In the bookstore, waiting for Svetlana to finish comparing different editions of Beowulf, I started flipping through Nabokov’s Lectures on Literature, and my attention was caught by a passage about math. According to Nabokov, when ancient people first invented arithmetic, it was an artificial system designed to impose order on the world. Over the course of centuries, as the system grew more and more intricate, “mathematics transcended their initial condition and became as it were a natural part of the world to which they had been merely applied. . . . The whole world gradually turned out to be based on numbers, and nobody seems to have been surprised at the queer fact of the outer network becoming an inner skeleton.”
Suddenly, all kinds of things I had learned in school seemed to fit together. Could it be true, what Nabokov said—that the abstract calculations had come first, and only later turned out to describe reality? Hadn’t the Greeks come up with the ellipse from doing solid geometry, from slicing up imaginary cones, and then centuries later, the ellipse turned out to describe the exact shape of planetary orbits? Hadn’t ancient people invented trigonometry, centuries before anyone knew that sound waves were shaped like sine waves? Fibonacci came up with the Fibonacci sequence just from adding up numbers, and then its ratio turned out to be encoded in the seed spirals on a sunflower. What if math turned out to explain how everything worked—not just physics but everything? Could that be what Ivan was studying?
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I went with Hannah to her Multivariable Calculus class. It was required for premeds. The instructor was a shaggy barrel-chested undergraduate wearing a bright green jogging suit. He started to talk, loudly. I couldn’t understand a word he said. It wasn’t because of the subject matter; rather, it was impossible to pick out a single recognizable syllable.
In the hall after class, Hannah and her premed friends were joking about how they would sabotage someone called Daniel who always broke the curve. Daniel was standing right there, smiling modestly.
“Could you guys understand anything that guy said?” I asked during a pause in the conversation.
One of the premed students, a beautiful girl with eyebrows like two wispy feathers high above her eyes, glanced over at me. “No, nobody can understand him,” she said. They all started talking about how they would set off a smoke bomb in Daniel’s dorm on the night before the exam.
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I went to the first meeting of the only math class in the course catalog that wasn’t required for premeds and didn’t have any prerequisites. It was called Sets, Groups, and Topology: “an introduction to rigorous mathematics, axioms, and proofs, via topics such as set theory, symmetry groups, and low-dimensional topology.” The chairs weren’t in rows so much as in a big crowd. I recognized Ralph’s roommate Ira and sat near him. More and more people kept coming in and sitting on the floor. It became very hot. A bearded man came in. He surveyed the room with melancholy eyes. “I am Pal Tamas,” he said. “This is my Hungarian name. That is why I speak with this accent. In English, I am Tamas Pal. Soon my assistant will come with the syllabus.”
I wasn’t even surprised when the assistant turned out to be Ivan. I could see that he saw me, too, but we didn’t smile or wave. He started handing out the syllabus, which was still hot from the photocopier and contained unexpected diacritics. Tamas Pal turned out to be “Tamás Pál,” and Ivan turned out to be “Iván.” The subject for the first week was “Continuity, Connectedness, and Compactness.” When I tuned in, Tamás Pál was talking about how it was impossible to trisect an angle.
“This is probably counterintuitive,” he said.
I couldn’t imagine what it would mean for an angle to be impossible to trisect. If a thing existed, couldn’t you cut it in three? The professor started sketching diagrams and equations on the board. I copied everything in my notebook. Ivan was sitting on the floor, leaning against the wall. There was a ragged spot in his jeans just below the knee. It made a much stronger impression on me than the proof about angles.
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I decided not to attend the second meeting of Sets, Groups, and Topology. Instead, I went to the science library to read a journal article about linguistic priming. Apparently if you had just seen a picture of an elephant it made you faster at recognizing the word “giraffe.” A picture of a train would help you recognize the word “trail,” and a picture of a pail would help you recognize “pale.” Didn’t the trains and pails prove that people thought differently in different languages? As I kept reading, I myself became less and less able to perform simple word recognition tasks. I increasingly didn’t know what to do with myself. This not-knowing was physically painful, like sleeplessness.
I went to the math class.
The professor was talking about set theory. “Consider the set of people in this room,” he said. “There are about forty members. Now let us choose a subset within this set. Let’s say: the people who know each other. Most of us are still strangers to each other, but not all of us. For example, I know Iván.” He pronounced it in a really specific way, stressing the first syllable.
“I don’t know how many other members belong to this subset of people who know each other, but my guess would be ten or fifteen. So I will draw some connectives, like this.” He drew a bunch of dots on the board and connected some of them, like constellations. Were Ivan and I among the connected ones—the subset of people who knew each other? What was it to know each other?
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In the evening, Svetlana showed me how to play squash. I had never been in a squash court before. Inside the blindingly white cube, our sneakers squeaked and Svetlana’s voice sounded strangely removed, as if over a telephone. The blue rubber ball was so small, so fast and crazy. To think this world was too deterministic for some people!
I remembered as we were walking back from the courts that Ivan was teaching a section for the math class at nine. An enormous moon hung over the sports center. I probably wouldn’t go to the section. I went home, took a shower, and got dressed. When I looked at my watch, it was exactly ten to nine.
I went to the Science Center. I couldn’t find the room, which was in the five hundreds. There was no fifth floor in the elevator—the buttons skipped from three to six. I got in the elevator anyway and rode to the eleventh floor and back, as if the fifth floor might suddenly appear. Back on the ground floor, the doors opened. Ira stepped inside. “There’s no fifth floor,” I said.
“Hey,” he said, and stepped into the elevator. “Are you going up?”
“Well, that’s the thing,” I said.
Ira pressed the button for the third floor. It turned out you had to get out of the elevator and cross a metal walkway that stretched across an atrium. A big messy garden was hanging over the atrium, in a shallow tray held up by chains. It was like in Babylon, back when everyone spoke the same language. On the other side of the atrium was a flight of stairs that went to the fifth floor.