“Okay,” Ben said. He must have wondered where I was going with all this, but he listened patiently, as if it was perfectly normal for him to have a strange woman standing in his living room, lecturing him on math.
“Kepler’s conjecture holds that the greatest density of stacked spheres that can be achieved is this.” I held out the notebook for him to see Lila’s notation:
“To achieve this density, the bottom level of the stack should be arranged in a hexagonal lattice, and the next layer should be placed on the lowest points atop the first layer. Each layer should follow this principle until the top layer of the pyramid—a single sphere—is reached—basically, the way grocers stack oranges.”
“Okay,” he said, nodding.
“Kepler’s conjecture seems perfectly sound,” I said.
“That it does,” Ben said.
“But here’s the thing. The conjecture has never been proved, to this day. I looked it up and discovered that, in 1998, a proof had finally been put forward by an American mathematician named Thomas Hales. In 2003, a committee that had been assigned to verify Hales’s work confirmed that they were ninety-nine percent certain of the proof’s correctness. But that one percent was key. The mathematical world is still waiting for the publication of the data that will prove the Kepler Conjecture definitively.”
“Sucks for Thomas Hales,” Ben said.
“I agree. But it makes sense that they have to be certain, doesn’t it? The thing is, I’m ninety-nine percent sure that Peter McConnell didn’t kill Lila, but until I find the final piece of evidence, until I can stack it all up in a neat configuration and make sense of it, everything is just conjecture. I just need to know for sure. Does that make sense?”
“It makes perfect sense,” Ben said, placing a hand on my shoulder. “I wish you luck, my friend.”
Twenty-six
ONE FRIDAY SIX MONTHS AFTER LILA’S death, I walked into her bedroom, following my mother’s request to “see what you can do.” Already, I realized I would not be able to throw away a single thing. The fact that Lila had never been a pack rat should have made it easier, but what her possessions lacked in quantity was made up for by the intensity of her attachment to them. Each item in the room had been cherished by her. There was little organizing to be done, as Lila had been obsessively neat. Most of her possessions fit into a series of red file boxes that she kept in the floor-to-ceiling shelves beside her desk, each box labeled with a white card on which she had typed the contents: keepsakes, financial papers, correspondence. Her math notebooks were arranged by date, left to right, on a bookshelf above her desk. Her sewing machine sat on a wooden table that fit snugly into the bay window; beneath the table was a basket containing bobbins, thread, scissors, a pincushion, and a slim metal sewing ruler. In the days before her disappearance, she had been working on a a patchwork skirt, and on the table to the left of the sewing machine was a neat stack of silk squares in various prints and colors. I picked up the stack and arranged the squares across her bed. None of them seemed to go together, but I knew that if Lila had finished the skirt it would have somehow worked. Lila had been sewing since third grade, when she’d taken a kids’ class at City College. After the class was over, she’d gone on to teach herself new techniques, becoming more competent with every garment. She’d tried more than once to teach me, but I’d never had the patience. My hems came out messy, my zippers and buttons off-kilter, the proportions all wrong.
“Why do you do it?” I’d asked her once, during one of those hopeless sewing lessons. “You know how Mom is about clothes. She’ll buy you whatever you like.”
Lila had a needle between her teeth and a seam-ripper in her hand, and was in the process of tearing out a dart I’d botched on a simple A-line skirt. “It makes me feel calm,” she said, her words slightly slurred by the needle. “Sewing has a lot in common with math. You’re looking for the most elegant outcome, putting things together in a way that’s precise, unexpected, and ultimately beautiful.” She held the fabric up to the light. “There!” she said, having extracted the dart. “Now, let’s start from scratch.”
That Friday, alone in Lila’s room, I could still hear her voice as clearly as if she were there with me, but I wondered how long that would last. My parents hadn’t bought a camcorder until a couple of years before. We had very few recordings of Lila’s voice. I knew there must be some point at which the basic imprints of a personality begin to fade in the mind. I dreaded the day when my memories of Lila would become foggy.
I wrapped the fabric in tissue paper and placed it in the top drawer of my dresser. I wasn’t sure what I’d do with it. Not a skirt, as Lila had planned—I’d only make a mess of it. But I thought perhaps I could pay someone to sew the squares into a quilt. I liked the idea of having them close—something tangible that I could touch, that would somehow convey her spirit. Dozens of times in the months to follow, I would remove them from my drawer, unwrap the tissue, and lay them out across my bed, arranging and rearranging them for hours, searching for some sign of her in the elaborate patterns. When I moved out of my parents’ house my junior year of college, I took them with me. When I traveled alone to Europe several years after she died, I sewed a couple of silk squares to the interior lining of my backpack. In later years, wherever I traveled, one or two of them made the trip with me.
I went back to Lila’s room and opened the closet door. All of the hangers were white and faced the same direction. Shirts came first, then skirts, pants, and dresses. “Keep the clothes you can wear and give the rest away to Lila’s friends,” my mother had said that morning before heading to Napa with my father for a friend’s wedding. In hindsight, as an adult, I would consider it so strange that they had left me alone to deal with the ghosts in Lila’s room, but at the time, I simply chalked it up to the absentmindedness and weird behavior that had hounded both of them since Lila’s death.
Standing alone in Lila’s small walk-in closet, sliding the hangers across the rack, I thought back to what my mother had said that morning. What world was she living in, that she believed in some bevy of phantom friends waiting in the wings to accept Lila’s old clothing? For all their attempts to be loving, involved parents, my parents had never really understood how solitary an individual Lila was. And I began to wonder if I, too, had been wrong about her all along. I had assumed that she spent all those weekend nights of high school and college at home with the family out of choice, because that was where she wanted to be. But maybe she had wanted friends and boyfriends, but hadn’t known how to go about it.
Ultimately, I ended up going to the hardware store a couple of blocks away and buying several large rubber containers, into which I placed the red file boxes, the sewing basket, the books and notebooks and bed linens. The only thing I kept for myself was Lila’s well-worn copy of G. H. Hardy’s A Mathematician’s Apology, a slim volume that I would read several times in the years to come, impressed by the simplicity with which Hardy described the beauty of pure mathematics.
One by one I carried the rubber containers into my parents’ closet, then pushed them through the small door that led into the crawl space. Once all the boxes were all inside, I took a flashlight and ventured into the stale, hot space, climbing through cobwebs and balls of dust. I shoved the boxes to the farthest corner. No one ever went in there. It was with no small degree of guilt that I contemplated the fact that Lila’s belongings would be completely alone. I knew my mother would not ask what I had done with them. Embedded in my parents’ departure that morning for Napa was an unspoken command: they wanted Lila’s things to disappear, and the responsibility was mine.
Later I would regret the fact that on that afternoon, I had called the one person in whom I could confide, Andrew Thorpe. Still reeling from the events of the day, I let him into our home and told him everything.
“Can I see?” he had asked.
So I led him up to my parents’ room and opened the door to the crawl space, and watched as he stooped and went inside, s
hining a flashlight on the boxes. I could not fathom why he would want to see that dusty attic space, could not make sense of his interest in Lila’s old things. Only later would I realize that he’d gone in there for the sake of authenticity—so he could describe the cramped dimensions of the crawl space, its musty smell, the blue sheen of the cheap rubber boxes.
Many years later, when my mother was preparing to sell the house and move to Santa Cruz, I received a phone call from her. “I went into the crawl space,” she said, her voice breaking. “I thought you’d given those things away.”
I realized that, for all those years, she had been unaware that Lila’s things were stored just a few yards from the bed where she slept. I left work early and drove to the house where I grew up. Together my mother and I went through the boxes. Among the things we found was an album by Cat Stevens called Numbers, which was released in 1975. Although it was part of a three-album box set, along with Izitso and Back to Earth, Lila had only Numbers. There was a period of several months when she played it every day after school, so often that the songs became stuck in my mind. At some point she stopped playing it, and I had forgotten all about it. I dusted it off and read the song titles on the back of the jacket, at which point some synapse fired in my brain, setting off a tangled stream of melodies and their accompanying lyrics. My first thought was to play the album, but then I realized I had nothing to play it on. My parents had long since done away with the turntable, and I couldn’t think of a single person who owned one.
“If you really want to hear it, I’m sure you can find a record player on eBay,” she said.
“Maybe I will,” I said, but I never did.
Twenty-seven
FIRST NAME STEVE,” THORPE SAID, “LAST name S-t-r-a-c-h-m-a-n.”
We were sitting at Simple Pleasures out in the avenues on a Monday night. I’d had an appointment earlier in the evening with the owner, Ahmed, who had been buying his beans from Golden Gate Coffee since the eighties. Although we still provided the beans, he had recently begun roasting them himself in a storefront two doors down from the popular café. The beautiful bronze machine was situated right in front of the window, and around four in the afternoon, neighborhood kids would gather on the sidewalk to watch it rumble to life. It was live music night, and a folksinger named Patrick Wolf was setting up in the little alcove beyond the kitchen.
I jotted the name Steve Strachman into my notebook, and read it back to Thorpe to make sure I’d spelled it correctly. “It rings a bell,” I said.
“He was a grad student in the math department at Stanford,” Thorpe said. “He was a contender for the Hilbert Prize.”
“The one Lila was supposed to get.”
Thorpe nodded.
The Hilbert Prize was awarded in the February of even-numbered years to a promising graduate student for work related to any one of David Hilbert’s famous unsolved problems. Nineteen-ninety was rumored to be Lila’s year. The prize had been a sort of beacon on the horizon in the months leading up to her death. She was giddy about the prospect of winning it.
“At the same time Lila was working on Goldbach,” Thorpe explained, “Strachman was working on the Hodge Conjecture. Not one of the Hilbert problems, mind you, but Strachman believed that progress on Hodge might ultimately shed light on the Riemann Hypothesis. Like Lila, he was somewhat of a prodigy. He’d made a name for himself as a high school student during the International Mathematics Olympiad in 1982. From what I gathered during my interviews, he wasn’t well-liked at Stanford. He was arrogant, competitive, used to irk the other students by trying to hone in on what they were doing, listen in on conversations without ever adding anything to the soup. Mathematicians as a group are extremely interconnected, constantly sharing information. But Strachman was notoriously cagey. Anytime he came up with an idea that he considered particularly interesting or valuable, he mailed it to himself in a sealed envelope so he’d have evidence of exactly when he’d first made note of it. He was so paranoid that someone would try to steal his ideas that he kept his math notebooks, and all those sealed envelopes, in a locked drawer at home. And here’s an odd little detail—the cops once came out to the house on a domestic disturbance call. Seems he caught his mother trying to break the lock while she was cleaning his room, and he went ballistic.”
“He lived with his mother?”
“Indeed he did.”
“Strike one,” I said. “Then again, Lila lived at home, and I never thought twice about it.”
“Right, but he was a guy—it’s different. And he was older.”
Wolf began to sing. He sounded good.
“Let’s move outside,” Thorpe said. “It’s getting noisy in here.”
On my way out I said hello to Wolf’s girlfriend—a preschool teacher named Mary—and to Peggy and Matt, who owned the Pilates studio across the street. I loved that about San Francisco cafés: spend enough time in any one of them, and you started to recognize the faces, learn the personal stories.
The temperature had dropped a good fifteen degrees in the last hour. The fog, which had been gathering over the ocean when I arrived in the early evening, was advancing up the avenues. When the fog was low to the ground like this, it reminded me of the cloud forests of Costa Rica and Peru. I pulled on my jacket and sat down opposite Thorpe at a small wooden table. He leaned over to pet a shaggy white dog that was tied to a parking meter.
“Are you cold, little guy?” His tenderness caught me off guard. Then he glanced up, as if to make sure I saw him, and it occurred to me that his affection with the dog, like so many other things about him, might actually be a calculated move to manage his image. After all, if he loved dogs so much, wouldn’t he own one?
“This Strachman,” I said. “So he was weird and competitive. That description fits a lot of people I know.”
“Granted. But listen to this. A few days after Lila died, Strachman asked one of his professors about the prize.”
“No crime there.”
Thorpe leaned forward. “His exact question, according to my source, was, ‘Who’s next in line for the Hilbert Prize now that Enderlin is out of the picture?’”
“And you didn’t find this important enough to put in your book?”
“I did put it in,” Thorpe said. “My editor cut it. She thought it confused matters to throw yet another Stanford mathematician into the mix. She had a point; a reader can only keep up with so many characters before they all start to run together.”
“Who was your source?”
“The professor to whom Strachman posed the question.”
According to Thorpe, everyone had known for months that the prize would go to either Lila or to Strachman. They had been neck and neck. But following the success of a paper Lila presented at Columbia in November, the odds had shifted; Lila’s victory was almost certain. Although she never would have admitted it, I knew that Lila wanted that prize so much she could almost taste it.
“Did Strachman win the prize?”
“Yes.”
“Where is he now?”
I braced myself for the news: that he was a world-renowned mathematician, that the Hilbert Prize had paved the way for grander successes, that he had proved the Hodge Conjecture and become something of a star. He’d be well into his forties now, living off the largesse of his earlier accomplishments. But I had it all wrong.
“He gave up math a long time ago. Tried his hand at engineering, and when that didn’t pan out he became a contractor. He was in the news a couple of years ago for repairing the Treasure Island on-ramp to the Bay Bridge after that fuel tanker disaster.”
“You’re kidding. It’s that Strachman?”
“Yep.”
The story had been big at the time. A truck carrying three hundred gallons of fuel had crashed through a barrier in the middle of the night, sending a fireball shooting high into the sky. The driver had been killed, but what really caught the public’s attention was that the much-used on-ramp had been destroyed. With one crash,
a tanker truck had turned a twenty-minute commute into three hours, minimum. Strachman’s company had won the bid to rebuild the ramp. It was supposed to take six months, but Strachman did it in thirty days. The entire Bay Bridge had been closed down on Labor Day weekend to complete the project early, and there was a lot of speculation in the news that the bridge couldn’t possibly reopen by Tuesday. But folks heading home late Monday night found that the bridge had actually reopened eleven hours ahead of the new schedule. It was this last bit of engineering finesse that had made Strachman somewhat of a local celebrity. His picture had appeared on the front page of the Chronicle, under the headline, “Most Efficient Man in SF.”
What was it about the Bay Area, that people always stuck around? The place was a vortex, an inverted pleasure dome on the banks of the frigid Pacific. Despite the outrageous cost of living, the gloomy fog, the certainty of an impending major earthquake, and the blight of homelessness, the Bay Area behaved like a giant swatch of flypaper. I couldn’t remember how many people had told me over the years that they’d arrived in San Francisco with a plan of staying for a couple of years, but had ended up digging their heels in for decades. Would-be rock stars, genius mathematicians, struggling writers, aging hippies—it seemed no one could find it in their hearts to leave. Maybe it had something to do with the water that flowed down from Hetch Hetchy. Maybe it was the climate. Or the food. Maybe it was the music. No matter—I understood completely.
THAT NIGHT, AFTER LEAVING THORPE, I WENT home and found Strachman’s problem in Lila’s notebook. At the top of one page she had written Hodge Conjecture, and below it:
Let X be a projective complex manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.
No One You Know Page 17
