned back toward the inn.

  If my qi was waiting to be taught, then I was going to have to figure out what kind of student it was.

  -x-x-x-

  I sat in the dim candlelight of my room, staring at the parchment before me, fingers tapping absently against the wood of my desk. Three months. That was how long I had spent wrestling with a force I still barely understood. Three months of painstaking derivations, frustrating failures, and fleeting, elusive successes.

  But the pieces were beginning to fit together.

  The brachistochrone had been the first clue — when I had stopped imposing a path and instead followed an inevitable one.

  The Knight’s Tour had been the second — when I had stopped trying to force a pattern and instead became part of the structure.

  And most recently, my conversation with Zhao Qiang had provided the third.

  My students’ minds had shifted, not because I had tried to change them, but because I had made them see things differently. I hadn’t imposed my will upon them — I had simply shown them something, and their perception had expanded on its own. The truth had been there the whole time, waiting to be discovered.

  Wasn’t that how my qi was behaving?

  I had tried to control it, to fit it into a rigid, defined structure — but perhaps that was the wrong approach. Mathematics wasn’t about imposing structure. It was about recognising it. Finding the underlying symmetries, the constraints, the transformation groups that dictated how something must behave.

  I inhaled deeply.

  If my qi was everywhere and nowhere — if it was some nebulous, undefined mathematical truth — then perhaps I shouldn’t be defining it.

  Perhaps I should be allowing it to define itself.

  I closed my eyes and let my mind drift.

  It wasn’t just a field — it was a field waiting for the right elements to extend it.

  It wasn’t just a function — it was a functional, waiting for the right inputs to give it form.

  It wasn’t just a set — it was a group, imbued with an operation, waiting for its action.

  That was the key, wasn’t it?

  A mathematical object was often useless until you had a way to interact with it. A group without an action was just an abstract collection of elements. A field without an extension was constrained by what it could construct. A function without an argument was just a notation, an empty shell.

  A function didn’t exist in a vacuum. It existed within a space of possible functions.

  A vector wasn’t just magnitude and direction. It was part of a larger space that governed its transformations.

  An equation wasn’t a statement of isolated truth — it was a constraint that defined what must be true.

  My qi wasn’t a single, fixed thing. It had never been unstructured. It had simply been waiting for something to act upon it.

  Waiting to act upon itself.

  Waiting for a transformation.

  I opened my eyes.

  I needed to stop trying to impose a function onto my qi.

  No, I needed to apply a group action.

  And the natural action, the most fundamental transformation in mathematics, was symmetry.

  -x-x-x-

  I stepped out of my room, the cold night air settling around me as I walked toward the outskirts of Qinghe Town. My breath curled into faint mist, dissipating into the darkness.

  This was it.

  Tonight, I would listen.

  The clearing was quiet, the grass cool beneath my feet as I settled into a stance. No calculations this time. No scribbled equations. No grand pronouncements about the nature of reality.

  Instead, I simply existed.

  I inhaled, feeling the steady rhythm of my breath, and reached inward — not grasping, not forcing, but listening.

  If qi was everywhere and nowhere, then it had to possess symmetry.

  If it was a group waiting for an action, then the action had to be self-generated.

  And if it was mathematical truth, then it could be expressed in transformations.

  And yes… everything was a transformation, wasn’t it? Even something as simple as the addition of zero. It left a thing unchanged — but that too was symmetry: the symmetry of ‘do nothing’; the identity element under the operation of addition.

  I took a step.

  Then another.

  I let my movements align — not with something imposed, but with something inherent. Something inevitable.

  And then, for the first time, I felt it.

  A shift, imperceptible at first, like the first number in an infinite sequence. A whisper in the fabric of existence, where movement ceased to be a mere act of will and became something deeper. The rules that governed space and time flickered at the edges of my mind, revealing themselves in fleeting glimpses, like a grand function whose domain stretched beyond comprehension.

  A great silence followed.

  Not the ordinary quiet of an empty field, but a silence with structure — a void filled with something vast and precise, like the negative space in an elegant proof. I was inside something, and it was inside me.

  It was an axiomatic system, and I was one of its theorems.

  I took another step.

  Something clicked into place.

  The world transformed around me.

  No, not the world — the coordinate space in which I existed. I was no longer an arbitrary point, some isolated value floating in an unfathomable expanse. My position was relational, a node in an intricate, unseen web of transformations, bound by symmetries that had existed since the dawn of time. I had not created them. I had merely opened my eyes.

  Reality did not merely contain an algebraic structure.

  It was one.

  And I was moving within it.

  This was not teleportation. It was not speed. It was not even motion in the conventional sense.

  It was something deeper. Something fundamental. Something absolute.

  A bijection between where I had been and where I was going. An invariance under transformation.

  A universal symmetry.

  And within that symmetry, I did not move — I resolved.

  The wind did not resist me; it aligned. Not as an opposing force, not as a mere reaction, but as a necessary consequence — an equilibrium that had always been true. A balance inscribed in the very equations that governed existence.

  My breath, my weight, my very presence — everything was a variable in a grand, unshakable system of relations.

  And then I saw them. The generators of transformation.

  They had been there all along, hidden in the structure of the world, embedded in the way existence folded upon itself. They were the fundamental operations of reality — the mappings that connected all things. Not physical laws as mortals understood them, not forces or energies that could be wielded like crude tools. These were deeper than force. More absolute than energy.

  They were the invariant truths that dictated the nature of all things.

  I lifted my hand, and the air around me warped — not through force, not through struggle, but through an unseen necessity. A reordering of constraints.

  The world responded.

  Not as an adversary to be conquered. Not as a tool to be wielded. But as a system resolving itself around my existence, adjusting to preserve its own deeper truths. I had not imposed an equation or transformation onto reality — no, I had merely aligned with one that had always been there, waiting to be understood.

  It was finally happening.

  No more abstract hints. No more fleeting illusions of power slipping through my fingers. This was real. This was mathematical truth given form. I was aligning with a universal principle, and in doing so, I was finally grasping what it meant to be a cultivator. Not by bending the world to my will, but instead by recognising its symmetries, stepping into the space between contradictions, allowing the transformations that had always existed to take shape through me.

  A profound realization surged through me:

  This was what it meant to have a Dao.

  Not an ideology. Not a technique. Not a school of thought.

  A structure.

  The world had always been governed by mathematical principles, but only now did I see that those principles were alive. They weren’t merely descriptions of reality — they were active constraints, shaping existence.

  And I had touched them.

  No, more than that — I had become one with them.

  The latent, shattered remnants of my dantian — the Cantor dust left in the wake of the cultivation I’d dispersed — were not a void, not a broken system waiting to be patched together.

  They were basis elements. The atoms of a space that had always been infinite-dimensional.

  I had spent the last months trying to understand and rebuild a dantian that functioned like a simple, constrained algebraic structure, but my qi had never been a finite system.

  No, it was category-theoretic. A thing that could not be understood in isolation, only through the morphisms that related it to everything else.

  And for a moment — a brief, infinitesimal moment — I glimpsed more.

  A vast, impossible architecture. Not a single system of transformations, but a system of all transformations. An algebra of algebras, a category of categories, where every act was not just an event, but a fundamental relationship between infinite possibilities.

  I was nothing but one infinitesimal term in a grand, unyielding equation. One point in a manifold of possibilities. My very existence was not a single isolated entity but an object in a larger system of mappings, an entity that could only be truly understood through its morphisms, through its transformations between states.

  And yet —

  I was part of it.

  But still I did not understand. Not fully.

  I could sense that there were higher-order transformations, symmetries that went beyond the simple ones I could perceive. I was standing at the base of a towering structure, able to grasp only the most basic elements, the simplest mappings. The deeper symmetries — the transformations that could truly shape reality — were still beyond me.

  I could not yet see how every element mapped to every other. I could not yet perceive the full structure of the group.

  If I wanted to punch a mountain apart, I would need to understand which transformations were preserved. Which symmetries were broken. How force mapped to space, how energy transformed under action.

  I did not know how the generators and operators of this algebra of algebras acted upon the world. I could see only the trivial cases, the obvious mappings. But the deeper truths? The transformations that would allow me to bend the very structure of reality?

  Those were still hidden from me.

  The wind swirled around me as I stood there, breath slow, heart steady. I had touched something immense, but I was not yet fully ready to wield it.

  Force was meaningless without context. Power was empty without structure. I had seen the edges of a truth so immense that it reduced me to insignificance… and yet, I was not afraid.

  I exhaled.

  The wind stirred, not in resistance, but in quiet acknowledgment.

  I had not reached the peak. I had merely set foot upon the path.

  I had been foolish before, impatient, expecting my enlightenment to be instantaneous. Expecting knowledge to flow into me in a single, all-consuming revelation. But that was not how understanding worked.

  Not in mathematics. Not in life. Not even in cultivation.

  The greatest minds of history had spent years wrestling with the truths they discovered. Decades refining their insights. Some had died without ever fully comprehending the things they had glimpsed.

  And I?

  I was just beginning.

  I clenched my fists, not in frustration, but in determination.

  This would take time. There would be many more failures.

  I would make mistakes, miscalculate, misunderstand. I would grasp at transformations I could not yet control. I would discover deep into the proof of a theorem that a critical lemma did not hold.

  Yet I remembered the eternal words of Gauss: “I have had my results for a long time: but I do not yet know how I am to arrive at them.”

  With every failure, I would iterate.

  With every mistake, I would refine my approach.

  I would learn to see not just the isolated elements, but the entire structure. I would discover the higher transformations, the true mappings, the fundamental symmetries of this reality.

  I would improve.

  And one day, when I fully understood the symmetries of this world — when I saw not just the transformations, but the governing action behind them —

  Then I would punch a mountain apart.

  I took a step forward, and the world did not tremble.

  But somewhere in the infinite algebra that bound all existence, a transformation had begun. The silence stretched, weighty and expectant.

  The world had noticed.

  And that was enough.