She moved to the second board. Walsh shifted in his seat and uncrossed his legs. He could see what she was doing. He had not expected her to attack the problem this way; the standard graduate school approach was to push through the equation as one long chain. The decomposition method took longer to set up, but worked better on complex structures. He had not taught Whitney to think this way; someone else had. He didn't know who, and that bothered him more than he wanted it to.
Whitney started on the second substructure. She tried the standard method first—the obvious move, the one any examiner would expect. It did not work. She stared at the board; three of her lines collapsed into a contradiction. She erased them. The audience murmured. Walsh smiled wider.
Whitney did not look at him. She tried a second method, a common alternative. It also did not work: four more lines erased. The chalkboard had a thin layer of dust on it now. Whitney's right hand was white to the wrist. There was a smudge on her cheek where she had wiped sweat with the back of her hand; she did not notice.
A junior faculty member in the second row glanced at his stopwatch and turned the phone toward his neighbor: eight minutes had passed.
"Take your time, Miss Tate." It was Walsh from the front row. His voice was warm now, almost paternal—the kind of voice a coach uses on a player he expects to lose. "We've waited a decade. We can wait an hour."
A few people in the back laughed. Some did not.
Whitney did not turn around. She stepped back from the second board and studied it. The standard method failed. The common alternative failed. The textbook had three more options; she could already see that none of them would work either.
That was the moment she remembered her own paper—the undergraduate thesis, the one Walsh had passed with the margin note: Ambitious. Will not generalize.
In that paper, she had introduced a substitution technique. It was not in any textbook; she had derived it herself two years earlier while sitting at the diner counter at 3:00 in the morning. A customer was sleeping in the booth behind her, the radio playing low. She had been writing on the back of an order pad. The first version of the substitution had taken her four nights; she had thrown out fifteen drafts; she had slipped the final version into her backpack on a napkin and walked the twenty minutes back to Roxbury through the snow.
She had used that substitution to solve a class of problems no one had solved before—including, possibly, this one.
She raised the chalk and erased the second board completely. The audience reacted with a wave of small sounds: confusion, doubt, sympathy. Walsh laughed once, loudly.
Whitney didn't hear him. She wrote her own substitution at the top of the board, then ran the second substructure through it. The parameter reduced: clean. Mini victory number two.
In the back row, Dr. Whitmore made a small sound in her throat—not quite a laugh, closer to recognition.
In the front row, Walsh's face changed. He recognized the technique. He had read that paper; he had been on the committee; he had told three colleagues that summer that the technique was interesting but limited, and would not generalize beyond toy examples.
Whitney was using it to solve his decade-old problem. His right hand tightened on the yellow sheet.