Underneath, after a moment, he wrote the thing his father used to say at the kitchen table when a problem looked down at him like a wall.
Then we climb it properly.
Chapter 16: The Library Nights
The main library at Whitmore closed at midnight, but the mathematics reading room, by special arrangement with a dean's office that wanted this settled as much as Harrow did, stayed open for exactly two people until four.
Isaiah arrived each night at nine with his father's notebook, his own three notebooks, a thermos Theo had filled with something Theo called coffee and Isaiah called a legal gray area, and a plan written on an index card. Chen arrived at nine-fifteen with red pens β plural, a detail that terrified him the first night and comforted him by the third.
"My job is to be Harrow before Harrow gets the chance," she told him, uncapping the first pen. "Every line I cannot follow, I mark. Every assumption you smuggle, I mark. I am not your friend in this room, Isaiah. I am the fourteen days."
"Understood," he said, and meant it, because she was the first person in the building who had treated his work as strong enough to attack honestly.
They built the proof the way masons build a wall in winter: slowly, checking every course before laying the next. Stage one, already public, took a single night to formalize. Stage two, the flawed mirror, took three β because writing it live at a board and justifying it on paper were different disciplines, and the justification required a lemma about almost-reflections that did not exist anywhere in the literature and had to be constructed from nothing, like a key cut for a lock no one believed was real.
Stage three nearly broke them. On the sixth night, at two in the morning, Chen sat back from a page covered in her own red ink and said, quietly, "This step assumes the very thing you're proving. Here. Circular."
Isaiah stared at the circled line until the symbols lost meaning. He had been so certain. He could see the truth of the whole structure β that was the curse of his gift, seeing the cathedral entire while other people needed the scaffolding β but seeing was not proving, and Harrow, he understood now, had built his whole challenge on exactly that gap.
"I need to walk," he said.
He walked the dark stacks for twenty minutes, past sleeping shelves of journals, past the bronze name of a Hale above a doorway, thinking about his father. Samuel Carter had seen farther than any man in his department and had died with his margins unpublished, because seeing, alone, had never been enough to make the world look. Isaiah had loved his father without reserve. He did not intend to repeat him.
He came back to the table with the answer forming like a photograph developing. "We don't assume it," he said, pulling the page toward him. "We earn it two stages early. Move the mirror lemma here β before the junction, not after. Then the step isn't circular. It's downstream."
Chen read. Her pen hovered. It did not descend. "Again," she said, and he walked her through it twice more, and at three in the morning she wrote, in the margin, in red, the words he would remember longer than any headline: THIS HOLDS.
On the ninth night his phone rang at midnight, and it was his mother, coming off a double shift at the hospital in Chicago, her voice full of that particular tiredness she had carried as long as he could remember.
"Baby, Theo's mother called me. There's a countdown on the internet about my son." A pause filled with hospital sounds, distant and ordinary. "Are you eating? Are you sleeping? Don't answer like a student. Answer like my child."
"I'm eating, Mama. Sleeping some. Dr. Chen makes me leave at four."
"Then Dr. Chen is my favorite person at that university." Grace Carter was quiet a moment. "Your daddy did his best thinking at a kitchen table at two in the morning. He'd come up for air and say, 'Grace, it's there. I can see it. I just can't make them see it.'" Her voice thickened, only slightly. "You make them see it, Isaiah. Not for spite. For him β make them see it the way you see it, so nobody can ever unsee it again."
After the call he sat a long time with his father's notebook open to the margin where three circles surrounded a quantity no one had wanted. Then he turned to stage four, and stage five beyond it, the two hardest climbs, waiting in the dark like the last flights of a stairwell.
On the tenth night, Theo began leaving sandwiches outside the reading-room door with notes attached β DAY TEN: EAT, GENIUS and, later, CHEN TOO, I KNOW YOU'RE IN THERE SAVING MATHEMATICS. Chen pretended to confiscate them. Then she ate hers at the table, pen in hand, without looking up from stage four.
Five days remained. Isaiah picked up his pen, and the library, that patient old building, settled around them for another night.