The Janitor Who Solved the Impossible

Chapter 2

Maya stayed up until two in the morning.

Her notebook filled, emptied, filled again. Her mother knocked at eleven and said it was a school night, and Maya said "five more minutes" in the tone that meant the conversation was over.

She tried the problem forwards, from the givens toward the conclusion. She got two lines and stalled. She tried it backwards, taking the conclusion apart to see what would have to be true one step earlier, and ran into the same wall from the other side. She tried it sideways, through two analogous problems she dug out of a forum thread by a graduate student in Toronto — a thread three hundred comments deep, which its own author had ended with the words: "I don't think this is a problem. I think it's a wall."

At one in the morning, Maya understood the Toronto student completely. She had two honest lines — almost as far as Mr. Dalton had gotten in the auditorium — and after them, nothing she wrote stayed true. She took Dalton's objection, the one Cole had cut off mid-sentence, and checked it herself, slowly, twice.

The third transformation assumes a lemma that doesn't hold.

Dalton had been right about that much. The proof broke at the third line no matter how she came at it, and she did not have the tools to fix it, and neither, apparently, did anyone else on Earth.

At two she closed the notebook. Tomorrow she would try again.

At that same hour, about two in the morning, Westbrook High stood locked and dark — all of it except one window.

Officer Grant, who did the night security rounds, noticed it on his second pass: one classroom lit on the first floor, Room 114, the only lit window in the building. He wrote it in his log, because he wrote everything in his log, and thought about the heating bill, and drove on.

Nobody saw who was inside. Nobody saw anyone leave.

Maya heard about it before she even reached her locker. It was Jess, breathless, catching her by the sleeve.

"Somebody solved the first step."

"What?"

"The Halden problem. First step. It's just — there. This morning. Complete. Somebody is about to be ten thousand dollars richer, Maya."

Room 114 was packed shoulder to shoulder by seven-fifteen — students standing on chairs, the entire math department in the doorway. Maya pushed through on tiptoe and stopped.

The board had been changed.

Below Cole's eleven lines, in a different hand entirely — smaller, denser, not one stroke wasted — the first transformation of the Halden problem stood complete. Every step justified. Every move inevitable, once you saw it.

And it used a notation Maya had never seen in any textbook: a small compressed symbol, almost like a signature, where any textbook would have needed six lines of algebra.

"It checks out," said Ms. Okafor, the youngest teacher in the department, and her voice came out strange and high. She had been down the new work line by line, one finger under each symbol. "I've verified it four times. Every step is valid. This isn't a trick and it isn't copied — the method is — I've never seen this method. Whoever did this didn't follow the published attacks. They went a completely different way. A shorter way."

"A shorter way that three universities missed?" someone said.

"Yes," Ms. Okafor said. "That is what I'm telling you. Yes."

The guessing started at once — a visiting lecturer, a retired professor with a grandchild at the school, a transfer student nobody had noticed. It got wilder by the minute, because the truth available in that room was too small to hold the fact on the board.

"Who did this?" Hargrove demanded from the doorway. "Who was in this building last night?"

Silence.

"It has to be one of the teachers," someone said.

"It has to be Dalton," someone else said, and Mr. Dalton, standing pale at the back, said nothing at all. Maya filed that away. A man who had written that step would have said something. A man who hadn't would say exactly what Dalton said.

Then Hargrove's eyes found the one person in the room everyone else had forgotten to see.

"Ward." The principal snapped his fingers. "This floor is filthy. I walked the corridor an hour ago and there was dust on the sill. Do I need to file another report?"

Elias Ward stood by the door with his mop, in the middle of the crowd. He looked at the principal. He looked, for less than a second, at the blackboard.

"Sorry, sir," he said mildly. "I'll see to it."

"See that you do."

The crowd flowed past him, out of the room, already arguing about which teacher was the secret genius of Westbrook High.

Elias waited until the doorway cleared. Then he crossed to the window, ran one finger slowly along the sill Hargrove had complained about, and held it up. It came away clean. Anyone could have seen it, if anyone had been watching him. Almost no one was. He wiped the sill anyway, one unhurried pass with the rag from his back pocket, and picked up his mop.

Only Maya saw it. She had spent the whole uproar watching the wrong thing — not the board. Everyone in that room had been unable to stop staring at the board.

Everyone except one man.

Elias Ward had stood by the door through all of it — the gasps, the photographs, Ms. Okafor's shaking voice, the principal's barking — with his eyes lowered and his mop held still. One glance at the blackboard, less than a second, and never again.

If I'd solved that, Maya thought, walking past him into the corridor, I couldn't have kept my eyes off it.

Unless I'd solved it a long time ago. Then maybe I could.

She stopped at the end of the corridor and looked back. He was already at work in the emptying room, shoulders rounded, strokes even, a man with nothing on his mind but floor.

Elias mopped Room 114 last that day, and he did not look at the board again — or if he did, there was no one left in the building to notice.

Late that afternoon, in the supply closet at the end of the science wing, he set down his bucket and opened the cabinet where he kept his things: a thermos, a folded sweater, a tin box that had once held tea, older than any student in the school.

The closet smelled of bleach and damp cardboard. He turned the tin over once in his hands before opening it. It had traveled with him through four states in one bad year, and then thirty years of a job that had nothing to do with who he was. His fingers remembered the catch on the lid better than he did.

Inside, wrapped in a strip of cloth, lay a single piece of chalk, worn down to a stub, its surface smoothed by fingers that had held it a thousand times, in another life, in front of other blackboards.

He unwrapped it and rolled it once across his palm, feeling the weight of it, how little of it was left.

"Hello, old friend," he said softly. "It's been a while."