The Mathematician’s Shiva (2 page)

“I don’t have a choice. I’ve already lost a lot of blood.”

“They could give you more. Blood. They have lots of that. Blood is cheap.” My uncle put a bottle of vodka on the nightstand. A nurse walked in to protest as he opened it. My uncle looked completely different than my mother, with dark Mediterranean skin and a perpetual five o’clock shadow. His curly thick black hair, graying in streaks, was combed straight back. When he looked at the nurse, he did so with the exact same expression that my mother had used, intentionally or not, to scare thousands of undergraduates over the years. The nurse scurried down the hall.

“Rachela, we should take off your jewelry,” my uncle said. He pronounced her name like it would have been pronounced in her hometown,
Rookh-eh-leh
. “Otherwise the
ganovim
at the funeral home will steal it.”

“He’s right,” my father said.

“Of course, he’s right. Shlomo knows these things.” She smiled faintly. “It’s getting hard to talk.”

“Don’t talk then,” Shlomo said. “Just listen.”

“I’ll have plenty of time to listen when the worms crawl into my grave. A little vodka would help.”

My uncle took the bottle to her lips and she had a sip. Then he lifted the bottle high and poured a shot down his throat.

“That’s better,” he said. “This is hard, you know. I can’t believe it.” He passed me the bottle. I drank with my uncle, which was nothing new. Even my father, Viktor, drank, although he refused to drink from the bottle straight and got a cup from a drawer in the room.

“Viktor, that’s a urine sample cup,” my uncle said.

“So?’

“This is good vodka. It isn’t piss. I’m not pouring good vodka into a piss cup.”

“All of a sudden you have principles?”

“All of a sudden you don’t have any class?”

“It’s a cup. I need a cup. The bottle already has your spit on it.”

“Enough, you two,” I said and looked at my mother.

“It’s like old times.” She smiled and coughed.

I took the bottle from my uncle and poured vodka to the top of my father’s urine cup. “I’m going to spill good vodka,” he said.

“It won’t be the first time,” I said.

He drank it down in one gulp. A smile flashed from his thin lips.

“It is good.”

“I told you it was. My sister is dying. I’m not going to bring cheap stuff.”

Three minutes later my father asked for more. “I want to make a toast,” he said. My mother’s monitor beeped as he raised his cup. “To my Rachela. Who gave me love, gave me a son, and had the strength to cheat death.”

“The vodka is making you sentimental,” my mother said.

“Yes, it is. I didn’t want to be here, you know. A dying woman. A hospital. A depressing thing. But I’m glad I came. Tomorrow it will be chaos. All of those mathematicians. Tonight it’s just us.”

“I’ll have another sip,” my mother said. My uncle dutifully obliged. “This bottle won’t last,” she said.

“I have a case in the car.”

“You should get more.”

“You won’t die while I’m gone? I want to see your last breath. I don’t know why I just said that. But I think it won’t hurt so much if I do.”

“I promise. I’ll wait until you get back.”

Shlomo walked out of the room. A nurse entered. “Is there anything I can do to help?”

My mother laughed. “Help? I’m here already. That’s enough. Go help someone who needs it.”

“Okeydokey,” the nurse said and walked out.

“There’s a cross over my bed, isn’t there?” my mother asked. I nodded.

“Take it down. I don’t want Yozl Pandrik looking down at me when I die.” I walked over to the bed, reached high, and yanked. Jesus wouldn’t come down.

“He’s nailed to the wall. I could have told you that,” my father said.

“Take a towel and cover him up. I won’t see him in the next life. I don’t want to see him in this one either.”

“Don’t start, Rachela,” my father said. He was slurring his words. He poured the last of the bottle into his cup.

“You’re right,” my mother said. My father pulled out his notebook from his suit pocket. He could work anywhere, and sometimes worked better drunk than sober.

“Riemann?” I asked.

“No, something else.”

“It’s always been Riemann,” I said. My father had been trying to solve the Riemann Hypothesis, a major problem in mathematics, for thirty years. He certainly wasn’t alone. But to try to achieve something massively significant in a field where you’re by and large useless after your fortieth birthday—and my father was seventy-seven—is the height of both delusion and optimism. That said, old mathematicians tended to shrivel up entirely intellectually. At least he was trying.

“Today it’s Navier-Stokes,” he said. This too was one of the great unsolved problems in mathematics.

“You have a big appetite, but you don’t know anything about partial differential equations.”

“And you do?”

“I know how to use them. Mother is the one who knows how to analyze them. And you’re at Wisconsin, not Minnesota.”

“Minnesota is for the dull witted,” my mother said. “Enough talk about nonsense. Now that you two are here, I want to say something.”

“Go ahead, Rachela,” my father said.

“I want to say the obvious. OK, this family isn’t the best. But neither is it the worst. We have our strengths. We are still close. I will die happy knowing this.”

“I’m glad you think we’re still close,” I said. Why did I say such a pissy thing? After all, my mother was dying. I should have let her be and enjoyed my last hours with the one person that I loved more than myself. I am not always proud of my behavior.

“You know what I’m saying. Don’t be an idiot. Not with me. Not with your father.”

“Mother told me she would rise from the grave if I didn’t spend time with you after,” I said to my father.

“I’m an atheist. I don’t believe in such things,” my father said.

“He’ll spend time with you,” she said. “He’s gotten old. He needs you. And you have the American sickness of niceness. You don’t hold a grudge.”

“And you’ll rise from the grave if I do hold a grudge?”

“Sure. If Yozl Pandrik can do it, then why not me? Go get the towel.” I walked into the bathroom and grabbed two brown paper towels.

“
Pani Karnokovitch?
” a man asked from the hall entrance. My mother spoke four languages fluently: English, Russian, Yiddish, and Polish. Her Hebrew and German weren’t half bad, either. But Polish was her mother tongue, and she spoke it like the dukes and duchesses of old. It was a formal style of speaking, long forgotten. My knowledge of Polish is spotty, and as a result, I never understood much of what she said when she talked to Poles. My father, a Russian native, was a little better. My uncle, who lived in Poland until 1957, of course was fluent. When I heard the words “Mrs. Karnokovitch” in Polish, I turned around.

“
Tak. Prosze niech ksiadz wejdzie
[Yes, it’s me. Please come inside, Father],” my mother said.

His name was Father Rudnicki. I didn’t know him.

I walked over to the priest, and shook his hand after I stuffed the paper towels into my sport coat’s interior left pocket. My father looked up from his notebook and mentally recorded the priest’s presence. “This is my son. He lives in Tuscaloosa,” he said. “I’ve never been.”

“You’re a long way from home,” Father Rudnicki said to me. “I understand it’s very pretty there.”

“He studies hurricanes, flies inside them to make measurements. It causes us a great deal of worry.” My father went back to his notebook.

“It’s good to have parents who care about you,” the priest said.

“Even at fifty-one, yes, I think it’s probably true,” I said.

A nurse with a golden smile walked in. “Is everything OK here?”

“I think everything is fine,” the priest said. “Nurse, did you know that Professor Karnokovitch is a hero in her Polish homeland. Please be good to her.”

“I didn’t know.”

“It’s fine what she’s doing,” my mother said. “A few more hours and the blood will drain out of me. I can say good-bye.”

“You still have your sense of humor,
Pani
Karnokovitch.”

“It’s not really humor,” she said. “It’s a statement of fact.”

“I’m sorry.”

“You shouldn’t be. I’ve had a full life. I can go now without any regrets.”

“How do you know my mother?” I asked.

“Through the diocese.” My mother, while working on her family history, had managed to wrangle the Wisconsin Catholic Diocese to help find records of her family in Poland. “I happened to see her name on the list of patients. Of course I had to come visit.”

“It’s good you’re here,
prosze ksiedza
,” my mother said. “Sit down. We have no more chairs, but you can sit on the bed if that is OK with you.”

“Of course.”

“My brother. You’ve never met him, but you’ll like him. He will be back soon. I do have a request,
prosze ksiedza
.”

“Anything.”

“The cross above my bed. As you know, I’m not a Christian.”

“Yes, I’m aware.”

“My son and husband say it’s nailed to the wall.”

“That is correct.” My father once again joined the conversation. “She’d like it removed,
prosze ksiedza.
”

“Thank you, Viktor,” my mother said.

I looked at my parents and then watched the priest, taken aback by the sheer nerve of my mother and father. This was a time for me to stay in the background. My parents were conjuring forth something from a place I could only witness with a mixture of worry and admiration, but never fully understand.

My mother had what in Yiddish are called
bzikes—
it comes from the Polish word
bziki
and
“
issues” I guess is the closest translation—and she had so many of them that some might have viewed her as an impossible walking tic. My father, when they were together, off and on accommodated, no, more like celebrated, every one of these
bzikes
. I think I know exactly why. Her craziness was happily wed to her intellect. There are no reasonable geniuses in this world, I am convinced.

“My wife, may the Lord bless her, is of the same faith as our Lord Christ. She has brightened the world in her own special way,” my father said. “Her views are peculiar, I know,
Ksieze Rudnicki.
But whatever fate befalls her in the world to come, she deserves to die with the dignity that comes of her own faith, yes?”

“Mister Karnokovitch,” said Father Rudnicki. “You know I cannot do this.”

“Yes, I understand. You cannot personally do such a thing. To be truthful, being of the same faith as you, neither can I. But for my son such a thing is possible. Perhaps you can arrange to have someone in the hospital provide him with the necessary tools.”

“I couldn’t even watch your son do this, to be honest.”

“I understand this, too. You do not have to be here when it happens. But it is a dying woman’s request.”

“I’ll see what I can do,” Father Rudnicki said and walked out of the room.

“He will be back, I’m sure,” my father said.

“No doubt,” said my mother. “And if not, Shlomo, I’m sure, has tools in his car.”

I
remember it this way. My father and I are sitting at the kitchen table. I am six years old, small for my age. One of my hands is playing with my long blond curly hair. The other holds a red pencil with white lettering. My hand-eye coordination is not the best, but my father, who sits next to me, doesn’t seem to mind my poor handwriting. In my spiral notebook, he has drawn a picture like this:

He tells me a story about a boy who lives in a city with six bridges. There are two islands in this city. On one of these islands there is a chocolate store. The only store on the other island has bananas. The boy wants to make chocolate-covered bananas. My father knows I like these things, of course. That’s why he’s added this detail.

“What’s the boy’s name?” I ask.

“He’s a boy. Just a boy like you. Does it really matter what his name is?”

“Yes, I want to know.”

“OK, then I’ll tell you. The boy who likes chocolate-covered bananas is named Leo. He is a German boy. Eventually he will grow up and move to Russia. He will become a very famous man.”

“Like a prince?”

“No, not like a prince. He will become famous for being very clever. Like your mother. A prince in Russia will adore him and give him everything he needs.”

“He can have whatever he wants?”

“Within reason, yes.”

“I want to be like him.”

“Of course you do. He had a good life. As a child in Germany, he liked to walk around his city. Back then children could walk wherever they wanted. Not like now.”

“What’s the name of the city?”

“Königsberg.”

“And he wants to make chocolate-covered bananas all by himself?” The thought of doing such a thing, of course, excites me.

“Yes, he knows how to do this. He is a very clever boy.”

“Can you show me how to make them?”

“Of course. If you can show me that you’re as clever as this Leo.”

“What made him so clever?”

“Well, once a week his mother gave him enough money to buy one banana and the chocolate to cover it. Some weeks he would go to the chocolate store first. Other weeks he would go to the banana store first. He’d do this on the way back home from school, and he would always walk across all six bridges in his city along the way. He liked to look at the water.

“But here’s what made him clever. He never crossed the same bridge twice.”

“That sounds easy. Anybody could do that,” I say. I start to imagine making my chocolate-covered banana, my father showing me how.

“Is it? Show me.”

I look at the drawing, chewing on the back of my pencil, tasting and sensing with anxiety the mix of metal and spongy plastic against my small teeth. How did Leo do such a thing? I think of myself in a city from long ago crossing from bridge to bridge. It isn’t hard to imagine. I have a glorious image of wooden arch bridges, the water under them crystal clear, abundant with jumping, silvery fish.

At first I make a mistake. I assume that the school and the house are on the same side of the river. I can’t find a way this boy Leo did this trick.

“Leo is very smart.” I’m so disappointed. In your youth, failure is never tempered. It always feels monumentally horrible, irrevocable, and complete (at least for an hour or two it does). I’ll never learn how to make chocolate-covered bananas! But then, and this is how it always works if it does work at all, the solution comes to me visually. “His school and house are on different sides of the river?”

“Yes.” My father shows a glint of a smile. I can always recognize that look, the way his face stretches taut. This is my father when he is lost in the moment. He knows I’m on the right track now.

I take the pencil out of my mouth and draw a path. “That’s easy. I could do that, too. There are lots of ways.”

“You’re a clever boy,” my father says.

I’m pleased with myself. In hindsight, I usually view my childhood ego as some monstrous thing. I thought that not only would I achieve greatness, but that I fully deserved it. My grandfather Aaron—who lived in our home through my childhood and beyond—called me his
ayzene kepl
, his little iron head. When I first heard this phrase translated, I thought he was teasing and calling me stupid. But I was quickly reassured that this was a good thing. I had something substantial in there, the mind of someone older.

“Can we make bananas now?”

“One. Just one. Just like Leo.” That’s what we do. We walk to a store on Regent Street and buy one Cadbury chocolate bar, its gold foil signifying its luxury. Then we walk to Park Street to the closest grocery, and buy one banana. We stand in the kitchen, and my father tells me that chocolate must be steamed to be melted. I stand over the stove on a chair and watch the chocolate liquefy and spread in the stainless steel pan, glistening and sending forth wisps of vaporized oil as it melts. My father has no taste for chocolate. It’s my mother’s weakness, not his. He eats apples, sometimes whole onions, after he peels the outer skin into a thin spiral with a pocketknife. But this land of plenty we live in never ceases to give him pleasure. I can tell he’s enjoying this activity because he now has the ability, within reason, to buy anything he wants and can do something as whimsical as cover a banana in chocolate.

Years later, I’ll remember this day and realize that the Leo in this story is Leonhardt Euler. In truth he’s not a boy walking across bridges but a man, one of the finest mathematicians ever known. He will found a field of study in the eighteenth century, topology, which will consume the mental energy of many friends of my parents. And yes, it will also take up the mind of the great Kolmogorov for some years, a restless mind that will touch almost all of mathematics.

If you think it’s torture to put a kid through such an exercise, I vehemently disagree. My father is teaching me to be a mathematician, and like most any other skill or art—and mathematics is definitely an art—those who learn early have an innate advantage. The tennis players you watch at Wimbledon and the quarterbacks you see in the Super Bowl are never taught their craft for the first time in high school or college. Why should it be any different for mathematics?

Just so you know, my father was being easy on me. The problem Euler faced was actually ridiculously and hideously more difficult. Euler wanted to cross seven bridges, not six, in his hometown of Königsberg. The real answer to the actual problem—crossing seven bridges—is that it doesn’t have an answer. It is impossible to walk across seven bridges without using one of them twice. Euler proved this to be so. If my father had given me, at the age of six, this impossible problem, tried to get me to realize the problem was impossible, and prove it was so, now that would have been torture.

A proof. An ironclad irrefutable statement of what is or isn’t possible. For three centuries at least, mathematics has been all about that one thing, and every new proof is celebrated by the community. Even minor proofs get a few minutes of sunshine.

I’m not a mathematician. Despite my early training, I don’t have my parents’ talent. I am good. I am clever. I am certainly not brilliant. But like my parents, I have a love for the elegance of proofs, their absoluteness.

Over the course of my childhood I will be introduced not only to little Leo but to little Isaac (Newton), Blaise (Pascal), Pierre (de Fermat), René (Descartes), Gottfried (Leibniz), and many more, all of these mathematicians playing the role of resourceful and independent boys, and all giving me the idea that solving problems always came with tangible rewards. Ah, if only life were so simple. Then there were the men and women, real men and women of today, not imagined boys, who came to visit us, and they knew the names of these mathematicians as well. In contrast to my father’s fastidiousness, many seemed unable to even tie their shoes correctly.

When my father warned of the horde of mathematicians that would descend upon our house after my mother’s death, I knew what to expect. They would be grieving, but not like my family. They would be mourning not my mother but the loss of ideas, the loss of intellect. They would no longer be able to sit in a room with her and feel the magical presence of someone with the talent to find the hidden gem in what is thought to be all dross.

The Hasidic Jews have a word,
dveykus
, for men who always possess the spirit of God inside them. My mother, unlike my grandfather, did not believe in such things literally, but when it came to understanding mathematics, she knew that she possessed the equivalent of
dveykus
. Like a
rebbe
with acolytes who feel blessed just to be around someone whose goodness and spirituality are always present, my mother had her followers. I had been with them all of my childhood. They sought me out for my secondhand
dveykus
even as an adult. Now they would come and I would have to be their gracious host for seven days, the days of shiva that are a traditional part of Jewish mourning. My uncle called them the
szalency
, the crazy people. Yet he would supply the vodka, and soothe them in his own way.

But I am getting ahead of myself. In this story, my mother isn’t even dead yet, and already I’m talking about her shiva. We need to go back to the hospital.