Chapter 5: The Notebook
He bought the notebook on Friday morning, before his first class, at the campus store, and he chose it with more care than he had ever chosen anything there: hardbound, unruled in the way he liked, thick paper that would not bleed. It cost nine dollars. He stood at the register doing the arithmetic he did automatically โ nine dollars was two lunches, or most of a textbook chapter copied legally โ and then he bought it anyway, and wrote on the first page, in his smallest hand: K. โ private. Test cold.
For three days he tested it cold.
He tested it before dawn while Theo snored through his alarm. He tested it in the library's basement carrel, with Harrow's assigned chapter open beside him like an opposing counsel. He tested it during his tutoring shifts, in the silences while his freshmen worked, and once during a lecture on an entirely different subject, for which his notes read, in their entirety: "cf. grouping โ does the term commute? (YES?)"
The six lines from the board had become twenty, and the twenty had not collapsed. That was the fact he kept returning to. Steps that should have failed in the old framing held in the new one โ not easily, but honestly, each deduction earning the next. Twice he found errors. Both times the error proved to be in his arithmetic, not in the approach โ a dropped sign, a subscript copied wrong. The corridor stayed open.
On Sunday night he reached a statement he could write cleanly at the top of a page, underlined once, the way Harrow underlined things he meant.
He read it three times. It was a lemma โ a stepping-stone result, not the solution itself. It said, in essence, that under the regrouping, a certain infinite process settled down instead of flying apart, which every published approach had assumed it must do. If the lemma was true, the Halvorsen collapse did not touch the new framing at all. If the lemma was true, the thirty-seven-year wall had a gate in it that nobody had seen because nobody had walked the wall from this side.
If. He wrote the word in the margin and circled it, as his father had circled it in the black notebooks, in pencil, in hope.
"Okay," Theo said from the doorway, returning with two cups of noodles. "Intervention."
"I'm studying," Isaiah said.
"You've been studying since Thursday. You didn't eat the rice. You called the RA 'Professor' yesterday, which he enjoyed too much. Andโ" Theo pointed with his chin at the desk, "โyou bought a fancy notebook. You only buy fancy notebooks for two reasons. There's a girl, or there's a problem. And since I would know about a girlโ"
"You would not know about a girl."
"I would sense a girl." Theo sat on the edge of the desk, and his voice dropped, because for all his volume he understood doors that should be closed. "Is it the equation? Harrow's thing? The impossible one?"
Isaiah was quiet a moment too long.
"Isaiah." Theo leaned forward. "Tell me you're not doing thirty-seven-years-of-geniuses-failed homework as a hobby."
"I'm not doing it as a hobby."
"That is not the reassurance you think it is."
He showed him, in the end, because Theo had never once made him feel that his presence required an explanation, and because some things become real only when another person has seen them. He explained it the kitchen-table way, with the map and the bridge that did not have to carry the weight. Theo, an engineer to his bones, followed the shape of it the way you follow a bridge design: not the proofs, but the load paths.
"Okay," Theo said at last. "Okay. Understand me: I believe that you believe it. That's level one. What level are you on?"
"I don't know yet," Isaiah said. "It holds. I keep trying to kill it and it holds."
"Then you have to show Harrow."
The name landed between them like a dropped plate.
"Or Chen," Theo said quickly. "Dr. Chen's supposed to be human. Show Chen."
"And say what? That the night cleaner has concerns about the framing?" Isaiah closed the notebook, gently, both hands flat on its cover. "Preston Hale's grandfather has a building here. His work gets read. Mine gets โ Theo, people like me get one chance to be taken seriously, and if I spend it on a mistake, I don't get another."
Theo was quiet. Then he stood, took the second cup of noodles, and put it deliberately on top of the closed notebook.
"Eat first," he said. "Genius after noodles. And Isaiah โ for the record, if that lemma is real? You were never going to be able to keep it in this room. Things that are true get out. That's kind of their whole deal."
Isaiah ate. The notebook waited under his hand all evening, patient as the numbers in the rain, and when he opened it again after Theo slept, the circled word in the margin looked back at him: If, in pencil, in hope, in his father's handwriting and his own.