The world held its breath.

  Liu Xun’s sword gleamed in the afternoon sun, an arc of polished steel that might as well have been a guillotine. His posture was relaxed — too relaxed. He still didn’t see me as a threat.

  I tightened my grip on the fallen sword. It still felt wrong in my hands, an ill-defined variable, but a variable was still something I could work with.

  Liu Xun exhaled through his nose, stepping forward in measured, confident strides. “I was going to let you walk away,” he said, his voice carrying the exaggerated patience of a man who had never had to wait for anything in his life. “But you had to interfere.”

  He lifted his blade, tilting it just slightly, as if appraising me under a new lens. “Jian Hong was careless. I won’t be.”

  I wasn’t sure what was worse — the arrogance or the fact that, objectively speaking, he was probably right.

  Still, an equation wasn’t solved by praying and hoping the variables randomly canceled out. It required method. Structure.

  Transformation.

  I took a slow breath and centered myself. The battlefield was a complex plane. Every movement an operation, every step a rotation about some unseen origin.

  Liu Xun moved.

  It was fast. Not the overwhelming, world-splitting speed of some grandmaster tearing the heavens asunder, but fast enough that he blurred at the edges. A linear trajectory, a vector cutting through space with no deviation. The shortest path between two points.

  An efficient function.

  I rotated, summoning the rudimentary style of swordsmanship I had been developing over the last month in my downtime.

  The Roots of Unity.

  eiπ/3, a sixty-degree shift — a primitive sixth root of unity. Not a mere sidestep, but a transformation of my position entirely, shifting my entire reference frame. His blade passed through the empty space I had just vacated.

  Liu Xun’s brows furrowed. He adjusted instantly, bringing his sword back in a tight arc, pivoting to face me once more.

  But I was already moving.

  eiπ/4 , a quarter-turn rotation. Another axis, another transformation. From his perspective, I was simply vanishing from where he expected me to be, my movement not following any predictable Euclidean path.

  He slashed again.

  eiπ/6. Smaller now, a fine-tuned shift. The blade grazed past my shoulder, missing by fractions of an inch. Another change in basis, another reformulation of the problem.

  I wasn’t dodging.

  I was iterating.

  Liu Xun’s expression shifted from idle amusement to mild annoyance. “You’re fast,” he admitted, though the words were more of a begrudging observation than praise. “But movement alone won’t win you this fight.”

  That was the problem with people who saw the world as a fixed system. To them, movement was just displacement, a function that changed position but not substance.

  But I wasn’t just shifting.

  I was composing functions.

  Liu Xun lunged, his blade moving in a broad, cleaving stroke.

  I composed two transformations — eiπ/3 followed by eiπ/4 — rotating through arguments, stacking one transformation atop another. A new function, the product of rotations, shifting my reference frame yet again.

  His blade whistled through another empty point in space.

  Liu Xun’s irritation deepened. He withdrew half a step, studying me. The arrogance hadn’t faded — he still saw me as a lesser function, an unoptimised algorithm — but now, I had become an edge case. A problem that needed solving.

  I adjusted my grip. My breathing was steady, my stance balanced.

  The battle wasn’t about sword against sword.

  It was transformations against transformations.

  A duel of x versus y.

  Liu Xun exhaled, shifting his weight, recalibrating. “Alright,” he muttered, rolling his shoulders. “Let’s see how long you can keep that up.”

  The world did not still. It rotated.

  Somewhere, in some distant place, the stars wheeled along their celestial orbits, unbothered by the trivialities of men and their swords. But here, in this moment, the world pivoted on a different kind of axis — one traced by footwork and steel, by rotations and reflections.

  I could feel it now, the lattice of possibility stretching out around me. A sea of transformations, an infinite domain of mappings waiting to be applied. Many of them were beyond me, unreachable, just as an undefined function collapses when evaluated at the wrong input. But the simpler truths — the ones I had spent a month internalising —those lay within my grasp.

  Liu Xun, of course, felt none of this.

  From his perspective, I was an irritating insect that refused to die on schedule. His stance was still loose, his blade held with casual confidence. The way his lip curled was telling — he believed himself engaged in the most tedious form of combat: the one where the opponent thought they stood a chance.

  I adjusted my grip. This sword still didn’t feel like an extension of myself, but a clumsy approximation. No matter. I wasn’t wielding a sword.

  I was wielding a function.

  Liu Xun moved.

  A fast, efficient strike, a perfect minimisation of distance and effort. No unnecessary flourishes, no wasted arcs. A simple, linear approach.

  Predictable.

  I applied a sixth root of unity — sixty degrees counterclockwise. Not a dodge, not a step, but a full transformation of my spatial reference. His blade passed harmlessly through where I had been, intersecting empty space.

  Liu Xun didn’t falter. His wrist turned, adjusting the angle in an immediate counterstrike.

  I rotated again — forty-five degrees this time, a composition of eighth roots.

  His blade found nothing.

  His eyes narrowed.

  Interesting. Had I finally entered the phase where I was no longer a nuisance but an actual equation that needed solving?

  “Not bad,” Liu Xun admitted, straightening slightly. His smirk returned, sharp and condescending. “But movement alone —”

  “— won’t win me this fight,” I finished for him. “Yes, yes. I understand that.”

  His grip tightened.

  Excellent.

  He lunged again, this time cutting horizontally. I stepped not backward, not sideways, but perpendicular to the entire engagement — an orthogonal step, a shift into a dimension of motion he had not accounted for.

  I lifted off the ground.

  Not jumping. This wasn’t a mere vertical displacement.

  Gauss had once argued that i, the so-called imaginary unit, should have been named the lateral unit instead. A misunderstanding of its nature had led to its unfortunate branding as something unreal when, in truth, it was a fundamental expansion of movement, of perspective.

  I applied it.

  A leap, not just up but laterally — an operation into a space where Liu Xun’s strike could not follow, where his swing had no meaningful projection. A transformation along an unseen axis, a perpendicular movement to reality as he understood it.

  Liu Xun’s blade passed below me.

  The world felt lighter, clearer. My position was no longer constrained to the Euclidean battlefield he had mapped in his mind. I could feel the rotations, the symmetries, the elegant simplicity of it all. The way transformations could be stacked, iterated upon, building one upon another in an endless recursive sequence.

  A cycle.

  The moment stretched. Liu Xun’s sword was rising, recalibrating.

  I completed my descent. A controlled vector.

  I landed behind him, my foot touching the ground at the exact moment his blade finished its arc.

  Liu Xun stiffened. The crowd murmured.

  The function had been executed successfully.

  I straightened, tilting my head at an angle. “You were saying?”

  Liu Xun inhaled sharply through his nose. “You’re starting to annoy me.”

  That was fine. I had spent a good fraction of the last month annoying myself with partial differential equations, so this was an improvement.

  I could feel it now. Not just possibility, but inevitability.

  I could win.

  Liu Xun lunged.

  This time, there was no pretense of restraint, no calculated measure of arrogance. His sword carved through the air in a wild arc, its trajectory aggressive and unchecked. This was no longer the footwork of a cultivator playing at refinement — this was frustration, an algorithm that had lost convergence, desperately iterating toward a solution it could no longer define.

  I stepped.

  Another sixty-degree rotation — one-sixth of a full revolution, another primitive root of unity. The world adjusted. Not a dodge, but a transformation. My position in the fight was no longer a continuous function of time but a discrete mapping, each step a point along a lattice of movement.

  His blade found empty space.

  Liu Xun did not stop. His grip shifted, pivoting mid-motion, forcing another slash along a perpendicular axis.

  Ah. He was trying to bracket me, reducing my degrees of freedom. Smart.

  I rotated again, stacking more transformations, an eighth-root of unity compounding over the sixth. A finer correction, a higher resolution shift in the complex plane. Again, he missed.

  A flicker of irritation crossed his face.

  “Stop running,” he snapped, twisting his stance to cut downward in a vicious arc.

  I didn’t run.

  I iterated.

  Another orthogonal step, one whose principles be still didn’t seem to understand. Upward and lateral, perpendicular not just to him but to the entire structure of the fight as he understood it. A transition into a space that he hadn’t mapped, hadn’t parameterised. I lifted from the plane of engagement, stepping into a higher-dimensional motion he had no answer for.

  Again, his blade passed beneath me.

  For a moment, neither of us moved. The silence stretched.

  Liu Xun’s breath was measured, but his shoulders were tense. His expression hadn’t changed, but his grip had tightened, fingers flexing slightly around the hilt of his sword.

  “I see,” he said, voice low. “Some kind of movement technique.”

  Ah, there it was. The reclassification.

  I was no longer just an irritant. No longer just a lucky commoner who had somehow avoided the first few strikes.

  Now, I was a phenomenon. A function that needed to be solved.

  Liu Xun exhaled and pivoted sharply, stepping forward as he slashed — not wildly this time, but deliberately, aiming to collapse my solution space.

  I sidestepped, but he had already accounted for it. The next strike came immediately, cutting off my expected angle of rotation.

  I adjusted. An eighth-root transformation, a fine shift along the lattice.

  He adjusted. A diagonal cut, fast, sharp, closing my escape.

  I was running out of variables.

  So I rewrote the equation.

  I stepped, but not in the way he expected. Not into an evasion, not into another Orthogonal Step.

  I stepped forward.

  Into the attack.

  For the first time, Liu Xun hesitated. His sword arced toward me, a function executing exactly as intended.

  I reached.

  Not for him. For the pattern. The rhythm of his strikes. The implicit structure underlying his form.

  This narrative has been unlawfully taken from Royal Road. If you see it on Amazon, please report it.

  The Knight's Tour.

  And I disrupted it.

  A shift — not an avoidance, but a counterterm, a calculated error introduced to his perfect solution. A perturbation that forced him to adjust, to recalculate.

  And in that moment —

  I struck.

  A clean, direct motion, my sword slamming into his midsection.

  A sharp crackle of qi burst between us — Liu Xun had reinforced his body at the last second, a defensive layer hastily applied.

  But hasty was not the same as perfect. The force of the impact sent him staggering back.

  Silence.

  Liu Xun’s gaze flickered down, his free hand brushing against the point of impact. He wasn’t injured. Not really. But the fact remained —

  I had touched him.

  And in the perfectly well-ordered worldview of xianxia young masters that had them as the supremum of the set, that was unacceptable.

  His eyes snapped back up to mine. Something in the air shifted.

  I inhaled slowly.

  Liu Xun’s expression was still composed, but the arrogance had changed. It was no longer presumed victory.

  It was certainty.

  “You,” he said quietly, “are going to regret that.”

  The parameters of the fight had changed.

  Liu Xun straightened, his breathing slow and measured. The golden glow in his eyes pulsed, faint at first, then growing brighter, suffusing his gaze with an unnatural radiance. It was not the overwhelming aura of a grandmaster, nor the suffocating presence of an elder unleashing his cultivation, but something else—a sharpening of perception, a refinement of prediction.

  I knew that glow.

  Oh no.

  This was it. The inevitable young master power-up.

  There was a predictable rhythm to these things. First, the arrogant opponent underestimates the protagonist. Then, the protagonist surprises them, scoring an unexpected hit. And just as hope begins to bloom, the opponent smirks, wipes the blood from their lip, and unveils their true power.

  It was practically a conservation law in xianxia physics: for every moment of protagonist triumph, there exists an equal and opposite moment of young master escalation.

  And, sure enough —

  “Hmph.” Liu Xun rolled his shoulders, the light in his eyes intensifying. “I suppose I should commend you. Not many can touch me in combat. You should consider it an honor.”

  I exhaled slowly. Ah, yes. The classic ‘I acknowledge your existence now’ phase. How generous of him.

  “But don’t think that means anything,” Liu Xun continued, voice brimming with the absolute certainty of a man who had never once considered the possibility of losing. “What you fail to realise is that you’ve already lost.”

  Oh good, the ‘you are already defeated’ phase. We were moving through the checklist at an efficient pace.

  “My Yin-Yang Divine Perception has now fully activated,” Liu Xun declared, and with those words, the very air around us seemed to shift. “A lesser opponent may evade a few strikes through tricks and deception, but I see through all things. Your feints, your rotations, your little footwork tricks — they are nothing before my sight.”

  He lifted his sword, pointing it at me.

  “Move,” he said. “Try whatever technique you like. It won’t matter.”

  I hesitated.

  And then I moved.

  A sixteenth-root transformation, the finest resolution shift I could manage. My foot touched the ground at an adjusted argument, my stance shifting seamlessly.

  Liu Xun’s blade was already there.

  I barely twisted in time, the sword’s edge whispering past my ribs. Too close. I pivoted, adjusting the function, shifting through a second transformation.

  He adjusted faster.

  I barely had time to block, the force of his strike rattling up my arm.

  Oh.

  Oh no.

  He really was reading me.

  The battle that had once felt like an elegant, flowing composition had suddenly become a brutal, desperate defense. My footwork, my transformations, my carefully structured mappings — Liu Xun intercepted them all. Where before he had swung into empty space, now his blade met me. Not always perfectly, not yet, but with enough accuracy that I was forced onto the defensive.

  It wasn’t luck. It wasn’t coincidence.

  It was something far worse.

  He was computing me.

  Liu Xun pressed forward, his sword carving through the air in precise, measured arcs. His form was sharp, but it was his perception that was suffocating. He was striking into my future, his blade arriving at the solution before I had even computed it myself.

  I dodged, barely.

  Then again.

  Again.

  Each escape was thinner, closer. Each step a desperate correction, a perturbation to his model that only barely delayed the inevitable.

  He was iterating faster than I could escape.

  Liu Xun’s smirk widened as he advanced. “So much for your clever footwork,” he sneered. “What good is movement if I always know where you will be?”

  I gritted my teeth. This was bad.

  This was very bad.

  For the first time since I had started training, my system of movement failed. Not because I had miscalculated, not because my understanding was flawed, but because Liu Xun had solved for me. I was no longer an unknown function. I was a fully defined variable, a closed-form solution sitting neatly in his perception.

  I needed to escape.

  I needed a new function.

  A diagonal slash came at me, faster than I could counter. I threw myself back, barely avoiding the edge. My chest heaved as I tried to recalibrate, to find some new symmetry that he hadn’t yet accounted for.

  Nothing.

  Everything I could apply, he could predict.

  I was trapped.

  Liu Xun paused, as if sensing my growing frustration. He exhaled softly, the golden glow in his eyes steady and unwavering.

  “I told you,” he murmured. “I see through all things.”

  The arrogance was unbearable.

  And yet, this time, I couldn’t deny it.

  I adjusted my grip, my stance, my breath. The sea of transformations around me, the endless lattice of possibility — it was still there.

  But he was standing inside it.

  He wasn’t just reacting. He was anticipating. Every movement, every shift, every mapping I attempted — Liu Xun’s blade was already there.

  He had computed my function before I had.

  And that meant —

  I was already in his domain of definition.

  A shiver crawled down my spine. This wasn’t just prediction. This wasn’t just fast reaction time. He had formed an approximation of me. A predictive model. A function that mapped my inputs to my outputs before I even had time to decide them myself.

  Liu Xun’s blade carved through the space between us in perfect arcs, no longer the careless swings of a young master toying with an insect, but the efficient, calculated strokes of someone who had accounted for all variables.

  I barely twisted out of the way, my function perturbing just enough to escape, but it was getting harder. He was refining his approximation with every iteration.

  The crowd gasped.

  “He’s toying with him now.”

  “That teacher had tricks, but the moment Young Master Liu got serious, it was over.”

  “No! Master Jiang, don’t give up!”

  Another voice, breathless with reverence: “They say it’s like seeing into the future.”

  I gritted my teeth as I staggered back, deflecting another blow at an awkward angle. Future, huh?

  Liu Xun tilted his head, golden light flickering before his eyes. “This is the difference between a talentless cripple like you and a true genius. From the moment you so much as twitch, I already know where you’ll move.” He took a single, deliberate step forward. “Every footstep. Every swing. Every evasion. I see through all of it.”

  The murmurs swelled.

  “Impossible…”

  “He’s not even reacting? He’s attacking where the teacher will be before he moves?”

  “This is the power of the Liu Clan’s techniques?”

  Liu Xun’s lips curled into a smirk as he raised his sword again. “You should feel honored. The Yin-Yang Divine Perception is among my clan’s greatest techniques, one that only the most talented can awaken.” He exhaled slowly. “You think your crude tricks — your amateurish movement techniques — can escape my sight?”

  I barely had time to move before he struck again.

  I dodged — or tried to.

  My step was too slow. Or rather — his cut had already arrived.

  Steel met flesh.

  A thin line of pain traced across my arm. The wound wasn’t deep, but the meaning was clear.

  He wasn’t missing anymore.

  My breath came hard and fast. Sweat clung to my back. Ru Lan, standing at the edge of the battlefield, had both hands clenched into fists, her lips pressed together as though she wanted to speak but couldn’t.

  Liu Xun laughed softly.

  “Struggling?”

  My grip on the sword tightened.

  I was running out of space. Running out of angles. Running out of mappings I could take that he wouldn’t already have a solution for.

  Liu Xun stepped forward again. His golden eyes gleamed. “What’s wrong? Where’s that confidence from before?”

  I panted, wiping the sweat from my brow. Damn it. Damn it. Damn it.

  I had known it. I had known this would happen.

  This was the law of young master escalation. They always had a trump card. A bloodline power. A hidden domain. An invincible technique that suddenly activated when the protagonist got too confident.

  I had nothing.

  I wasn’t a secret young master of a fallen clan. I didn’t have a divine-grade martial soul lurking in my dantian. I had no lost inheritance, no golden finger, no hidden master to swoop in and save me.

  All I had was my little understanding of math.

  And math wasn’t working.

  Liu Xun’s blade flicked up. “If you’re out of tricks, I’ll end this now.”

  I raised my sword again, breath still heavy. My legs burned. My mind spun through possibilities, through solutions, through anything that could turn this around.

  He was predicting me. Seeing into my future.

  I needed something he hadn’t accounted for.

  I needed —

  “Enough playing,” Liu Xun muttered. “It’s time you learned the gap between heaven and earth.”

  His golden eyes pulsed.

  The moment I moved, he would already know.

  He would see my first step — no, even before it was taken — he would expand the function, extrapolate my movement, and converge onto the correct answer before I had even finished computing it myself.

  My stomach twisted.

  Liu Xun exhaled, his golden irises burning with light.

  “I can see everything. I predict all your moves. I alone see the flow of the river of fate. Before your sword even moves, I already know where it will be.”

  I froze.

  A single thought slammed through my mind like a hammer.

  Wait.

  Wait.

  Seeing everything? Predicting my movements? The moment I move, he already knows? The flow of the river of fate?

  My mind latched onto the words. Stared at them. Examined them from every possible axis.

  Prediction.

  Approximation.

  Convergence.

  Expanding —

  My breath caught.

  Wait.

  No.

  No.

  It couldn’t be.

  …surely not?

  Liu Xun’s golden gaze narrowed. “Your stance is faltering. Have you realised it? Have you accepted it yet?”

  My heart pounded in my chest.

  Was it…?

  I squinted, peering at the truths visible only to me.

  It was.

  It absolutely, unequivocally was.

  This wasn’t some mystical divine technique.

  This wasn’t fate-defying combat precognition.

  This —

  …wasn’t this just the Taylor Series?

  -x-x-x-

  I stared at Liu Xun.

  I stared at his glowing, golden eyes, his smug, self-assured smirk, his whole holier-than-thou posture as he declared his absolute victory.

  Then I focused again, reaching outward, seeing not with my eyes but my mind.

  I stared at that grand world of mathematical truths that Hermite spoke of. I pored over the shimmering field of possibility that surrounded him — the pulsing operators, the ghostly specters of approximations and differentials trailing behind his every motion, his entire form suffused with the recursive glow of infinite series expansion.

  This — this was it?

  This was the grand, divine, bloodline-exclusive technique of one of the young masters of Longtiao City? This was the sacred art that was going to crush me beneath the weight of inevitable fate?

  This was just the Taylor Series?

  I almost dropped my sword.

  I mean, sure, the Taylor Series was important. Revolutionary, even. A cornerstone of modern analysis, an infinite sum that let you approximate smooth functions locally with nothing but derivatives evaluated at a single point. You probably couldn’t do any analysis without it. Hell, to even be analytic was literally defined on the Taylor Series.

  But this was their supreme technique? The one passed down through generations, accessible only to the most talented?

  I hadn’t even studied math formally and I knew this!

  I felt a laugh bubble up in my chest. I tried to suppress it. I really did. But the absurdity was too much.

  A month ago, I had been staring at a world of incomprehensible cultivation techniques, qi-based movement arts, footwork that defied classical physics. I had spent weeks developing a mathematical framework just to understand the smallest sliver of possibility. My table had a dent in the shape of my forehead from my frustration at trying to recreate complex analysis, just so I could figure out what Riemann had done to provide the foundation for his famed hypothesis.

  And now?

  Now it turned out they had been using basic calculus all along.

  I burst out laughing.

  Liu Xun froze mid-step.

  The peanut gallery whispered in hushed tones.

  “Master Jiang is laughing?”

  “Has he lost his mind?”

  “This is too cruel…”

  “Perhaps he’s simply broken under the pressure. Young Master Liu’s divine perception is beyond mortal comprehension!”

  Beyond mortal comprehension, my ass! Any random high schooler could do this!

  Liu Xun scowled. “What are you laughing at?”

  I shook my head, still chuckling. Oh, this was perfect.

  How could I have been so blind? I had been standing in the midst of a sea of mathematical truth, clawing for understanding, while these young masters had been unknowingly wielding basic mathematical concepts as divine arts.

  It was almost cruel.

  Almost.

  Because now, I understood it, too.

  Liu Xun’s golden eyes flickered, his frown deepening. “You’ve finally gone insane. Accept it. No matter what trick you play, no matter how fast you try to move — I already know where you’ll be.”

  He stepped forward, slow and deliberate, each movement layered with that shimmering prediction, an expansion of my function before I could even compute it myself.

  I wiped the corner of my eye, still grinning. “Oh, I see it now.”

  Liu Xun tensed.

  “I was struggling so much,” I murmured. “Trying to find a way past your perception. Trying to disrupt your function. But I was thinking about it all wrong.”

  I exhaled, centering myself, and let go.

  The world shifted.

  I had been so focused on transformations, on rotations and mappings, on evading within a fixed system. But that was the wrong perspective.

  Because if Liu Xun was expanding me into a series —

  Then I could expand, too.

  I reached into the sea of possibility, into the shimmering field of mathematical truth that had always been there, and I aligned myself with it.

  The first derivative — velocity.

  The second — acceleration.

  The third — jerk.

  The fourth — snap.

  The approximations unfolded before me in infinite layers, each term cascading into the next, recursive, iterative, inevitable.

  Liu Xun flinched.

  For the first time, he hesitated. The golden glow in his eyes trembled.

  I wasn’t just an input into his function anymore. I was the function.

  The world exploded into possibility.

  A gasp rippled through the crowd. The murmurs turned to shouts.

  “He — his eyes! They're glowing!”

  “It’s the same golden light!”

  “Impossible! Master Jiang is using the Yin-Yang Divine Perception as well?!”

  “He is a hidden master! I win the bet!”

  Liu Xun flinched. His stance shifted, not in preparation for an attack, but in uncertainty. Then his smirk returned, but it was thinner now, stretched too tight.

  “A trick,” he spat. “A pale imitation. You don’t even know what you’re wielding.”

  I tilted my head, watching him. No, I wouldn’t explain. I wouldn’t waste my breath giving him a lecture on Taylor expansions and how his so-called perception was just a glorified polynomial fit. How the weaknesses of it were so glaring, it was almost laughable.

  That would be too cruel.

  No, I had other ways to demonstrate.

  “Tell me,” I said, voice quiet, steady. “How confident are you in your calculations?”

  Liu Xun scoffed. “The Yin-Yang Divine Perception is absolute. Your every movement is already known to me.”

  I smiled.

  “Good. Then —” I lifted my sword. “Prepare for a lesson.”