By the third week of official tutoring, Aryan Carter had stopped checking the clock.
It was strange—once, time had dragged in Cowel's office like gravity doubled inside the walls. Now, the hours blurred without warning. He'd look up from an equation expecting five minutes to have passed and find it was nearly sunset.
He arrived that Thursday afternoon balancing two coffees and a grin. "For you, Professor. Liquid fuel for brilliance."
Cowel accepted the cup without glancing up from his papers. "I see you're trying to bribe your way to higher marks."
"Think of it as an academic sponsorship."
"Your sense of entrepreneurship is misplaced."
Aryan dropped into the chair opposite, flipping open his notebook. "Then let's call it gratitude."
That made Cowel pause. Just briefly. "Gratitude for what?"
"For not giving up on me."
The professor's pen stopped midline. He looked up, gaze unreadable. "Flattery, Mr Carter, is a poor study strategy."
"Good thing it's genuine, then."
Cowel exhaled through his nose—the closest thing Aryan ever got to a smile. "Let's begin."
The board filled quickly. Today's lesson was a labyrinth of geometric proofs that seemed to defy gravity, each line dependent on the last.
Cowel explained with measured precision, chalk tapping rhythmically as he worked. "Every proof," he said, "is a pattern in disguise. If you learn to see the structure beneath the symbols, it becomes… predictable."
"Predictable sounds boring," Aryan said.
"Predictable means comprehensible."
"Still boring."
"Only until you discover elegance."
Aryan tilted his head. "You make it sound like poetry."
"Mathematics is poetry," Cowel replied without hesitation. "But most people are tone-deaf."
Aryan smiled. "Guess I'm learning to carry a tune."
They worked in companionable silence for a while, exchanging few words. The hum of the ceiling fan, the faint smell of chalk, and the rustle of papers became their background music.
When Cowel paused to refill his mug, Aryan studied the half-finished proof on the board. Something about it itched at him.
"Wait," he said. "You're treating the function as symmetrical, but it isn't."
Cowel turned. "Explain."
Aryan stood, stepping closer to the board. "If you use substitution here—" he drew a quick line of algebra "—you can bypass the entire second derivative step. It folds back into itself like a mirror image."
"That's not the standard approach," Cowel said.
"Doesn't mean it's wrong."
"Prove it."
Aryan grinned. "Gladly."
He worked fast, numbers spinning into place with confident rhythm. Cowel watched in silence, arms folded, expression neutral. When Aryan finished, he stepped back.
"There. Simpler, faster, same result."
Cowel studied the board. The silence stretched.
Finally, he said, "You've ignored an assumption."
"No, I adjusted it. Look closer." Aryan pointed. "The constraint cancels naturally once the variable's range is shifted. You were treating it as static."
Cowel's brow furrowed. He checked the logic, line by line. It held.
After a moment, he said, "Acceptable."
"Just acceptable?"
"Efficient. Borderline reckless. But correct."
Aryan leaned against the desk, triumphant. "So… you're saying I beat the book?"
"I'm saying you learned to think outside it."
"I'll take that as a win."
Cowel almost smiled again. "Small victories, Mr Carter."
As the session continued, the air in the room changed. It wasn't teacher and student anymore—it was something closer to dialogue. When Cowel made a point, Aryan challenged it; when Aryan stumbled, Cowel asked questions instead of correcting him outright.
By the time the clock struck six, the board was a battlefield of ideas—scribbles, arrows, annotations, half-erased formulas.
Cowel stepped back, rubbing a streak of chalk from his sleeve. "You realize you've just rewritten three accepted solutions?"
"Guess I'm accidentally innovative."
"Accident rarely involves this much precision."
Aryan smirked. "You complimenting me again, Professor?"
"I'm acknowledging statistical anomaly."
"Sure you are."
Later, as they packed up, the conversation shifted from formulas to philosophy.
"Why do you push so hard?" Aryan asked suddenly. "Most professors would've stopped at good enough."
"Because 'good enough' is mediocrity with better lighting," Cowel said.
Aryan chuckled. "You have a quote for everything."
"I've been teaching longer than you've been procrastinating."
"Impressive. That's saying something."
Cowel gave him a sideways look. "Why do you persist in downplaying your intelligence?"
Aryan hesitated. "Habit, I guess. Easier to joke than fail."
"Yet failure is what you've learned from most."
"Touché."
"Perhaps try learning from success for a change."
Aryan nodded, quiet for a moment. "Working on it."
Outside, the sky had darkened to deep indigo. They left the building together, the courtyard almost empty.
"Professor," Aryan said as they reached the steps, "do you ever get tired of it? Teaching, I mean."
Cowel considered the question. "Not of the subject. Occasionally of the noise."
"Students like me, you mean."
"Precisely."
Aryan laughed. "Fair. But… you don't really hate it, do you? The noise."
Cowel's expression softened—barely perceptible. "No. It reminds me there's still something to teach."
Aryan grinned. "Guess I'm doing my part, then."
"I'll send you the invoice for therapy," Cowel replied dryly.
They parted ways at the gate, Aryan heading toward the dorms, Cowel turning down the faculty path.
That night, Aryan couldn't sleep. His mind kept looping through the proof they'd built together—the way it had unfolded, the rhythm of their discussion, the brief moment when Cowel had gone silent, impressed.
He pulled out his notebook and copied the final equation neatly, labeling it Proof No. 17 – Carter Method (Unofficial).
Underneath, he wrote:
"Mathematics is poetry. But I think I'm finally hearing the rhythm."
He smiled to himself, closed the notebook, and lay back. For once, he didn't feel like the failing student trying to keep up. He felt like he belonged in the conversation.
---
Meanwhile, in his office, Cowel sat reading through Aryan's notes again. He rarely kept student work past the week, but this one he set aside in a separate folder.
The handwriting was still a little chaotic, the lines uneven—but the logic was flawless.
He remembered the way Aryan had stood at the board, explaining his shortcut with that irreverent spark of confidence. Most students who challenged him did so out of arrogance; Aryan did it out of curiosity. It was, Cowel admitted privately, far harder to teach someone like that—and far more rewarding.
He leaned back, murmuring to himself, "Proofs and patterns…"
For years, he'd told students that equations were static truths. Yet here was one boy rewriting them as if they were music—changing tempo, skipping notes, still landing on the same truth.
He smiled faintly, shaking his head. "Reckless, yes. But remarkable."
The following morning, Aryan walked into class humming under his breath. Mina caught him near the back row. "You seem annoyingly happy."
"I'm an artist now," he said. "Poet of numbers."
"Right. Should I start clapping?"
"Please do. Quietly. It's math poetry—needs ambience."
She rolled her eyes. "You're impossible."
"Statistically probable," he shot back, grinning.
Cowel entered then, cutting off the banter. The lecture began. Halfway through, he introduced a new concept—a tangled, complex identity proof that made half the room groan.
Aryan watched, fingers drumming, as Cowel explained the traditional approach. The professor's gaze flicked toward him once, deliberately.
"Mr Carter," Cowel said, "how would you approach this differently?"
The class turned. Aryan hesitated only a second before standing. "I'd fold the variable range here," he said, walking to the board. "It simplifies faster than substitution."
Cowel gestured for him to continue. Aryan did, chalk squeaking against the board.
When he finished, the result was clear—and clean.
Cowel studied it, then faced the class. "Note this," he said evenly. "A nonstandard approach, but effective."
A ripple of surprise moved through the students. Aryan returned to his seat, trying—and failing—to hide his grin.
After class, Jules cornered him. "Did you just correct Cowel? Publicly?"
"Collaborated," Aryan said. "Let's call it that."
Jules shook his head, laughing. "You're insane."
"Statistically probable," Aryan repeated.
But as he walked out of the hall, his grin softened into something quieter. Cowel hadn't just let him speak—he'd invited him to. Trusted him.
That trust meant more than any grade ever could.
Back in his office, Cowel wrote another line beneath Aryan's file:
Not imitation. Innovation.
He paused, then added:
Learning to think, not repeat.
He set the pen down, thoughtful. The proof on his board from the day before still lingered half-erased, the faint outline of Aryan's handwriting visible beside his own.
He decided to leave it there.