And in the quiet hall, with the chalk dust settling like the first snow of the year, Isaiah believed her completely.
Chapter 25: Peer Review
By Monday morning, the applause in Harrow Lecture Hall had faded, and a harder test had begun. Isaiah's proof left Whitmore in sealed envelopes and encrypted files, bound for mathematicians who owed him nothing, who did not know his face, his age, or the story the campus told about him. They knew only the work. That was exactly how he wanted it.
Dr. Chen explained the process over coffee in her office, drawing a small map of the road ahead on a whiteboard. "Three independent teams," she said. "Princeton, Oxford, and Kyoto. None of them will talk to each other. They will check every line, every lemma, every hidden assumption. It usually takes a year. Sometimes two."
"A year," Isaiah repeated.
"For a claim this large, yes." She capped the marker. "If it survives them, it survives anyone."
The waiting was stranger than the scrutiny had been. Isaiah went back to classes, to problem sets, to his evening shifts at the tutoring center, while somewhere across the world strangers dismantled his proof board by board on paper.
On the ninth day, the first question arrived. It was not a rejection. It was three precise pages from the Oxford team, asking whether the transformation in the fourth lemma held when the underlying surface was folded twice instead of once. Isaiah read the letter twice at the library table where he and Dr. Chen had built so much of the proof, and felt his stomach tighten. It was a fair question. It was the question he would have asked.
He worked for two nights. On the second night, past midnight, he remembered his father's handwriting in an old margin: when a door will not open, check whether you are pushing on the hinge. Samuel Carter had meant it about stubborn students, but Isaiah suddenly saw the mathematics inside the sentence. He had been forcing the fold from the wrong side. Approached from the hinge โ from the fixed point instead of the moving one โ the transformation held cleanly, even more elegantly than before.
He wrote the answer in eleven careful pages and sent it before dawn, too tired to feel afraid.
The Oxford reply came four days later, and Dr. Chen printed it and carried it to the tutoring center herself, walking between the desks until she found him helping a freshman with integration. She said nothing. She simply laid the page in front of him. Isaiah read the first line, then read it again, because his hands had begun to shake.
The argument is correct, the reviewers wrote. Moreover, the response to our query strengthens the result.
"They're not just accepting it," Dr. Chen said quietly, while the freshman pretended very hard to study his textbook. "They're admiring it. There's a difference, and referees almost never do the second one."
Princeton reported the following week: no errors found. Kyoto took longer, because that team rebuilt the entire proof inside a computer system, translating every chalk mark into formal logic that a machine could interrogate without mercy or fatigue. For six days Isaiah checked his email before his feet touched the floor each morning. On the seventh day, the message was waiting. The formal verification was complete. The machine agreed with the boy.
Harrow, who had spent thirty-seven years on the other side of the question, asked permission to read the reports in Dr. Chen's office. He read them standing up, slowly, the way he had once interrogated Isaiah's boards. When he finished, he removed his glasses and was silent for a long moment. "In my day," he said at last, "we said a proof was not finished when the author believed it. It was finished when his enemies could not break it." He folded the pages with unusual care. "Yours is finished, Mr. Carter."
The journal moved faster than anyone predicted. The editor telephoned Dr. Chen personally, an honor she reported to Isaiah with wide eyes: the Carter proof would be fast-tracked, published with the referees' reports summarized alongside it, so the world could see not only the result but the rigor that had tested it. A result that had waited thirty-seven years, the editor said, had waited long enough.
That evening Isaiah called his mother from the steps of the library. In Chicago, Grace Carter answered on the second ring, still in her scrubs, and he told her the words he had rehearsed all the way across the quad.
"Mom. It's real. Strangers checked it. It's real."
He heard her sit down. He heard her laugh and cry at the same time, the way she had on the night he won his scholarship. "Your father," she said, "is somewhere being very difficult to live with right now. Telling everybody he knew it all along."