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Chapter 6. Proof by Contradiction

  The days settled into a rhythm. Not an easy one — certainly not a peaceful one — but a rhythm nonetheless. Mornings were devoted to the classics and calligraphy, afternoons to literature, poetry, and arithmetic, and the evenings… the evenings were supposed to be for my personal studies, a time to finally sit down with numbers and lose myself in mathematical exploration.

  But reality had other plans.

  I still studied math when I could, still worked by candlelight on finding the proofs to theorems whose key results I vaguely knew of. Yet far too often, my nights were spent poring over the texts I was supposed to be teaching these children. My knowledge of the classics had been shamefully shallow. I knew the famous passages, the oft-quoted verses, but that was not enough.

  The classics, literature, history — I had assumed that I could get by with surface knowledge. That as long as I could keep the students engaged, I wouldn’t need to be a master of Confucian thought or poetry. But Zhang Xian had other ideas.

  The boy had the infuriating habit of asking questions. Not the polite kind. The kind designed to trap me, to expose the cracks in my knowledge. And I had been bluffing my way through those cracks for weeks now, barely keeping ahead of him.

  I had to be better.

  Which meant sacrificing my own time.

  Which meant, to my great frustration, less math.

  I tried not to think about it too much, but of course, that only made it worse. Every time I sat down with a scroll on proper conduct or a treatise on the duties of a gentleman scholar, a small voice in the back of my head whispered, You could be proving something right now. Instead, I was memorizing yet another passage about filial piety, which, if Zhang Xian was feeling particularly troublesome, would undoubtedly be used to question why I, a grown man with no apparent family, was here teaching rather than serving his ancestors.

  It was a balancing act — holding authority over a class that seemed determined to test me while maintaining just enough leniency that they didn’t actively revolt. I was, to my great relief, not the only instructor at the school. The other teachers managed their own groups of students in separate rooms, and though I hadn’t spoken much with them, I had gleaned enough to understand that they, too, were embroiled in their own battles.

  Instructor Liang, a severe man with a perpetually furrowed brow, handled the older students, those who were preparing to take the county examinations. His teaching philosophy seemed to revolve around scaring them into competence. Instructor Ma, the oldest among us, was far more patient, more prone to quiet sighs of disappointment than actual scolding. The youngest instructor, Miss Shen, was the only one who seemed to genuinely enjoy the profession, though I had caught a few glimpses of weariness in her eyes when she thought no one was looking.

  Between classes, we exchanged nods, the silent acknowledgment of comrades-in-arms. Once, when I emerged from my classroom after dealing with an ink-spilling incident, Instructor Liang caught my eye and grunted, “They test you yet?”

  “They test me every day.”

  “Hm.” He nodded. “Good. That means you’re still worth testing.”

  I wasn’t entirely sure how to interpret that, but before I could ask, he had already turned and walked away.

  And so, I settled into my new role, slowly learning more about the students in my charge. Some were bright, eager to prove themselves. Others were less academically inclined, their interests lying elsewhere.

  Zhao Qiang, the blacksmith’s son, had a natural knack for numbers but no patience for poetry. “What’s the point?” he grumbled after yet another failed attempt at composing a verse. “If you have something to say, say it plainly.”

  “Some things cannot be said plainly,” I told him. “Some things can only be understood when felt.”

  He squinted at me. “That sounds like an excuse.”

  “Possibly.” I didn’t push him further. His father, from what I’d gathered, was a man of few words, and it showed in Zhao Qiang’s blunt way of thinking. He would never be a poet. But he might, given time, come to appreciate poetry all the same.

  Chen Meili, on the other hand, was meticulous in all things, from her handwriting to the way she folded the sleeves of her robes before beginning a task. Raised in a merchant family, she had an innate understanding of negotiation, which she frequently employed to try and reduce the amount of written work I assigned.

  “If we copy three passages instead of five,” she proposed one afternoon, “we can still demonstrate our ability while also having time to reflect on their meaning.”

  “You don’t want to reflect on their meaning. You just don’t want to do the extra work.”

  She smiled, entirely unrepentant.

  And then there was Ru Lan, who I was beginning to suspect might be my favorite, if only because she was one of the few students who never deliberately caused trouble. She was quiet, careful, and always followed instructions, which in a class that included Wu Liang was something of a miracle.

  But even she had begun looking at me strangely at times.

  I knew why.

  Because something was strange.

  It wasn’t obvious. Not in the way a thunderstorm announces itself with dark clouds and rolling winds. It was subtle. A sensation just beneath the skin, an awareness that prickled at the edges of my thoughts. A feeling that, if I were being completely rational, I should have ignored.

  But I couldn’t.

  It was there in the way my brush never quite seemed to run dry, no matter how much ink I used. In the way my voice carried across the room with an unnatural weight, silencing even the rowdiest of students without the need to raise it. In the way I caught things that should have slipped from my grip, as if my hands knew before my mind did.

  Most of the time, I told myself it was nothing. Tricks of the mind. Coincidences.

  And then, sometimes, I would meet Ru Lan’s gaze.

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  She never said anything. Never pointed it out. But there was a weight in the way she looked at me, as if she, too, could sense something just slightly off. And that was worse than any amount of suspicion from Zhang Xian, any challenge from Ma Rui. Because Ru Lan wasn’t the type to speak without certainty.

  And if she was noticing, then it wasn’t just in my head.

  -x-x-x-

  It was almost two weeks since taking up this job, and I was quickly understanding that something was wrong.

  Not in an immediate, catastrophic way. No assassins lurking in the shadows. No powerful cultivators descending from the sky, demanding to know how I had dared survive my own crippling.

  No, this was worse. This was subtle. The kind of wrong that made me question my own sanity.

  None of it was overtly supernatural. None of it was something that would make anyone stop and say, ‘That man is a cultivator!’

  But I knew.

  Cultivation required meditation, required gathering and condensing qi within the dantian, shaping it, refining it, strengthening it. I had not done any of that. And I could not do any of that, because my dantian was in pieces.

  Fractured. Shattered. Broken into smithereens.

  It should not be able to hold qi.

  And yet, something was happening.

  It didn’t make sense, but then, neither did a lot of things in my life. I had transmigrated into the body of a failed protagonist, abandoned a destiny of cultivation in favor of mathematics, and was currently locked in an ongoing war of attrition against a class of children who oscillated between cute and unruly. Logic had not exactly been a constant.

  Still. This was different.

  The feeling crept in at odd moments. When I wrote, the brush seemed to move with an almost unnatural ease, the ink flowing in smooth, even strokes that should have required years of refinement. When I spoke, my words carried — more than they should, more than they had any right to, like the quiet authority of a master lecturer commanding an auditorium.

  But the strangest part was my reflexes.

  There was no conscious thought to them. They happened in the gaps — between movement, between calculation, in the fractions of time that should not have existed. A book slipping from my desk, caught before I even registered it was falling. A student tripping over a bench, only for my hand to be there, steadying them, without a single conscious decision made.

  The human brain was good at pattern recognition. That was what made mathematics so beautiful — seeing the connections, the inevitabilities. And my brain had begun to recognise that something didn’t quite fit expectations.

  It wasn’t a single moment that tipped me over the edge, but a series of them. Subtle things. The kind of things that could have been dismissed if they had happened in isolation.

  A brush never running dry was one thing. A fortunate reaction time could be explained away. But the accumulation of impossibilities was something else entirely.

  It was Ma Rui’s inkpot incident that lingered in my mind the longest. He had knocked it over, that much I was certain of. I had seen it tip. I had reached for it, but I had been too far — too slow.

  And yet it hadn’t fallen.

  It had hovered for just an instant, long enough for me to snatch it upright and pretend nothing had happened. Long enough for me to question if my eyes had deceived me.

  Only Ru Lan had noticed. She hadn’t said anything, but I had felt the weight of her gaze. Thoughtful. Observant.

  Watching.

  I had ignored it at the time. Ignored the creeping unease, ignored the way my fingers had tingled in the aftermath, ignored the fact that my pulse had been steady — too steady.

  But I wasn’t stupid.

  The pieces didn’t fit.

  I wasn’t meditating. I wasn’t absorbing qi. My dantian wasn’t just damaged — it was gone. Completely and utterly. It did not exist. I had no vessel to hold qi, no means of channeling it.

  There was a pattern here. I just wasn’t sure what it was yet.

  If I had to describe it mathematically, it was like trying to find a limit that refused to settle. The closer I looked, the more it slipped through my grasp — each instance insignificant on its own, yet, in sum, forming something undeniable. I hadn’t been meditating, hadn’t been cultivating, hadn’t even thought about my dantian in weeks beyond the occasional pang of regret. And yet, my body was adjusting to something.

  There was a kind of smoothness to my actions, a continuity where there should have been rough edges. I should have stumbled, should have miscalculated, should have had at least one embarrassing moment of dropping something or knocking over a stack of books. But I hadn’t.

  Not once.

  Luck had statistical distributions, and coincidence had limits. This was neither.

  The realization sat heavy in my mind as I dismissed the students for the day, their voices spilling out into the courtyard in waves of unbridled relief. The moment they were gone, I sat down at my desk and took a deep breath.

  One: Cultivation required meditation, required intent. It required gathering qi and refining it within the dantian.

  Two: My dantian was shattered. Not cracked, not damaged, but disintegrated. My plan had been to repair it only when my understanding of mathematics grew to the point that I could truly benefit from immortal insight.

  Three: I had not engaged in any cultivation practices whatsoever.

  Four: And yet, something was happening.

  I tapped my fingers against the wooden surface. What changed? I had only been teaching. Only reading, writing, solving problems, thinking. Thinking a lot.

  Mathematics had always been a mental exercise, but never a physical one. There was no reason solving an equation should make me more aware of my surroundings, no reason it should sharpen my reflexes. I did still hold on to my belief that mathematical insight could manifest in cultivation techniques, but such arts required qi.

  And I had no dantian to hold qi with. A proof by contradiction.

  Except… contradiction implied impossibility. And yet, here I was.

  I stared at the wooden surface of my desk, fingers drumming lightly against it as the thought settled deeper. Contradictions in mathematics weren’t always dead ends. Sometimes, they pointed toward the need for a new framework, a reexamination of axioms. The discovery of irrational numbers, the rejection of Euclidean parallels, the realisation that infinity wasn’t a single concept but a whole uncountable hierarchy — each had been born from contradictions, from things that should not have been possible but somehow were.

  So what did that make me?

  I pushed my chair back, rising to my feet. The schoolhouse was empty now, the echo of children’s laughter fading into the distance. Outside, the town moved with the steady rhythm of daily life—merchants calling out their wares, oxen pulling carts over dirt roads, the scent of evening meals beginning to rise from the houses.

  I walked to the doorway and let my gaze drift, focusing not on anything in particular but simply… observing.

  The world felt sharp.

  Not in an overwhelming, heightened sense kind of way, not like the stories where cultivators suddenly found themselves able to hear the flapping of a butterfly’s wings. No, this was different. It was as if my mind had become more efficient, as if I were noticing details just a fraction of a second earlier than I should have. The way a breeze stirred the fabric of a vendor’s stall before ruffling the hair of a passing child. The way the weight of a bird on a tree branch slightly altered the shadow it cast. It was a kind of awareness — not mystical, not divine. Just… precise.

  Was that all it was? A kind of subconscious pattern recognition? The culmination of days spent thinking, analysing, breaking problems down into their smallest components?

  A memory surfaced, unbidden — Jiang Lingwu, the original one, in the days before his downfall. Training. Meditating. Seeking enlightenment through swordplay, through qi refinement. He had always struggled, always lagged behind those with better talent, stronger constitutions, superior bloodlines. But when he had finally found his fortuitous encounter, when his dantian had surged to life with power…

  This felt nothing like that.

  That had been heat and motion, the flood of energy pouring into his core, surging through his meridians like a rushing tide as he broke through to the next realm. That had been visceral, unmistakable.

  This was quiet.

  Not an expansion, but an absence.

  I let out a slow breath.

  It didn’t matter. Not yet.

  If there was an explanation, I would find it. In time.

  For now, the more immediate concerns were my students, my job, the careful balance I had to maintain in this town. I had no enemies here, no sects breathing down my neck, no young masters seeking revenge for past humiliations.

  I was not about to disturb that peace by chasing something I didn’t yet understand.

  No. For now, I would do what I always did.

  I would observe.

  I would wait.

  And when the answer revealed itself, when the pieces finally aligned into something comprehensible…

  Then I would act.

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