Characteristic Classes

This story is part of a series entitled Leaving Mathematics. See also:
1. The Baltimore Snowstorm; 2. The Italian School; 3. Characteristic Classes

Rainer noticed the pattern halfway through July. He had constructed smooth surfaces in a certain four-dimensional smooth algebraic variety, using the Chern classes of vector bundles. He noticed that he could anticipate these surfaces’ Hodge numbers. “This seems to amount virtually to something like a non-existence result,” he wrote, later that day, in an email to a junior faculty member at another school.

Rainer soon sank into a deep depression. “I go full days without saying a single word,” he told Diego, over the phone. “I try to practice mindfulness each day as I walk to school. The outside world seems meaningless and false.”

“You sound like a cliché,” Diego said. “I’ll come visit soon.”

Diego and Rainer had grown up together. Diego left for Yale when Rainer went to North Carolina. Diego befriended a strange group there. “We’ve been watching Tarkovsky films,” he told Rainer once over the phone.

One of Diego’s friends from Yale, Gavril, grew up in Baltimore. “We’re going to the thrift shop real quick,” Diego told Rainer, when the group arrived in the city. Their car eventually pulled up along the university’s busy fronting thoroughfare.

“I can see you’ve been to the thrift store,” Rainer told the group, grinning as he entered the car and craning his neck backwards towards Gavril and the two young women in the back seat. Diego wore a bizarre jacket, tiled by square leather patches of all different colors with studs at the corners. One of the girls wore a white, red, and teal one-piece jumpsuit.

“We’re not wearing what we bought,” Diego offered tactfully from the driver’s seat, after an instant of painful silence. “We actually didn’t buy anything.” Rainer’s face became hot.

“Rainer studies math at Hopkins,” Diego told the back seat. “We’ve known each other since middle school.” Rainer turned back once again, and smiled weakly.

Diego and Rainer talked to Helene, one of the women, in line, at a coffee shop south of campus. “I don’t often leave campus, or drink coffee, for that matter,” Rainer told them. “Coffee affects me strongly.” Helene was more relaxed than Rainer was. “It might be because you have anxiety,” she said, bluntly, looking at him and shrugging. Rainer remarked at her candidness—and at her insight.

Diego and Rainer talked at a table, later, as the others browsed through the store’s books. “You could take a year off,” Diego suggested. “Live in New York.” Diego had moved to New York after graduating. He worked in an “alternative film collective”.

“Why not just wait until I graduate?” Rainer asked.

“More of your youth will be gone by then,” Diego said. The prospect horrified Rainer. “What are you here to do?” he asked.

Gavril arrived at the table with the others. He held up The Collected Works of Borges. “He led a circle of writers in Buenos Aires in the 1930s,” Gavril said.

*    *    *

Among the classroom’s ample supply of old-fashioned desks, with attached rotating side tables, three or four, pulled apart from the others towards the front of the room, were occupied, by an old professor with his legs crossed and head inclined forward or by a Chinese postdoc gazing expectantly towards the board. Rainer was the only graduate student there.

The speaker, a Chinese woman in her late twenties, arrived. She was elegant, dressed uncharacteristically smartly, and was pretty. She was visiting from the Institute for Advanced Study in Princeton. “The Tate conjecture for abelian varieties over number fields” was written on the board.

The talk was excellent. The audience was sad. Mathematics, at its best, unfolded on the board, and we alone – four or five silent, pathetic souls – bore witness. The speaker smiled frequently, and a professor in the front interrupted her occasionally. No one else asked questions.

“I enjoyed your talk,” Rainer told the speaker, after it ended, smiling cautiously. “I wrote a paper you might enjoy reading…”

“The IAS is like a mathematical paradise,” the speaker told Rainer and one of the postdocs after dinner, as they walked together with her to her hotel. “Every week there are mathematical talks, with tea,” she said. “Unfortunately, there is nowhere to buy food on the weekends…”

*    *    *

“The old man at the conference asked me if we wanted to continue our discussion somewhere more quiet,” Leila told Rainer, some time after they sat down in a restaurant in Hampden, west of campus. “I was ashamed that I hadn’t detected his intentions earlier.” Rainer had met Leila a few nights earlier, at a party. He was informed later that she thought he was “cute”.

Rainer sat upright and bit his lower lip. “I’m sorry you had to go through that,” he managed. He looked at her and put his hands in his lap. “That is not fair.”

Leila smoked vigorously outside the restaurant, staring at the buildings across the street between inhalations.

Leila insinuated that the place was provincial. She was right, in a way. The orange streetlights above them lit up the dingy row of one-story buildings across the street; these included a few dive bars and a liquor store. “I want to live in New York, and commute,” Leila said. “The only problem is I have to be here at least three or four times a week.” The prospect seemed extravagant to Rainer.

“Our characters are very different, don’t you think?” Leila asked Rainer, later, as they took their places again at the table. She tilted her head slightly.

“What do you mean?” Rainer stumbled. Though her accent was hardly perceptible, Leila was not a native speaker of English. Rainer hoped optimistically that the connotations of referring to one’s “character” were not known to her.

Rainer felt defeated. He sensed that his attempts to be emotionally mature, with Leila – worldly, impatient, and five years older than him – had failed. He had sympathized with her, and had wanted to reach her.

The waiter brought out one of their dishes. It was lobster, immersed in mashed potatoes, all resting in a martini glass. “This looks like the sort of thing they would have served in New York ten years ago,” Leila said.

*    *    *

Rainer set out into the park across the street from his apartment building, one day, weeks later. The fall morning was bright and cold.

Rainer squinted against the sun, and lowered his eyes. He had gotten used to shying away from it – the sun, and the park’s trees upon which it reflected brightly – as he walked to campus, choosing instead to look down at the dirt path beneath his feet, and, frequently, to think about mathematics.

Rainer forced himself to look up. This sun’s brightness, it suddenly struck him, was not excessive. It was not the physical light that pained him. It was the intensity of the stimuli; it was the overpowering bandwidth of the sensory information that assaulted him. The leaves in the trees above him quavered and shimmered, and the sun slanted inwards, illuminating the edges of the orange leaves and the dust particles that occasionally drifted, slowly, downwards, through the empty space between the trees.

“To really be mindful – to really apprehend all of this information, even for an instant – would be overwhelming.”

Rainer looked up. He ceased resisting, and the details of the atmosphere poured into him. He felt connected to the world, but only because he had finally allowed it to influence him; he had finally mustered the capacity to absorb it; he had let down his guard. He had interacted with others recently, too.

Pure mathematics – the refiner of souls – had refined his soul, and diminished his self. He had found himself with nothing left. He felt the presence, nonetheless, of something growing within him, of a capacity to interact with the world around him. He loved the world around him.

Rainer loved even mathematics, and four-dimensional algebraic varieties, then, and he felt that these objects, too, played a part in those trees, somehow. He decided to visit New York soon. He was not sure whether he would come back.

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