Sullivan walked to the lectern, put her finger on the button, looked once at Whitney, looked once at Walsh, and pressed it.
The red digits lit up: 30... 29... 28...
Whitney turned to the board, raised the chalk, and did not stop moving until the clock hit zero.
What she wrote across the next thirty seconds was not the long path; it was the short one:
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In the first line, she rewrote Walsh's entire equation under a single change of variables. The substitution reframed the problem into a different mathematical space—an older space that mathematicians had been studying for sixty years.
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In the second line, she pointed the equation directly at a known theorem: a result proved in 1962 by a French mathematician, a theorem that appeared in every graduate textbook on the subject.
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In the third line, she applied the theorem.
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The fourth line was the answer.
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The fifth line translated the answer back into the original language of Walsh's problem.
That was it: five lines.
Twenty-five seconds in, the graduate student in the third row gasped audibly. He had recognized the change of variables; he nudged the colleague next to him; they both stared.
Twenty seconds in, Walsh leaned forward in his chair, his mouth opening slightly. He recognized the change of variables. He had not seen it—in twenty years of working with modular forms, he had not seen it.
Fifteen seconds in, Dr. Whitmore stood up quietly behind the back row, where almost no one saw her.
Ten seconds in, Dr. Sullivan put a hand over her mouth.
Five seconds in, a first-year graduate student in the third row whispered the words, "Oh, my God," into his hand and could not stop himself.
Two seconds in, Whitney set the chalk down on the tray. She turned to face the audience.
The clock hit zero. The buzzer sounded.
The room did not move. For three long seconds, no one moved.