Let’s take another look at the problem: the boy and the girl across the lake. He can get her the ring if you find the solution. No need to rush: this isn’t a timed exam, and in the story the girl and boy never age. Nothing will happen to them until you’ve figured it out—no one will fall in love with anyone else, no war will break out to take anyone away, no one will fall sick or die. So take your time. Later, when we come back to them, they’ll still be there, the shining lake and the old ferryman between them, waiting for us to bring them together.
Chapter 10
PETER HALL AND I DIDN’T SPEAK AGAIN UNTIL THE FALL semester of my second year, when I took his class on celestial mechanics. The course dealt with dynamical systems, which I’d become interested in by eavesdropping on the physicists whose offices were across the hall: my office was located right at the border between the departments, and unlike my own officemates, my neighbors were always in their office or in the physics lounge, which was next door. Even when I shut my door, I could often hear them talking and joking. The mathematics lounge was pristine, but the physics lounge was filled with gadgets and wiring and models, and a rotating ceiling that a former student had built, pierced with holes in the exact arrangement of constellations in the night sky.
The students in the office directly across from mine had built an elaborate train set that took up their entire room—“because the engineers have one,” they said—and they were constantly tinkering with it. The circuitry for the train set was underneath the table the train ran on, and so they spent most of their time down there, like mechanics in an auto shop, a row of feet poking out as they talked.
All their gadgets reminded me of the things my father had built for me growing up, and I came to appreciate their friendly banter coming through my walls like disembodied radio voices. Sometimes I would linger in front of their office door, listening and trying to track their conversations, until one day, they caught me.
“We’ve got a guest,” a dark-haired young man announced, scooting into a sitting position out from under the table. He sat up and smiled, a warm, open, dazzling smile. “I’m Rob,” he said and wiggled the shoe next to him. “That’s Leo.”
“Hello,” I said, holding out my hand.
“Well,” Rob said, getting up to take it. “For the sake of all that’s holy and good, tell us your name—we’ve enough mysteries on our hands as it is.”
I laughed. “I’m Katherine.”
“Pleased to meet you,” Rob said.
“Welcome,” said Leo, crawling out from underneath the table with a grunt. He was disheveled and covered in dust, and clutching tools in his hands, but when he looked up at me, he blinked into the light and smiled.
I spent many afternoons in their office, crowded around the big table with physicists and books and the menagerie of exotic houseplants Leo was cultivating to serve as forests for the train set. I liked the social atmosphere, and it was the first time I’d been invited to join a group so easily—as if I already belonged. I started wearing pants so I could go under the table with them and stare at the dazzlingly complex circuitry they’d set up to keep the train running, the gates going up and down, the lights in the houses blinking, and so on.
They occasionally asked me to explain some math they needed for whatever they were working on, and I was only too happy to be useful. Leo and Rob were generous with their ideas and shared them openly. Their train set was a model for how they worked: anyone at all was welcome to come and tinker with it—to add something, to change something, to make the circuitry more efficient. I learned a lot watching them work, and I observed how this ethos translated to their research as well—it was as if no one had authorship or ownership of a single idea—they threw it into the pot for everyone to attack together.
Sometimes when I was with them I thought with a pang about my father, and how much he would enjoy meeting them. But whenever I called him, he wanted instead to talk about the future, and then he said things I didn’t want to hear. “You have to think of how difficult it will be to get a job as a woman,” he said. “Most departments aren’t going to want to hire a woman professor.”
“So I’ll do something else,” I said.
“I think we should talk about this,” he said.
“I’m done with this conversation,” I said. And I called him less than I had, and when it came time for vacations, I found myself saying I was too busy to go home.
CELESTIAL MECHANICS fell outside Peter’s field of expertise, but he preferred to teach classes on subjects he was unfamiliar with—to use his classes as an excuse to learn something new. He was an exciting, charismatic teacher, and on the first day, as I entered his classroom, I felt a jolt when I saw him standing there in front of the room, frowning down at his desk, and scribbling furiously. Back then, he was always in motion, pacing across the room, covered in the chalk dust he picked up by brushing against the board or rubbing his arm absentmindedly while he held a piece of chalk in his hand. And when he broke it writing on the board, which he often did, he would kick it across the room, so that it’d ricochet against the walls or the chair legs of the students in the first row, and when class was over there’d be pieces of chalk strewn all along the floor, little hazards that people sometimes slipped on or crushed into powder beneath their feet.
On that first day, though, Peter waited until five minutes after the official start time, until the room was packed to bursting and there were students standing up on the stairs along the edges of the rows. The first day was always like this for Peter, with both undergraduate and graduate students eager to see him in action, whether they were registered in the course or not. The room was loud with the buzzing of voices, but when Peter stopped scribbling on his paper and stood back on his heels to look at us, we were immediately silent. He paced up and down the length of the room, looking at us, his gaze running along the rows of students who had come to hear him. For a moment his eyes rested on me. For a moment, they paused. But then his eyes slid away and moved on, searching other faces.
“The way I like to choose a problem,” he began, “is to take two ideas that seem very far apart, and try to find the connection that brings them together.” He held his hands wide and brought them close. “I was told earlier today,” he continued, “that there are several nonmathematicians in this class. I was just trying to see if I could tell them apart from the mathematicians.” He paused, and I felt an uncomfortable prickling under my skin, afraid of being singled out like Richard’s joke had singled out Kovalevskaya and Noether. But then Peter smiled and shook his head. “I couldn’t. You all look alike.”
Everyone laughed, and I joined in relief. He grinned back at us. He seemed eager for us to like him, and simultaneously confident that we would. Humble and arrogant at once. He began again, energized now, and pleased that he had gotten his first laugh. “As we all know, the closest distance between two points is a straight line, but sometimes the closest distance between two ideas is a long and winding path. Perhaps you will feel that way in this class.”
And he laid out the basic framework of what we would be studying in the class, beginning with the founding of celestial mechanics and Poincaré’s assertion that the solar system is unstable, to Kolmogorov’s argument that the solar system actually tends toward stability. We’d cover the Boltzmann equation, partial differential equations, and the laws of thermodynamics. We’d be looking at microscopic physics and macroscopic physics, reversible and irreversible phenomena, and predictions and observations in theoretical physics that were still waiting for mathematical explanations.
All semester long, that class was magic, and not just for me, but for everyone who stayed in the course. We grew closer than a class usually does—talking long after the class time was up, sharing ideas, even meeting out for the occasional group meal. Peter became especially close to Leo and Rob, quizzing them in class to fill in his own gaps of knowledge in physics. As a result, they came to class incredibly well prepared, studying ahead of time, to ant
icipate what he might ask of them. They took to bringing ten books between them, as references, and Peter took to throwing chalk at them when they were too slow or came up short. There was a lot of laughing and high-spirited argument in that class, and it bred a camaraderie among everyone that Peter became famous for, and as his students, it spurred us forward. As for me, there was an extra little buzz that surrounded everything he did. For years, I could remember entire lectures he’d given, word for word, everything he’d said and exactly how he’d looked when he said it.
DURING THE WEEK, Peter would often invite Leo and Rob to the faculty lounge to sit and talk with him, and to make use of the giant sliding chalkboards that lined every wall of the room. In that room, you could go round and round, sliding those chalkboards up in a spiral that rose above you. After those meetings, Rob and Leo would stop by my office, exhilarated.
They’d begun to pick up his mannerisms—the way he had of suddenly leaning forward before he asked a question and fixing you with his eyes, or the way he broke whatever he was holding in his hands—chalk, pencils, bits of paper—into smaller and smaller pieces as he thought. I found myself flirting with them on the days they came back from spending time with Peter.
Rob, who was married, flirted gently and amusedly back, but made it clear, quite firmly, that he was not interested. Leo, who—it is possible—had never had an extended conversation with a woman before I joined their duo, and who may not have noticed I was a woman until that moment—was baffled, enjoyed it, and tried hard not to care. But mostly, we were all obsessed with Peter.
“He’s brilliant,” they said. “He grasps everything immediately, intuitively. He could be a great physicist if he wanted. You too, Kat. You could be good at anything you put your mind to, if you were a man.”
They had taken to adding that last bit—“if you were a man”—as a joke to everything after I told them about the professor in college who’d said he’d make me his assistant, if only I were a man.
“Very funny,” I said.
ONE DAY, I was in Leo and Rob’s office when Peter came by looking for them. I was perched on the edge of a plush leather armchair, and when he came in, I straightened up. “I was just heading out,” I began, starting to rise.
“Nonsense,” said Rob. “You weren’t doing any such thing. Don’t be a spoilsport, and come with us, won’t you?”
I looked at Peter.
“We’re talking about parabolic curves,” he said in the tone someone might say we’re having cookies or we’re having champagne.
“Okay, I’ll come,” I said. And then we just stood there, looking at each other. The blood in my body rose and grew warm with his nearness.
Leo cleared his throat. “Shall we get going then?”
Peter and I blinked and broke eye contact. But in that long look had been a promise, and I’d recognized it for what it was—the kind of intimacy that precedes intimacy.
LEO BROUGHT A FOOTBALL with him. I knew he liked to toss it around in the math faculty lounge. “All that wasted space!” he’d crowed after his first day with Peter. Now he groaned, “We won’t be able to, with her,” nodding at me and twirling the ball between his hands.
I plucked the ball from his hands and tossed it to Rob. “What, is this how it works?”
Rob laughed and tossed the ball to Peter. “Gotta keep your eye on the ball, Leo, or you’re going to have it stolen right out of your hands,” he said.
“Yeah, Leo, you throw like a girl,” Peter said, tossing the ball back to me. He winked. “No offense.”
“So do you.” I hurled it back as Rob and Leo hooted with laughter. “And none taken.”
Leo leapt for the ball, Peter dodged and tossed it back to Rob, who kept it away from him, running along the perimeter of the room with Leo chasing and yelling at his heels. The door opened, and Rob jumped aside quickly, but Leo ran right into Paul Mapleton, the chair of the department, and a very serious man.
“What’s going on here?” Mapleton cried. “This is the faculty lounge! For the faculty!” Then his eyes focused on Peter, and he did a double take. “Sorry, Hall, didn’t know you were in here.”
Peter laughed. “Apologies are mine to make,” he said. “We were working out a problem on arcs and trajectories, that sort of thing.”
“I see, of course,” Paul Mapleton said. “Well, carry on.”
So we settled down and got to work, talking and laughing and brainstorming ideas to solve—as it turned out—some problems having to do with arcs and trajectories. The time passed so quickly I didn’t notice the afternoon turn into evening, and then it was dark outside and dim in the lounge, and Rob started and looked at his watch and said he had to go home to his wife. Leo also took his leave. “I should be going too,” I said, after a brief pause and followed them out.
I couldn’t concentrate when I returned to my office, so after half an hour or so had passed, I gathered my books and my coat to leave. I’d taken less than five steps in the hallway, when suddenly a brisk footstep joined mine. Peter was next to me, smiling.
“I was just heading out as well,” he said, and we walked through the long hallway and down the stairs without speaking. When we reached the door, he leaned over and took my coat from my arm, shook it out, and held it open for me. I stepped into the arms of my own coat as easily as if it we’d rehearsed it. He smoothed it over my shoulders, and when I looked up to thank him, I was suddenly aware of everything around us—the wood paneling of the interior of the building, the smell of floor polish, the dying light filtering in through the old lead-glass windows—and I felt dazzled by the moment of acute perception, as if I’d finally stepped firmly into the real world, into my life.
Outside it was winter, and the lamplight shimmered on the bits of snow that clung to the frozen blades of grass, which crunched under our feet. We started walking without any destination in mind, and after a while I realized we were walking in circles around campus. All the while, we talked. We talked about what the other students and faculty members were working on, and sparred over a controversy that had arisen within the ranks in response to a recent article condemning the “new” way math was taught to elementary school students. When I interrupted to note we’d circled the campus three times as we argued, Peter laughed, and said he would walk me home. But when we reached my apartment building, we were still deep in conversation, so we turned around and walked all the way back to campus. We went back and forth like this until the sun had sunk all the way down, and the evening had turned into night.
I couldn’t stop looking at him: people passed us on the sidewalk, cars drove by on the road, all of it an impressionistic blur—only Peter stood out, exuding a glow under the streetlights that seemed to strike others as well, because people kept stopping to turn and look at us as they passed by. But for once I didn’t care about being stared at. I was with him so it didn’t matter. I was happy.
THAT NIGHT PETER TOLD ME how his family had lost both of his older brothers in the war when he was ten years old, and how he’d grown up in the shadow of that loss. Rick, the eldest, had been a popular high school and college football player, and he’d been lost for six months after a battle in Italy before they finally identified his body. Johnny had been nineteen years old, and just proving himself as a talented mathematician, when he was killed in France. A week after the news of his death, a series of letters had arrived containing a mathematical proof of rare insight and reach. His parents had sent the proof along to a professor at Princeton, who’d verified the importance of the results, and who’d had the paper published in a major journal. Twenty years later, and Peter was brilliant, famous—more than fulfilling the promise of his lost older brother, but haunted by the sense that no matter what he did, he could never make up for the loss or match the sacrifice. He was always competing with a ghost.
When we got close to my apartment building on our last circuit, Peter turned to face me. “You’re shivering,” he said. “I’ve kept you too late. I’ll let you go in
this time.” He smiled. The streetlight fell over his face and hair, slantwise, so that the part of him that was lit up seemed brighter than anything around us. He took a deep breath. “Come to my office and work with me,” he said. “Whenever you like. Starting tomorrow. I have an extra desk and could use the company.”
“All right,” I said. I felt a surge of happiness—to be seeing him tomorrow, to have had this walk with him. I turned and ran to my building, calling out “Good night!”
Chapter 11
WHEN I WAS A CHILD, MAYBE FOUR OR FIVE YEARS old, my father used to let me sit under his desk to read or draw while he worked. For the most part we ignored each other, though sometimes I’d lean my drawing pad against his legs and line my colored pencils up between his socked feet. Sometimes while I read, he’d reach out one searching foot and poke me in the side with his toes. I’d bat him away, declaring in my most irritable grown-up voice, “I’m working!” There was a Do Not Disturb sign I’d post to the side of his desk, and I’d crawl under there even when my father was elsewhere, for the feeling of calm delight it gave me, puffed up with self-importance at being allowed to work in the proximity of his work on my own all-absorbing tasks.
When I first started working with Peter in his office, I went four times a week. On the days he taught Celestial Mechanics, I went to class separately and spent the rest of the day in my office. The rest of the week, the routine went like this: we spent the morning in silent contemplation, then we had lunch together, and then for an hour in the afternoon we told each other what we’d been working on, throwing ideas around. If I had another class or he had a meeting, we took our leave wordlessly, and just as wordlessly came back. Sometimes we called one of the graduate students or faculty members in to get their take on whatever we were doing. Then we took a walk, exactly the same walk of about forty-five minutes, either the two of us or a little parade of mathematicians and scientists, and when we returned we either kept working until evening or went our separate ways—I to my office, he to his, or I to my apartment and he to his house. Then we both worked separately, deep into the night. We would meet again in the morning and start over. That was it.
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