The Mathematician’s Shiva (10 page)

“Of course,” Catherine said.

“Well, it hasn’t been good care. We’re going to take a blood sample. I’d bet my left nut that you’re hyperthyroid.” That’s how doctors talked back then. They still smoked. As in mathematics, there were few women in the medical field, and the men all seemed to behave like gods. These displays of braggadocio look vain and ridiculous in retrospect. Be that as it may, the doctor could keep his left nut. The blood sample proved he was right.

Medication was carefully administered. Catherine’s heart rate dropped. The constant patter stopped as well. There was halfhearted talk of having her retake her Ph.D. prelim, that her medical condition might have impaired her, but it was quickly dropped. So was our marriage. I continued to work on my dissertation with fervor. Catherine went back to beautiful California, to the lovely home of her parents in Marin County. Then she went somewhere else. New Zealand is where I guessed—that was where all her relatives were—but I didn’t inquire about the details. My mother was right in one way. My Catherine was not one to fight back from blows either intellectual or emotional. “We don’t think it would be a good idea for you to contact her anymore,” her parents told me when I called after she moved out of their home and I tried to get her new phone number. They were always so polite. They simply couldn’t just tell me to fuck off.

I would be at best obtuse if I didn’t also recognize that my failure didn’t end with Catherine’s leaving. I can’t understand to this day why for decades I was not willing to make the slightest effort to find her. It was as if I took her parents’ desire for me to disappear as some sort of edict from on high. I, of course, did not forget that Catherine would give birth to a child, our child. But what was once so real quickly transformed into the fuzzy and theoretical. What kind of pathology led me to let go completely, to have no need or desire to come face-to-face and touch or even hear the voice or see a picture of my own child? I still don’t understand it to this day. Yes, Catherine left and made no contact with me, but a real man with a real heart would not have let that deter him.

My wife left, papers were eventually signed, and somehow I managed casually and coldly to erase two years of my life. I found the perverse will to forget that I was a father to someone who undoubtedly wondered who I was and felt my absence with at least a touch of sadness.

After Catherine left Madison, it took only a little amount of time before I began a new era, the phony era, of my love life. It was winter, and it was even colder, of course, than in the fall. One Saturday night I was in bed feeling crappy. Being on the first floor of the building meant that the heat rose to the upstairs units almost as fast as it blew into the apartment from the anemic vents. The large house had not a stitch of insulation, and its exterior was covered in red tar paper made to look like brick. Outside it hadn’t risen above freezing in forty or so days. It was maybe fifty degrees in my apartment, and I heaped blanket upon blanket on my body.

I knew I wouldn’t get a smidgen of sleep that night. I decided to put on my clothes and go back to the basement of the computer science building to my faithful DECwriters and debug my code, which had a habit of blowing up sometimes. It wasn’t blowing up in the traditional way of having numbers go to infinity. Instead, the numbers oscillated. These oscillations were, you could bet your left nut on it, driving me to complete distraction.

It was probably minus-twenty-five degrees outside, which my mother would have told you—like Zhelezniak and Kolmogorov and I don’t know how many Russian mathematicians—is fantastic weather for clearing your mind. It’s the best weather for coming up with original ideas and problem solving.

I walked around the Capitol building and looked up at Miss Forward, lit up on the dome and pointing west. It was where I knew my soon-to-be ex-wife had gone. But that’s not really what I was thinking about. Just random thoughts went through my head. There was an album that I was listening to nonstop at the time, a jazz album mixed with modern African rhythms. They were so exotic to me, these patterns. The rhythms went in and out like waves at the seashore.

Then it came to me. Those rhythms were like my fucking computer program output. There was nothing wrong with what I had done. My computer code was good. The oscillations were real. They were meant to be there. Idiot. The solution was meant to oscillate. Idiot. There was nothing that needed to be fixed.

I’d already written two chapters of my dissertation. Those chapters examining data from low-altitude balloons during storms were adequate science. They represented the kind of journeyman work that used to get people decent but not particularly prestigious assistant professor jobs at places like the University of Alabama. Nowadays everybody and their mother gets Ph.D.’s, professorships are hard to come by, and work like I’d done in those two chapters would get me a decent but not particularly prestigious postdoc at a place like the University of Alabama.

This third and final chapter of my dissertation was special. I knew it would be. I was trying to simulate the movement of air and moisture in a way that mimicked—yes, that word so negative in my mother’s lexicon but so positive for a person concerned with computer simulations of nature—the observations from those balloons. Using computers to solve equations that, as Hilbert had noted long before, still needed to be tied to the foundations of mathematics was heady stuff when I was a student. I didn’t know what I would find. My advisor thought I was crazy for doing this work, that my first two chapters were more than enough to make a dissertation, that I already had a job, and that I was simply trying to do the impossible. But I had the liberty to do such work through the munificence of a National Science Foundation scholarship and computer time that cost little if you ran your programs after midnight.

No one had found anything like this before in computer simulations of the atmosphere. All I had left to do was prove that these solutions were indeed real. Not many atmospheric scientists could prove such a thing. But an atmospheric scientist who had been pushed to pursue pure mathematics and had “rebelled” to study something rooted in the physical world could certainly do so. The mathematical proof turned out to be fairly trivial.

It had been a bad few months, a horrible few months, in fact. I kept working through it all because my computer program, however problematic, was something tangible. Solving equations is not an abstract thing. To even a mediocre mathematician like me, an equation is as solid as an oak tree in my mind. If it wasn’t, I couldn’t solve it. People’s emotions are, on the other hand, much more abstract. You, or at least I, can go crazy chasing after such vaporous things.

I knew then and there that my last chapter was essentially done. I also knew that this would be the kind of work that would draw attention to me in ways that it rarely did to any newly minted Ph.D. in my field. My personal life was rotten, but my professional life was about to take a hugely positive turn. As I walked down the beginning of State Street, I decided to celebrate. The bars would be open for another half hour or so, and I needed to take advantage of what they had to offer.

I walked into the first bar I saw, a narrow little Greek joint next to an old movie theater from the Depression era. I sat down next to a woman maybe thirty years old, with dark hair and ivory skin. To me she looked old, of course. “You look cold,” she said.

“Yeah, cold and happy.”

“You like the cold, I guess.”

“Well, you know, I’m Russian. I’m used to it.” I dropped into my ridiculous Russian accent. The woman was intrigued. My little act worked. We all have tricks to make up for our inadequacies. I drank vodka, of course. She drank gin. The woman had been married and divorced. I had been married and would soon be divorced. We had so much in common. The bar closed and we walked together in the cold air. We continued our conversation in my apartment.

Now how do I put this in a nice way? Well, I can’t. I absolutely cannot put this in any way that makes me seem like anything but a jerk. Here it is, though. All of my life, I had been surrounded by smart people, smart women. Intellect is everything to me. Even drunk, it’s everything to me. Here I was with a woman who couldn’t possibly understand the first thing about what I did intellectually. But she was impressed in a way that no woman had ever been impressed with me. When I told her what I did, her eyes grew big, and she said, “Oh, you must be a big brain.” I liked that. Yes, it’s trivial and petty to like such stupid flattery, but I liked it.

I liked her, too. Laura, her name was. She had two children and a lousy, mean ex-husband who made me seem like an angel in comparison. It was easy to be with Laura. She expected so little of me that it was a relief. Here’s another thing. American women can be so optimistic about what the next minute of life will bring. Where does this sense of a better world just around the corner come from, anyway? It’s a wondrous bit of character, this optimism and hope. No one in my family possesses it. We pound and pound and work until something breaks and a little opening of light appears.

I suppose it could be called optimism that we assume we can see that light eventually. But no, it’s really different. It’s not American at all. It’s our egos at work, not blind optimism about the world around us. It’s the idea that despite all the obvious and unforeseen obstacles, we will manage to beat the devil. It’s desperation that fuels us.

But not Laura. She felt that her life on this Earth would change for the better one day. It was a feeling she held as deeply as the devout believe in God. This was something new to me, this belief in the power of positive thinking. I couldn’t believe it myself, but to be around that glow was life affirming. Who wouldn’t want that?

I never saw Laura after I moved to Tuscaloosa. I never tried to meet her when I came to visit my parents. Years later I got an e-mail from her. She had seen me on a CNN show about a hurricane that had hit the Gulf Coast. “I always knew you’d be famous someday,” she wrote.

There would be other Lauras in Tuscaloosa. Of course they had different names. I liked the women in Alabama a great deal. I liked the flattery they dished out, little pieces of candy to make a man feel strong and powerful.

This is what Anna and my mother meant about me giving up on love. But I didn’t really think that was true. I had given up on the kind of romantic love they wanted for me, yes. Their ideal was that I should find an equal, someone strong and as intense and powerful as they were. Anything less was unacceptable. The truth was that I didn’t believe I possessed the strength to be with someone like that, at least romantically. I’d tried that once. Catherine was like them in her own way, independent and judging others by lofty standards.

How many demanding women can one man have in his life? How many judgments can be made on him before he starts to feel their weight and feels inadequate, clumsy, and lacking? I had two women like this. Their constant evaluations of me were something that, while difficult, were also valued because they pushed me to do more. At the time I was convinced that there would be no more Catherines in my life. Instead, there would be only Lauras. These women weren’t trying to achieve anything artistically or intellectually, weren’t striving to live the kind of life that leads to write-ups in magazines and in the
New York Times
, and weren’t even consciously trying to make the world a slightly better place. They wanted their houses to look nice. They wanted their children to be respectful. They starved themselves to keep their figures and spent copious amounts of money on clothes and makeup. My mother couldn’t understand my attraction to these
lalkas
and neither could Anna. My father was indifferent. My uncle understood perfectly.

“Not every man needs to find a woman who understands him. Sasha already has that anyway,” he would say to my mother in my defense. Thank you, Uncle Shlomo. You know what it’s like to be ordinary.

T
he mathematicians arrived. They came to the land of Badger Ingenuity on flight after flight on a ridiculously cold day. A Canadian high-pressure mass descended on my home state, and it looked like it would stay put for at least the entire shiva. This was a good thing in a way. It wouldn’t snow. The sky would remain blue day after day. If we were lucky and ventured north a bit outside of town, we might even be able to get a peek at the northern lights at night. But the absence of clouds meant a prolonged period of temperatures below zero, perhaps minus twenty in the wee hours of the morning. I was going to freeze to death. Bruce, too. We had become weather wimps, and in our family, being a wimp about anything was a definite black mark. We had both heard the withering criticism about any of our complaints as children. “You’re kvetching over this? Over this? Have a soldier put the muzzle of a rifle to your nose and then you’ll have something to complain about.” We couldn’t compete against our parents’ past misery, and they never let us forget it.

Some flew directly to Madison. Others found their way through Milwaukee or Chicago. Calls came from the most narcissistic and cheap of the bunch to provide a free airport shuttle service and housing. I had no patience for such nonsense. I could feel a crustiness that I had worked so hard to smooth over in Tuscaloosa return quickly. Maybe I was even emboldened by the absence of the crustiest of the crusty, my dearly departed mother. Whatever the reason, I dealt curtly with these
shnorers
and would say, “This isn’t a wedding, you cheap bastard. It’s a funeral.” I would speak sometimes in English, but usually in Russian. “Rent a car. Take a cab. Walk. I don’t care. Mooch off your math friends in Madison. There’s a HoJo’s walking distance, more or less, to the synagogue if you need it.” I didn’t wait for any response before I hung up.

Our block of rooms reserved at the HoJo’s by the math department’s secretary—or I should say the H Jo’s, since the “o” light in the “Howard” had burned out twenty years before and had never been replaced—filled up quickly. One of the sweetest mathematicians on this planet, Ollie Knutson, came forward to organize the logistics of housing these people and shuttling them around town. Ollie was a number theorist of considerable note who had “come home” from UCLA to take a professorship. His father, like my parents, had been a part of the faculty in the math department since the 1950s. Ollie was a saint that week. I can well imagine what he endured.

They came from Russia, France, Israel, Korea, Germany, and Japan to pay their respects to one of the two students of Kolmogorov who probably exceeded the genius of the master. The other one? Vladimir Zhelezniak, sly, humorous, self-deprecating, everything my mother was not. He was also my mother’s mortal enemy. Zhelezniak would be there as well. “He’ll come to dance on my grave, that one,” my mother said to me when she was sick. She rarely mentioned his name, but every time I heard something negative about “that one” or “him” or “the bastard” as a child, I knew to whom she was referring. “Don’t give him the satisfaction.”

I’d never met Zhelezniak. I’d seen pictures of him, beagle-faced with sad, big eyes. His bald crown was fringed with curls. A man possessing a face like his, so obviously Semitic to the Russian eye, would have had a difficult time as a child and a young man, I knew. He would have had to prove himself quietly and never make himself and his genius too visible, except in the presence of someone like Kolmogorov. My mother’s beloved great Kolmogorov didn’t give a shit who your parents or grandparents were, and only cared about the size of your brain. At nineteen, Zhelezniak shocked the mathematical world by solving Hilbert’s thirteenth problem. My mother, however, was not shocked. She was outraged.

It was 1957. I was eight years old. My mother was on the phone in the kitchen with Kolmogorov himself. Who knows how many Soviet agents were listening along? My mother complained bitterly about being usurped, about being unrecognized for a major contribution to solving this problem that she made in 1947 but had not published. Why hadn’t she published it? It wasn’t close to the full solution. In my mother’s opinion, no proof was worth publishing unless it was substantially completed. Kolmogorov knew what my mother had done. He passed her partial solution on to Zhelezniak, who finished her work. In my mother’s opinion, a nineteen-year-old boy was taking credit for everything because that’s the way the Soviets wanted it. It was a good piece of propaganda for them. “This will never happen again,” she swore. “My work will not be stolen. Never.” I didn’t hear the other half of the conversation from Kolmogorov, but I could tell that he was trying to console her. His efforts weren’t working.

My mother had other enemies as well, although in the balance, she had many more friends. Her warmth and coldness were without pattern. Of course, she was warm to me nearly always. I was her flesh and blood. She remained warm to my father as well, even after they separated. I think this was partly in recognition of his having to deal with her difficult nature for so many years. Her brother and her father, too, she always held dear, as well as Bruce and Anna. But with strangers, you never knew how my mother would react. She would make snap judgments, and once those judgments were made, they did not change. A person was wonderful or they were an idiot or selfish or amusing or creative. Everyone she met was put in a pigeonhole almost instantly. Emotional nuance? I don’t think she had time for it.

According to my mother, Vladimir Zhelezniak was an unrepentant thief. That he continued to excel in mathematics for decades following his solution of Hilbert’s thirteenth problem, just as she had following her solution to Hilbert’s fifteenth problem at a similar age, meant nothing.

My mother’s mercurial nature, I’m sure, added to her allure in the mathematical world. She wasn’t just a mathematical genius but one about whom stories could be told. There were lots of them. Here’s one that involves Zhelezniak. It took place in 1968 in France, a crazy time of student riots. Nowadays, when you go to the University of Paris and notice its proto-IKEA tackiness and ugliness, you can blame it on that terrible year. After the riots, French muckamucks quietly made sure that any new parts of the university would have campus layouts designed to make it difficult for students to congregate in large numbers.

The unruly demonstrations in Paris and elsewhere in the 1960s and 1970s were predictably accompanied by a period of overheated sexual behavior throughout the West. My mother found the sexual revolution to be crass and tasteless. It was all too mechanical and depressing for her. She brought along a female Ph.D. student to give a talk at the Paris conference. Part of my mother’s job, or at least she thought it was part of her job, was to make sure that her students didn’t do something stupid at these conferences that they would later regret. “They should have ‘premorse,’ but not remorse,” was how she put it.

Zhelezniak approached the Ph.D. student to compliment her on her presentation. Perhaps he was trying to do more. Who knows really, but when my mother saw Zhelezniak with her student at a table during a break in the proceedings, she seethed. I’ve seen that look in her eyes. I can well imagine her grimace as she looked around the room. Her eyes spotted the carafes of coffee in the center table—bad coffee can be found in France as easily as it can be found elsewhere—and her plan immediately came into focus.

She grabbed a carafe, walked over to them, and asked Zhelezniak if he would like more coffee. Perhaps this was the first time my mother had said a word directly to Zhelezniak in eleven years. Zhelezniak held out his cup. My mother promptly dumped the entire pot into his lap.

Acts like this—one great mind dumping hot coffee into the lap of an adversary—can be, and usually are, remembered for decades in academic circles. The truth was that she hated the notoriety caused by her flare-ups.

“Everyone thinks their children are special,” my grandfather once said to me. “They delude themselves about their sons and daughters, their beauty, their minds.” He said that in Russia people thought he was deluding himself about Rachela, who to most simply looked lost, absent from the world. But he knew. “I could see her mind working like a machine,” he said. “When Grozslev came to our little hovel and began to give your mother lessons, his face that first day had such a surprised look. ‘What have we here?’ That look said it all.”

“We do not come from stupid people,” my grandfather would sometimes say to me when he sensed that I was showing signs of “being an American,” which to him was any sign that I was relaxing my mind and resolve. That is certainly true. Stupidity also was not present in any of my mother’s friends or admirers, at least when it came to mathematics. Some had talents in other realms as well. Music, of course. Painting and sculpture, too. Some were engaging conversationalists, and others managed to operate in the real world with ease and without a trace of overt strangeness, without giving away the fact that they were different.

“They’re here.” My father called me from his office. “All of them. They are crawling around the building like giant ants.”

“Why don’t you leave? Go home. You can come here if you want.”

“I have work to do. Serious work. I need an office. A chalkboard. A desk. Something austere and uncomfortable. I’ve shut the door. Locked it. Those bastards keep knocking. They know I’m here. Some want to get into your mother’s office. They want the key.”

“Tell Marie not to give them access. No way. Ollie, too.”

“I know, I know. I called to tell you about Otrnlov. I heard he’s coming to the house. He’s walking over right now.”

Konstantin Otrnlov. It was a name I knew well. From a theoretical standpoint, it’s perhaps expected that a great mathematician would attract a crazy acolyte or two. As a practical matter, these acolytes can be at best a pain in the ass and at worst dangerous. Konstantin Otrnlov wasn’t sane, was devoted to my mother, and you never knew just what he might do.

Otrnlov had come to the United States from Latvia in 1978, and while he had been unable to obtain a position at an American university, he eventually earned a tidy sum of money with a carpet business in New Jersey. It was enough to allow him to return part-time to his love, mathematics. His admiration for my mother turned into an obsession in about 1990. He proposed marriage to my mother. He mailed her jewelry, which she would promptly return. He even bought her a car, which he tried to give her at a conference. One summer he rented a house across the street from my mother, living there when he wasn’t in New Jersey. My mother ignored him. He was never let into our house.

My mother viewed Otrnlov’s obsession as harmless until 1998, when he apparently anointed himself protector of all things Karnokovitch and physically attacked a mathematician at a conference for the sin of asking my mother a question that Otrnlov deemed hostile. Otrnlov was not a small man. I’m sure those blows hurt.

“You be careful with him,” my father said. “He has some ridiculous idea that the proof is in the house. Anyone else home?”

“Bruce is, yes. Anna is visiting an old friend.”

“Tell Bruce to get out of there fast.”

“He’s in the tub trying to warm up.”

“Otrnlov’s ideas. I’ve heard some of them. After Otrnlov leaves, throw Bruce out of the fucking tub, give him the keys to the car, and tell him to go somewhere, anywhere. I am not kidding.”

“Anna has the car.”

“
Yob tvoiu mat
. If Otrnlov asks about Bruce or Shlomo, tell him you don’t know anything. You don’t know where they are. Tell him that Bruce took off and went somewhere. Do not tell Otrnlov that Bruce is in the house. Understand?”

“Why?”

“I don’t have time to explain it. I need to get back to work. But Ollie knows.”

As my father hung up, I looked out the window and waited. It was a twenty-minute walk from Van Vleck Hall to our house. He’d arrive soon enough.

Otrnlov did love my mother. It was a deranged love, certainly, but he had come to Madison to honor her. With the others I was beginning to think that the hoopla was less about my mother than it was about the field of mathematics itself.

Imagine mathematics as a canvas where every mathematician of worth fills the missing white spaces. Hilbert came along in the twentieth century to do something no one had done well before. He assessed the canvas of mathematics and identified what white space was left. Since Hilbert, much of that white space had already been filled by both those painting details with the smallest of brushes, people like my father, and those who filled in the bigger blank spaces, people like Kolmogorov, Zhelezniak, and my mother.

Eventually, the canvas would be full, essentially complete in all its beauty. What would be left would be trivial. Mathematics had already gotten to the point where the canvas looked beautiful. My mother knew it. “It’s a good thing I came when I did,” she said. “Since the 1970s, what have been the discoveries? Not much.” Partly people were coming to honor my mother, sure, but they were also coming out of nostalgia for a time when mathematics was still great, when one highly skilled and gifted mind could do so many remarkable and exquisite things.

At the time of my mother’s death, Otrnlov reportedly was working on a biography about her. I knew that he had gone through each and every article and word my mother had ever published. I’d heard that he’d wanted to write about my mother’s personal life as well, but if so, he hadn’t contacted me yet. I knew that when he did I wouldn’t cooperate.

Otrnlov walked up to my mother’s house in a New York Giants parka. A fedora covered his still-full head of hair. His thick mustache had turned completely gray since the last time I had seen him. I swear I could smell him on the other side of the door, which I wasn’t going to open. I waited for a knock.

“Otrnlov. Get the fuck out of here,” I shouted.

“Sashaleh, is that you?”

“Yes, of course. Who else? Now get the fuck out of here and don’t come back.”

“I just came to say hello to you, Sashaleh. Your father said I should come by.”