Chapter 8: The remainder theorem

The fluorescent lights of the competition hall hummed, a  buzz that felt like it was vibrating inside my skull. It was a sterile, unforgiving sound, the kind that usually helped me focus, stripping away the noise of the world until only logic remained. But today, the silence of the hall felt heavy, a space  that my thoughts were rushing to fill with images I couldn’t solve for.

I stared at the booklet in front of me, my hands covered in pencil lead that looked just like the dark circles under my tired eyes.

Solve for the unknown variable.

The problem was a complex trigonometric identity, a tangled web of sines and cosines that should have been my sanctuary. Usually, when I looked at a page like this, the numbers sorted themselves into neat, orderly rows. I could see the path to the solution before my pen even touched the paper. But today, the ink seemed to bleed and shift. All I could see was the way Noah had looked in the dim light of my bedroom, the way he had handed me that hoodie as if it were a piece of himself he was letting me keep. I could still hear the ghost of his voice, dropping an octave when he mentioned Madison’s "recalculation."

I forced my eyes back to the paper, my breathing shallow. I needed a constant. I needed something that didn't change when the wind blew. 

I stared at the equation: \sin^2(x) + \cos^2(x) = 1. 

A fundamental identity. No matter how high x climbed, the pieces always fit together to form a perfect, closed circle. A promise of stability. I wished my life had constants like that. I wished I could plug the last eight years into a clean formula and get a result that didn't leave a remainder of guilt. But in my world, the math never closed; the sum of us was never a whole number.

"Five minutes remaining," the proctor announced, his voice echoing off the high ceilings like a gavel.

Beside me, Dani  was a blur of efficiency. Her pen was flying, a rhythmic scritch-scratch against the booklet that signaled she was in her element, her "functional limits" pushed to the max. She lived for the pressure. I, on the other hand, felt like a complex system experiencing a total catastrophic failure. My logic gates were jammed. I managed to scribble the final steps of the proof, my handwriting shakier than it had been since the day the police arrived at the Callahans' door when I was ten.

When the bell finally rang, signaling the end of the session, the silence finally broke, It was replaced instantly by the collective exhale of fifty students and a hundred different conversations erupting at once.

"That third problem was an absolute nightmare," Dani said, stretching her arms over her head as we gathered our things. Her glasses had slipped down the bridge of her nose, and she looked exhilarated. "The logic flow on the integration part? Pure evil. But you? You were a machine, Isla. I saw you staring at that last page like you were trying to set it on fire with your mind. I actually checked for smoke."

"I just wanted it to be over, Dani," I admitted, clutching my bag to my chest as if it could keep my ribs from cracking open. My voice felt thin, like a worn-out pencil lead.

"Well, it's over. And judging by the look on the proctor's face when he collected your sheet, you probably just secured a seat at the state finals." She nudged me with her shoulder as we shuffled toward the exit. "Which means you can officially stop worrying about the 'unknown variables' for at least three hours. It’s Senior Week, Izzy. We’re supposed to be celebrating our impending freedom, not calculating the slope of a curve."

I wanted to believe her. I wanted to step out of that hall and feel the weight lift. But as we pushed through the heavy double doors leading back to the main hallway, the "world" we had tried to leave behind came rushing back with the force of a tidal wave.

The hallway was transformed. The quiet, academic air of the West Wing had been replaced by the loud, aggressive energy of North Hills "Titans Pit." Blue and silver streamers were draped like vines across the lockers, and the scent of floor wax was buried under the smell of cheap popcorn and athletic spirit. A massive, hand-painted banner hung from the ceiling:GO TITANS! And right beneath it, framed by the light of the trophy case, stood "The Unit."

Noah was leaning against a locker, his posture projected a casual ease that I knew was a lie. His arm was draped casually, almost performatively around Madison’s shoulders. She was a vision of suburban perfection in her tiny pleated skirt, her smile bright and sharp enough to cut glass. She was mid-conversation with a man in a gray tracksuit who held a clipboard like it was a holy relic..a scout from West State.

Noah’s eyes were scanning the hallway, skipping over the groups of students, the teachers, and the banners until they landed on me. For a split second, the "unit" mask slipped. His arm stayed on Madison, but his gaze was heavy, dark, and searching. He was looking for a signal. He wanted to know if I was still okay after the hot cocoa, the minefield of a conversation with his mother, and the heavy silence that had followed us to our separate rooms.

"Isla! Over here!" Madison called out, her voice cutting through the noise like a siren. She waved me over with a perfectly manicured hand, her eyes locked on me with a terrifying focus.

I felt Dani stiffen beside me. "Vector shift in three, two, one..." she whispered under her breath. "Brace for impact."

I walked over, my heart doing that familiar, painful stutter against my sternum. Every step felt like walking through deep water.

"Tell the scout how hard Noah’s been training," Madison gushed as soon as I was in range. She leaned into Noah, her fingers digging slightly into the fabric of his jersey, a silent command for him to stay still. "Isla lives with us, she’s practically his biggest fan, aren't you, sweetie? She sees the early mornings and the late nights. She’s the 'anchor' to our 'ship,' as Elena always says." She is his best friend “. 

The man in the tracksuit looked at me, his pen poised over his clipboard. He looked like a man who dealt in facts, not metaphors. Noah looked at me, too. His jaw was so tight I thought I heard his teeth grind. He looked like he wanted to bolt, but he was pinned in place by the weight of a hundred expectations.

"He doesn't need me to tell you how good he is," I said. I kept my voice low and steady, drawing on the same cold logic I used for calculus. "The numbers on the scoreboard usually speak for themselves. In this house, we focus on the data."

The scout nodded, looking impressed. "Spoken like a true mathlete. I heard you girls had your own big day today. Regional finals, right?"

"Isla is going to win it ," Noah said. It was the first thing he’d spoken, and the sound of his voice sent a shiver down my spine. It was thick, roughened by a lack of sleep. He ignored Madison’s pointed, warning look. "She’s the best in the district. She solves problems most people don't even know exist."

"Top three, Noah," I corrected, looking down at my shoes. The praise felt like a burn. "I just need the top three for the scholarship."

"You're the best," he repeated. He said it with a finality that made the rest of the hallway disappear. For a heartbeat, the scout and Madison and the blue and gold streamers faded into a gray blur. It was just the boy from the porch and the girl who was terrified of being a substitute. It was a moment of truth that we couldn't afford.

"Anyway!" Madison interrupted, her voice an octave higher as she stepped physically between us, reclaiming the scout's attention. "We have the victory bonfire tonight, and then the Showcase tomorrow. It's a huge forty-eight hours for the Callahans. For all of us."

She looked at me then, her smile widening into something predatory. There was no warmth in her eyes, only a cold, calculating intelligence. She had seen the way Noah looked at me. 

"You're coming to the bonfire, right, Isla? Elena is making her famous chili. It wouldn't be a celebration without our favorite person ." “ Isn't that right baby?”. 

That word Favorite person  landed like a slap. A reminder of my status. I looked at Noah. He was watching me, his eyes pleading for me to stay and warning me to run, all at the same time.

"I'll be there," I said. The words felt like a surrender.

As I walked away with Dani, the "Titans Pit" cheering echoing behind us, I realized that Madison’s plan was a masterstroke. She wasn't pushing me away; she was pulling me into the center of the frame. She was keeping me exactly where she could see me, weaving me into the "unit" until I was just another prop in their perfect life.

She knew that as long as I was "family," I was safe. And as long as I was safe, I was silent.

"You okay?" Dani asked as we reached the parking lot. "Your heart rate is probably hitting 110 beats per minute. I can see your pulse in your neck."

"I'm fine," I lied, looking toward Noah’s truck. The glass prism of my trophy was tucked in my bag, but it felt like I was carrying a shard of ice. "I just have to survive the next forty-eight hours. Then the variables change."

"Or they collapse," Dani muttered, unlocking her car.

I didn't answer. I just watched the streamers dance in the wind, wondering if there was any equation in the world that could account for the remainder of a broken heart. In math, you could always round up or down to make things fit. But as I looked back at the school, I knew that in our story, the remainder was going to be the only thing left.