A Map for the Missing(72)
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From the window he looked down at the taxi stand. He saw her exit from the revolving doors, the surprise of the attendant as he shook himself from his doze and rose from his chair. She stood just to the side of the overhang. Yitian watched her silhouette as the attendant waved down a taxi. She was as poised as he’d ever seen her, but he could read in the tap of her fingers against her purse strap that she was eager to leave.
The attendant returned, followed by a cab. He opened the door for her. She pulled her long, black coat against her neck, disappearing it from the world. She already had one foot into the car when she suddenly looked up. He was not sure what the hotel glass might have obscured, but he nodded, and she nodded back. The shadow of her chin dipped against the pale skin of her neck. Then the attendant closed the car door, and he felt, finally, the weight of her absence in the room.
Twenty-eight
FEBRUARY 1978, BEIJING
Forget everything you knew before. Calculus, trigonometry, whatever . . .” Professor Leng said. “The purpose of this class is to rebuild your knowledge from the ground up. We will work to provide the foundation of all the rules you have learned. Your previous task was to memorize. Now, your job is to understand.”
Out of all his classes, Yitian had been dreading Real Analysis most. The older students had told him it would be the most difficult of the first-year core, but so far, the class hadn’t been nearly as hard as he’d anticipated. In math classes in high school, they had been instructed to simply memorize all the properties and axioms without any context or reasoning behind them. Each of those properties had drifted around Yitian’s mind, unconnected to the others, vanishing quickly from his memory. He had always found himself asking why. Why is this formula true, where did it come from? “There is no why to fundamental things like this,” his teacher in primary school had said, and then rapped his palm for being so insolent.
Professor Leng’s Real Analysis class was teaching him that his old teacher had been wrong. Each property required a proof, which, in turn, was based on certain fundamental principles. All of these could be traced all the way back to a single starting point. This process was the same way he’d learned history from his grandfather, from the origin point of the Yellow Emperor to all the branches that derived from it. This way of learning math allowed him to watch how each law or property grew from a previous one, a lineage created from the first axioms, much easier for him to behold and remember than the equations he’d learned in any math class before. He surprised himself with how easily the thinking came to him. He wondered if his grandfather would feel the same if he were still alive, sitting in this lecture. Even now that he was at the best university in the country, he still thought his grandfather was the smartest person he’d ever know.
Still, he couldn’t say he felt the same immediate yearning and interest for mathematics that he did for topics of history. In class, he had to force himself to focus and deliberately guide his mind back to attention each time he drifted off, as he did now when Professor Leng announced, “Today, we’ll be learning the triangle inequality—the most important of all of mathematics.” He wrote on the board:
If a and b are any two real numbers, then
|a + b| ≤ |a| + |b|.
“In other words,” Professor Leng said, “the absolute value of the sum of two real numbers is always less than or equal to the sum of their absolute values.”
The inequality seemed simple enough, so basic that Yitian couldn’t understand why they were spending so much time on the proof. But as Professor Leng wrote out the lines, his certainty lessened. For example, if he let a = Hanwen and b = Yitian, was it true that:
|Hanwen + Yitian| ≤ |Hanwen| + Yitian|?
On the left-hand side of the equation was the sum of Hanwen and Yitian, the way they were in the village. On the right was each of them individually, walled in their different worlds, as they were now. It didn’t seem obvious to Yitian that the sums of their separatenesses was greater than what they were together.
He tried another case. Let a = Yishou and b = Yitian:
|Yishou + Yitian| ≤ |Yishou| + |Yitian|.
He didn’t even add a question mark after the inequality, because it seemed so patently true to him; Yishou would have been better off alone.
The bell rang, signaling the end of the class period. Professor Leng, still in the middle of writing a line, dropped the piece of chalk. The unfinished equation hung uncertainly on the board, the equal sign rendered into a subtraction by the loss of its second underline. Yitian fought the urge to rise and correct it.
He allowed his focus to relax, his attention returning to the dull bleakness of the classroom, the gray light hardly filtering through dirty windows, and the rows and rows of his classmates, many of them who’d been secretly sleeping. He packed his bag quickly and deliberately. He had a particular task that he needed to complete now, one he’d been considering the entire morning.
The other students rushed out of class to fight for the most popular dishes at the canteen. He walked in another direction, toward the history department. He’d been going there every afternoon after mathematics classes ended in the morning. While the rest of his roommates napped, he snuck into the history classes, so often that some students had already asked him what year of the major he was in.