I.

The number on the screen was 47.

Rango had been expecting bad. He had not been expecting 47. There is a specific sort of academic grief that arrives not with a dramatic crash but a slow, pressurized deflation, like a tire going flat on the 401. And sitting in the MIE common room at 11:43 PM on a Wednesday, Gradescope notification still glowing, he was experiencing it in full. The fluorescent lights above him had been flickering for the better part of an hour. Nobody had done anything about them. This felt appropriate.

He opened the breakdown. The last questions had been the real damage; four questions on improper integrals, and he’d managed to talk himself out of the right answer on all of them. Question seven was the one that really stung: the integral of one over x-squared from one to infinity, convergent or divergent. He had written divergent. He had then second-guessed himself for four minutes, crossed it out, written convergent, stared at his own handwriting like it had personally betrayed him, and moved on. It diverged. He had known it diverged. He had just stopped trusting himself somewhere between setting up the limit and evaluating it, and the result was a small red zero in a box on the screen in front of him.

His phone buzzed. Bennett: how’d you do

Rango turned the phone face-down.

Outside, the February version of St. George campus did its best impression of a place people chose to be. The trees along King’s College Road were stripped bare. A couple of first-years in matching F!rosh shirts were speed-walking toward the Medical Sciences building, and Rango watched them with the weary benevolence of someone who had recently been that optimistic and could no longer remember how.

He thought about office hours. He turned the thought over once and put it back down like a stone. More importantly, he thought about Shane.

Not productively. The thought arrived the way it had been arriving since October; uninvited, inconveniently specific, and dragging the whole SUDS night behind it like a coat caught in a door. The amber light. The Bnad chant. Outside of class, anyway. He had spent an entire semester trying to inter that memory and it kept resurfacing. The worst part was that the memory had company now: layered on top of it, sealed over it like a bad patch job, was the other thing. The fanfic, or, the reason he had spent all of MAT188 sitting in the third row and staring at the board while avoiding eye contact by all means possible.

He was going to have to go to office hours.

He closed the laptop and sat for a moment in the flickering light.

II.

That cursed document had achieved, what one may call, legendary status. Yet Rango did not find this comforting.

It had started circulating near finals season, if he had to guess. Rango had been in the fourth-floor Myhal study lounge, half-conscious over a problem set, when his summer Calculus I TA materialized beside him seeming like someone who has just witnessed a car crash and wants to warn you but is also, if he is being honest with himself, a little bit excited.

“So,” he had said. “I need you to not panic.”

“I’m not panicking.”

“You will be. Okay. Someone found that creative writing thing.”

The creative writing thing, or more specifically, Rango’s fanfiction. It was a piece Rango had written in the second week of October for fun—a few hours that he had not taken remotely seriously, and which he had therefore populated with real names and a real bar and feelings that were, in retrospect, extremely recognizable as his own. He then sent it to his friends, and the student satire newspaper: the Toike Oike, as nothing more than a joke. He’d forgotten about it because he was eighteen and had another midterm due Thursday and genuinely could not conceive of a world in which it would breach containment. He did not think that his friends would forward it to all of their friends. He still did not fully understand the chain of custody. He had stopped trying.

What Rango knew was: by the time he’d found out, approximately half of Skule^TM had read it. The writing was not even that bad, which almost made it worse. If it had been bad, it could have been dismissed as a joke. Instead it was earnest and specific, and it described Shane Scohen, by name, in recognizable detail. It described him as someone whose hands Rango had spent more time thinking about than was appropriate, and whose voice sounded different outside of a lecture hall, and who had stood in a bar in October and said I noticed in a way that Rango had apparently decided to just put directly into a short story and handed off to the public.

The memes had been bad. The printouts appearing in the ECE common room had been worse. Someone had made a commemorative sticker design. That had been… a lot. Shane had not, as far as Rango knew, acknowledged it in class. He had continued teaching MAT188 like always. His eyes moved through the lecture hall with the same pattern as always, except for the third row, where they moved a little faster. Internally, Rango was reasonably certain, it was never going to end.

Then winter semester arrived with the miserable Toronto slush and storms. Then MAT187: Calculus II, taught by Professor Shane Scohen, Mondays, Wednesdays, and Fridays, 5 to 6. Rango had stared at the course enrollment screen for a full minute before accepting that this was just his life now. 

Then came the midterm.

III.

He arrived at two-seventeen, which meant seventeen minutes of standing in the Galbraith hallway examining the door of office 143 before he knocked. A student came out of the room. Rango waited until she’d turned the corner, then knocked.

“Come in.”

He had, without intending to, formed a mental image of what Shane’s office would look like. He hadn’t expected it to be accurate. Books everywhere, in columns that obeyed a logic he couldn’t decode, on the desk, along the windowsill, two piles on the floor that had stopped pretending they were temporary. A whiteboard along one wall half-covered in what looked like the aftermath of a proof that had gone several rounds. Shane was at the desk, reading, with his wireframe glasses on. 

“Rango.” Professionally warm, and almost worse than cold.

“Professor Scohen.” Too stiff, but he pushed through it. “I got a 47 on the midterm.”

Shane set down what he was reading. He took his glasses off and set them on the desk.

“Sit down.”

The chair across the desk was the standard office-hours chair, engineered for function over comfort. Rango sat and put his bag in his lap.

“Walk me through the exam,” Shane said. “Not the grade — that I can see. What went wrong when you were actually in the room?”

“The convergence questions.” Rango opened his laptop. The exam PDF was bookmarked — he had been opening and closing it for four days, the way you touch a bruise. “I kept second-guessing the limit behaviour. I’d set up the integral right and then somewhere between the setup and the conclusion I’d flip my answer.”

“Show me one.”

He turned the screen around. Question seven. Shane leaned forward to read it, and Rango became very focused on a point to the left of his shoulder.

“Okay. What did you write?”

“Convergent. I had it divergent first and talked myself out of it.”

Shane picked up a marker and turned to the whiteboard without preamble.

“What’s u equal to, if you substitute?”

“ln x.”

“So you get one over u du. Which evaluates to—”

“ln of ln x. And the limit—” He could already see it. “The limit of ln(ln x) as x goes to infinity is infinity.”

“Not a finite number. The integral diverges.” Two lines on the board, clean. “The intuition: logarithms grow slower than any power of x, which means when your denominator is a logarithm, it isn’t shrinking fast enough. Heuristic, not a theorem, but on multiple choice it saves you.”

Rango wrote it down. His handwriting was slightly uneven, which he attributed to the chair.

“Comparison tests,” he said. “I kept picking wrong.”

“What’s your instinct when you can’t integrate something directly?”

“Find a simpler function that bounds it.”

“Right. Most people pick the comparison function first and verify the inequality second — backwards. Start from the dominant term, figure out what the function’s doing for large x, then find something comparable you can evaluate. The comparison falls out of that.” He paused. “Try question twelve.”

They worked through four problems. The February light moved across the whiteboard in slow increments. At some point Shane refilled his coffee from a French press on the windowsill; the source, Rango now understood, of the cedar smell he had attributed last October to some kind of cologne. It was just very good coffee. This did not make anything simpler.

IV.

He came back Tuesday. And he came back the Thursday after that.

By the third week it was a thing. It was not quite routine, not quite comfortable, but established. Rango arrived with a problem set; Shane worked through it; the whiteboard filled and was erased; they orbited the material like neutral territory, which it mostly was. They didn’t discuss October. They didn’t discuss the document, which was presumably still circulating in several Discord servers and which Rango tried not to think about while sitting four feet from its subject. They kept things clean and Rango kept telling himself this was fine, this was exactly what office hours were supposed to be.

“You’re better at this than you think,” Shane said one Thursday in early March, looking over a convergence proof. “The logic is right. You’re hedging when you don’t need to.”

“I second-guess the last step.”

“I know. You’ve been doing it since September.” He handed the notebook back. “Stop asking the answer for permission.”

Rango stared at him. “Is that a general note or a calculus note?”

“Currently calculus,” Shane said, and returned to what he was reading, and Rango wrote it in the margin of his notebook and did not examine it further.

Three weeks out from the second midterm, Shane arrived at office hours with the energy of someone who had come directly from a meeting that lasted ninety minutes longer than it needed to. He dropped into his chair, rubbed a hand over his face, and looked up to find Rango already across the desk with a notebook open.

“Committee,” he said, by way of explanation.

“I didn’t say anything.”

“You were thinking it.” He straightened, made the visible effort of reassembling himself. 

“Second midterm Thursday. Where are you?”

“ODEs. Separable and linear first-order are fine, second-order homogeneous I’m okay on. The particular solutions for nonhomogeneous—” Rango made a gesture.

“Undetermined coefficients?”

“Mostly. I keep forgetting to check if the forcing term is already a solution to the homogeneous equation.”

“The modification rule. If your guess is already in the homogeneous solution, multiply by t.” Shane picked up the marker. “Show me one where you got stuck.”

They worked for an hour. Rango asked about complex roots of the characteristic equation—the cases where you ended up with e to the power of something complex, where Euler’s formula had to come in —and Shane walked him through it in the way he had of making things that seemed abstract become, briefly, obvious.

“If your characteristic roots are α ± βi,” Shane said, writing it, “then your solution involves e to the αt, multiplied by a combination of cos βt and sin βt. The real part controls growth or decay. The imaginary part gives you the oscillation frequency.”

“So the complex roots don’t actually give you a complex solution.”

“They give you a real solution written in complex terms, which you then convert. The complex exponential expands into sinusoids via Euler’s formula. Nothing in the final answer is imaginary. People think complex roots mean complex output. They don’t.” He set the marker down. “The complex number is a tool you used to get there, not a thing that stays.”

Rango wrote it down. He had the feeling he would be writing it again on Thursday. He was zipping up his bag when Shane said, without looking up from his desk, 

“The piece. From the fall.”

Rango’s hands stilled on the zipper.

“I’m not bringing it up to make things strange,” Shane said. He looked up then, direct. “I read it. I thought you should know I thought it was good and… flattering.” A beat. “I realize that’s an odd thing to say about a piece of writing that, among other things, described my collar in some detail.”

Something in Rango’s chest did a thing. “I’m sorry,” he said — for approximately the fifth time, across all mediums. “I genuinely did not think—”

“I know you didn’t.” Plainly, no performance of generosity. “I’m not absolving you, I’m contextualizing. You were new, you wrote about, well, something, and the distribution was unfortunate.” A brief pause. “The commemorative sticker design was… I have some feelings about.”

“I had nothing to do with that.”

“I know.” The corner of his mouth moved. Not quite a smile, but close. “It was well-executed.” Rango laughed. Surprised out of him, really; it came out a little ragged. Shane’s expression did the thing it occasionally did in lectures, the thing that meant yes, this is the correct response.

“Go home,” Shane said, in the voice without the professional distance in it. “Get some sleep.”

V.

He got a 74.

He found out on a Sunday morning, face-down in bed, laptop open, already in the specific dissociated state of someone who has slept ten hours and still feels like they haven’t. The grade appeared in Gradescope. He read it three times, then got up and made coffee.

74. From 47 to 74, and the curve had not been that generous.

He went Thursday, with nothing prepared; no questions, no problem set. Shane was at the desk with his glasses on. He raised his eyebrows in the wordless question of what are we doing today.

“74,” Rango said.

Shane set down his pen. “Good,” he said, and he said it in the way that meant something. It was not a well done from a professor to a student, but flat and genuine, the voice from the bar. “That’s good.”

“Yeah.” Rango sat. He hadn’t planned to stay, technically; he had come to say the number and leave, drawn back to this room the way you return to a place that was present for something. “I wanted to tell you.”

“I’m glad you did.” Shane leaned back slightly. “How does it feel?”

“Weird. Good weird.” Rango looked at the whiteboard, the layered ghosts of old problems. “I kept hearing your voice on the exam. The modification rule. The Euler formula thing.”

“That’s how it’s supposed to work.”

“I didn’t know that. I thought I was just—” He stopped. “I thought you were just a good teacher. I didn’t know it was supposed to stay like that.”

Shane was quiet for a moment. Down the hall, the printer did its reluctant thing. The radiators clanked through a cycle.

“I taught for three years before anyone told me what I was actually doing in that room,” he said. “I thought I was explaining mathematics. It took a specific set of circumstances to understand I was trying to give people a way of thinking that lasted after the course was over.” He picked the pen back up and turned it in his fingers. “So yes. That is what it’s supposed to do.”

Rango thought about stop asking the answer for permission, sitting in the margin of a notebook he was keeping. He thought about the book: The Shape of Incomplete Arguments, which he’d signed out from Robarts on a Tuesday and started on the subway home, which was dense and funny in equal measure and which argued, in an essay on topology, that the most interesting thing about any boundary was the question of what it was between. He’d thought, reading it, that Shane was a writer who meant more than one thing at a time and expected you to notice.

“I read some of your book,” he said.

Something shifted in Shane’s face, small, genuine, quickly controlled. “Did you.”

“The topology essay. And the one about incompleteness theorems.”

“Those are usually the most read.” A pause. “What did you think?”

“I thought the topology essay was about more than topology.”

Shane held his gaze. The professional distance did what it always did. It stayed in place, maintained, like a proof holding under pressure. Then something in it shifted, not gone but acknowledged: the thing between them, legible now, sitting in the room without either of them having to perform ignorance of it.

“Most of it is,” Shane said, quietly. “That’s how essays usually work.”

The room settled around this. Something had been said that they had both been careful not to say, and it turned out the saying was… manageable. Not resolved. Not close. But present, in the open, where it could be looked at.

“I have a question,” Rango said. “Academic question.”

“Of course,” Shane said, in the tone of someone who understood perfectly well what was and wasn’t being flagged as academic.

“Final exam. Series convergence is coming back. If I’m looking at a function with a logarithm in the denominator—”

“Almost certainly divergent. You know that.”

“I know that now.”

Shane picked up the marker and turned to the whiteboard. “Fine. Let’s go through it properly, from the comparison test up.”

The radiator clanked. Rango opened his notebook. Outside, the February sky was attempting something tentative with the late afternoon light. Not spring, not quite, but the suggestion of it, with the light lasting a little longer than it had last week.

VI.

He left at four forty-seven.

The Galbraith building released him onto the front steps and he stood there for a moment, taking in the state of the campus: slush in the King’s College Road gutters, coffee smell from an open window somewhere above him, a cluster of EngSci students on the Sandford Fleming steps with the vacant stares of the recently examined. February was still doing its worst but the light was coming in at a slightly different angle than a week ago, the shadows stretching the wrong way for winter. Rango put his headphones in. He didn’t play anything.

He thought about the most interesting thing about any boundary is the question of what it is between. He thought about I’m not absolving you, I’m contextualizing, which was genuinely the most Shane Scohen sentence he had ever heard in the wild. He thought about four months of office hours and the specific act of returning to a room, week after week, past the point where the academic reason fully covered the actual reason.

His phone buzzed. Bennett : still alive?

Rango: Yeah.

He passed the Mechanical Engineering building, where two undergrads were having a heated laptop argument about concrete. He passed the Mining building, where a Godiva Week poster had survived taped inside a window since November, yellowed and resolute. The campus had its early-evening quality; fewer students, the building lights coming on, everything settling into itself.

The final exam was in six weeks. After the final exam, there would be no legitimate academic reason to be in that office.

He thought about this. He thought about Shane saying that is what it’s supposed to do, meaning something that didn’t stop at calculus. He thought about “currently calculus,” implying a future tense. He thought about the book and the essay on topology and what it meant that a person spent their working life thinking carefully about what boundaries were between. Six weeks. Then a different question entirely, one without a problem set attached, and without a whiteboard to turn to.

He crossed University Avenue, turned south, and walked home through the dark blue February evening.