Peter’s parents had always been unimpressed by his accomplishments. He had been born late in their lives, long past the time when they were expecting children, and so he was always treated like a disruptive and not entirely welcome surprise. As the youngest child of a household long accustomed to functioning without him, he’d always felt somewhat overlooked by his family, but when both his beloved older brothers died, that had been the end. While they’d been away fighting, Peter and his parents listened to the radio together, read the news, scoured the names of the missing and the dead. Peter had been the one to find his brothers’ names in the newspaper one after another. By some cruel fluke, his family had not been informed before their names had been printed. Peter had sat stunned and disbelieving: his brothers hadn’t even been in the same countries—what kind of coincidence could this be? It seemed impossible. He kept closing and reopening the newspaper, and when his father—annoyed at the rustling noise—asked him to hand it over, Peter had folded it up and refused.
“Give it here,” his father had said, impatient and unknowing, and Peter had sat on the paper and pushed his father away from him with shaking hands. All he knew with any certainty was if he let his father read it, it’d be true. He didn’t remember what happened after that, didn’t remember his father finally taking possession of the newspaper and reading what he had tried to hide from him, or his mother receiving the news. He had blocked it out.
What he knew was that in the days and months that followed, his mother became increasingly anxious about his physical safety—opening and closing his door half a dozen times at night and standing over his bed to make sure he was breathing. He would wake with a start to her hand a few inches over his mouth, feeling for his breath. Every time he opened his eyes, she would leave the room without a word.
For Peter, everything was tied up with that initial tragedy. When, as an undergraduate, he met Sal, whose age was the midpoint of his two siblings, Peter felt like he’d acquired an older brother. Sal teased and played pranks on him. He talked to him about math, but also gave him lessons for an hour a day on his piano, and told him to feel free to borrow any of his books. Sal introduced him to all the faculty as “our newest most brilliant colleague,” and when Peter was despondent, Sal told him to buck up, that he’d win the Fields Medal one day, which turned out to be true. So Peter’s loyalty to Sal was fierce. And when Sal asked him to come with him to Los Alamos to work on the hydrogen bomb, Peter didn’t think twice. He believed in Sal, and also that the only way to achieve a lasting peace was to develop as many weapons as possible and to use them to enforce the peace.
When his brothers had died, he’d been too young to stand beside them, to contribute to the war. He’d been too small to protect his family. His willingness to help build bombs, to strengthen the military, came (I have always thought) from the desire to make it up to them somehow. He was in opposition to many of the scientists who’d worked on the first generation of nuclear bombs, who had reversed their positions and were against developing any more.
Long after the project was over, Peter would be made to defend his choice over and over. A few times he’d been the target of anti-Vietnam activists who’d accused him of being paid by defense funding, and of turning MIT into a branch of the military. Neither of these things was true, and in fact Peter was against the war in Vietnam, but against his critics he always responded the same way: World War II had been a different beast, and he’d helped build the hydrogen bomb to secure the nation’s future and keep America safe. He was a patriot who wanted to serve the country that he loved.
I was convinced of the sincerity of his feelings, though I didn’t agree with the conclusions he drew from them. They seemed too simple, too innocent, even. When he had been at Los Alamos developing the hydrogen bomb, I had been in grade school, getting drilled by my school teacher to duck my head under my desk in case an atomic bomb hit our town. Still, the innocence of his convictions made me feel tender toward him, made me feel gentle, even though I suspected it was precisely that kind of innocence that made possible the most dangerous things. Perhaps I should have known then that one day I would be made to suffer for his innocence too.
That night, Sal and Peter and I went to the Green Mill to listen to jazz. I had never gone out late at night in a city before and was exhilarated by the cool breeze on my face and legs, the lights of the street blinking in and out. I linked arms with the men and felt as if we were connected with all the other people on the sidewalk making their way to the jazz club, as if the night bound each of us together. And once we were inside I felt it even more, because now it wasn’t only the night, but the music, which wove in and out of the space between us and turned it into song.
We had drink after drink and then Sal stumbled home, kissing us each on both cheeks before he left.
“I like Sal,” I said.
“I love Sal,” Peter said. He said it again, louder. “I love Sal.”
We were giddy and drunk and the room was dark, and Peter was holding me in his arms as I leaned against him in his chair. The voice of the jazz singer ascended and descended, and all around it, the piano and bass and horn wove in and out. A woman walking past us stopped in front of our table and said, “I wish I had a camera. You are a beautiful couple.” Peter’s arms tightened around me. When I thanked the woman, she said, “Never fall out of love,” and though I laughed, I felt a prickle of danger at her words.
Chapter 13
THE CONFERENCE, WHEN IT STARTED THE NEXT DAY, was an intimidating affair. It was small enough to be intimate if you knew everyone, but too small to lose yourself in if you didn’t. Recently anointed stars, like Stephen Smale, who’d proven the Poincaré conjecture for all dimensions greater or equal to 5, and the meteorologist and mathematician Edward Lorenz were there. A few years back, Lorenz had published the solutions for a mathematical model of atmospheric turbulence that came to be known as chaotic behavior and strange attractors, and more popularly in later years, the butterfly effect. Heavyweights like Peter and his contemporaries—most memorably Grothendieck, one of the creators of algebraic geometry and the leading expert in topological vector spaces—were also there, and between every talk and during every snack or meal break, they were swarmed by younger mathematicians trying frantically to impress them.
I wanted desperately to meet Grothendieck, who was already on his way to becoming a legend, mostly for his mathematics but also for his radical political views. Starstruck, I hung back and felt shy. I had told Peter to socialize without me, feeling nervous about being seen as his girlfriend instead of his collaborator—as a woman instead of a mathematician. But now I felt stranded, unsure of how to approach. I worked my way toward the group Grothendieck was standing in, but lost my nerve. I stood at the edge of the crowd and listened awkwardly.
He was talking about the étale cohomology theory of schemes that he’d recently developed and would later use to prove the Weil conjecture. The following year he would lecture on category theory in the forests surrounding Hanoi while it was being bombed to protest the Vietnam War. I was fascinated by him. I suppose all of us were. He had a nervous, passionate way of shifting from one leg to the other as he talked. He’d been born in the 1930s to anarchist parents and grown up in internment camps in France, which he’d escaped as a teenager with the intention of assassinating Hitler, and then he’d been hidden in a village in France where he’d been allowed to attend secondary school and first became fascinated with math. His mother contracted the tuberculosis that would later kill her in an internment camp; his father was sent to Auschwitz, where he perished. After the war, Grothendieck went to Paris, where unpolished, lacking formal training, and coming as he did from such a deprived and tragic background, he shocked onlookers by ascending to mathematical stardom. I did not know any of this background then, only what he had accomplished, and that upon being invited to Harvard he’d famously refused to sign a pledge promising not to overthrow the United States government. When he was told he could b
e sent to prison, he’d cheerfully replied he didn’t mind as long as he’d have access to his books.
I wish I’d had the nerve to talk to Grothendieck when I had the chance. Soon after the conference, upon learning his position was partially funded by the military, he would quit his job as a professor. From there he’d grow increasingly estranged from the mathematical community, eventually cutting off contact, rejecting prizes, yet continuing to produce monumental works in isolation. All the while he’d denounce a scientific culture that he claimed was governed by competition and hierarchy, and the outright theft of ideas.
By the time I saw him at the conference, he already felt—he would later say—that he was living and working in a golden cage. But all I noticed then was how the people crowded around him, wooing him, and felt too constrained myself to join. This must have been what Cinderella felt at the ball before she danced with the prince, I thought: I had dreamed of being in the presence of so many of the people attending, and now here I was, eavesdropping on their conversations. I lurked on the outside fringe, watching the clock, fidgeting and feeling out of place.
Someone asked me once if the loneliness I always felt came from being alone in a field in which there were no other women, but that wasn’t it, exactly. I wasn’t alone. There were in fact two other women at the conference, but by unspoken agreement, we avoided each other. This was pure instinct, an understanding that by being seen with each other we would draw attention to ourselves as women, and that would do us more harm than good. I caught glimpses of the other women from time to time—one of them always at the center of attention, talking loudly, putting herself forward—the other hanging back at the edges of things, like a girl waiting to be asked to dance—like me. I always turned away when I saw one of them, and I suspect they did the same when they saw me.
Which is why, I think, from the moment I met him, I wanted to be friends with Charles Lee. He was not a star like Grothendieck, but he exuded an outsider aura that I responded to with a feeling of fellowship. I met Lee in the elevator on the morning of the second day. We were wearing our name tags for the conference, so though we had never met, we recognized each other as fellow participants. I was so startled to see another Asian face that I said, “Oh!” out loud. He gave me a slight nod and then stood facing forward, observing a polite but alert and friendly silence—until the elevator gave a sudden small lurch. I yelped and put a hand out to the elevator wall, but nothing else happened. Lee assumed a crouched and ready stance, hands up, knees bent—as if preparing for a fight. I hadn’t looked at him directly until this moment, but now I watched him rise back to his full height with fluid grace.
He was a small man, five five or five six maybe—an inch or two shorter than me—and as slim around the waist as a girl. I would have guessed him to be in his forties, though it turned out he was already in his midfifties.
“Hello,” he said, turning toward me. “I think the elevator broke.” He turned back to the front of the elevator. He bounced up and down on his toes, gently, as if to test it or to prove his point. He spoke with an accent that reminded me of my mother’s, and the way he smiled felt comfortably and unexpectedly familiar. I felt not only at ease, but trusting—as if he would get us out of this.
I looked up at the ceiling, pressed my hands against the door. “What shall we do?”
“Well,” he said, looking all around us—at the door, the ceiling, the walls—“I guess we press this button.” And he pushed the red Alarm button on the elevator panel. Immediately, an alarm inside the elevator started ringing, shockingly loud and insistent.
We both covered our ears. “Turn it off!” I cried, laughing.
He pushed the alarm button again and again to no avail. It kept ringing. He returned to covering his ears with an exaggerated shrug. After a couple minutes of uninterrupted ringing, the alarm finally stopped.
“My God, what was that?” I laughed again. “Why would they sound the alarm inside the elevator when we’re the ones who pushed the button?”
Lee leaned against the elevator wall in mock exhaustion and relief. He gave me a wry look and shrugged. “Perhaps someone will come now to fix the elevator and let us out.”
“I hope so,” I said. And then, “I’m Katherine.”
He gave a slight bow. “I’m Lee. Are you here for the same conference as me?” Here he pointed at my name tag. “I ask, but I know the answer. What are you presenting here?”
“I’ll be presenting on elliptic cohomology with Peter Hall,” I said. I realized he was the first person to ask me what I was presenting on—the first to assume that I was. “But I’m also working on the Mohanty problem.”
Something in Lee’s face grew more alert. “A very interesting problem.” He smiled. He seemed about to say something, but then there was banging from the elevator shaft and voices shouting down at us.
“How many of you are there?” the voice called.
“Two,” Lee shouted back.
“We’ll be lowering you manually,” the voice called down.
“Did he say manually?” I said. “As in they’re lowering us down in this elevator by hand?”
“Not the most efficient or reliable method, but perhaps the speediest one available to us now?” he said. And then we were going down, jerky and slow, with a sudden dip that made me gasp out loud before we lurched and steadied. The door was forced open by two sets of hands. Lee and I looked at each other. He smiled at me and gestured with his hand to exit first.
We had only been lowered to the eighth floor, and I groaned, “We’re going to have to go down six flights of stairs.”
“It could be worse,” said Lee. “We could still be in the elevator.” He laughed cheerfully. “Or it could be worst, we could be splattered inside the elevator, crushed at the bottom of the chute.” And with that, he bounded down the stairs.
MY PRESENTATION WITH PETER went well: the room was full to capacity, standing room only, and afterward we were inundated with congratulations, well wishes, and every kind of attention. But as it turned out, we were overshadowed by another presentation that became the talk of the conference. In the hallway, we ran into a guy named Mac, a former student of Peter’s who had been at Lee’s lecture. “It was incredible,” he said. “There was this old Chinese number theorist whom no one had ever heard of before, and he proved part of the Mohanty problem, the one everyone said would take at least two more decades for someone to solve.”
“Could you repeat that?” Peter asked as I gasped out loud.
“How did he do it?” I asked.
Mac went on to describe precisely the approach I had originally proposed to Peter.
This kind of thing happens fairly regularly in mathematics: Bolyai, Lobachevsky, and Gauss came up with non-Euclidean geometries at the same time, independently, for instance. And Gauss was constantly one-upping Legendre, who—practically every time he proved something—would be met with Gauss’s maddening, “Oh yes, I came up with that result myself years ago and never got around to publishing it!”
To write a proof or discover a new object or tool or start an entire field is not the same as creating or inventing a truth: it is more like being the first to arrive at a truth. And yet it is still a creative act, one that requires your imagination to arrive at a previously unknown understanding of a deep problem. It is something like designing and building a spacecraft, figuring out the necessary path you need to chart through space, and flying to some location you don’t yet know exists, a location it feels like you discovered but also invented because it is an idea or an understanding more than an actual place.
“Lee’s solution was ingenious,” Mac said. “He set up a specific case of the general question, and then using the specific case, he was able to solve it for all even numbers.” As he described the process, it became clear that he’d proceeded along the lines of the proof in exactly the way I had originally proposed.
I looked at Peter and he looked at me. He reached out and took my hand. I squeezed it.
I could tell Peter felt much worse about the whole thing than I did. If anything, I felt vindicated, and pleased that it was Lee who’d done it. There was a momentary pang of regret that I had not been the one to solve the problem, but it was mostly outweighed by the pleasure I could take in having my thinking confirmed.
“What about for odd numbers?” I asked.
“Not yet,” Mac said. “Because obviously it’s a trickier case. But it seems inevitable that that will come next.”
“Yes,” I said, feeling some relief that it wasn’t all over, that there remained further work to be done on the problem I’d wanted to tackle.
I didn’t get the chance to talk to Lee again at the conference: every time I caught a glimpse, he was surrounded by other conference-goers and he looked tense and uncomfortable.
The story circulating about Lee was that he’d never really been accepted by mathematicians before. He’d been something of a star in graduate school, but then he’d had a falling-out with his graduate advisor and had been unable to get an academic job. He’d worked as a janitor and a florist and chopped vegetables at a Chinese restaurant in his town. It had been hard for him to hold down a job. He was unkempt and distracted, and when he ran out of paper, he wrote notes on the backs of his hands. Even now that he’d proven this important result, what most of the other mathematicians felt for him was a reluctant admiration coupled with a sort of alarmed and curious contempt.
What I felt for Charles Lee was neither curiosity nor contempt, but kinship. Even now, after his triumph, he was alone. I wanted to approach him, to break through the crowd to ask him when and how he’d solved his problem. But I was aware that I was nobody, and that I’d already told him I was working on the Mohanty problem in the elevator. I didn’t want it now to seem like I was trying to claim something that wasn’t mine, so I stayed away.
EVERY CULTURE HAS ITS FAIRY TALES: the same is true for mathematics. The most famous math fairy tale goes like this: Once upon a time, in a tiny town in South India, there lived a husband and a wife who were so poor they slept on the dirt floor of their hut. They wanted very much to have children, but year after year, no child came to fill the wife’s womb, and so she went on a trek to pray at the temple of her family’s goddess. While she was there she was blessed with a dream that she would bear a son who would speak in the language of the gods.
The Tenth Muse Page 9