The Mathematician’s Shiva (23 page)

“
Która porcja jest wieksza
?” Amy asked. I’d never heard Polish spoken with a New Zealand accent before. Pascha didn’t seem to mind. She reached down and pecked at the five-Cheerio dish. Amy took the four cheerios off the other.

“She got it right, see? So far, she’s only got it wrong once. She knows which one has more.”

“That’s a smart bird, Amy,” Andrea said. “But what did I tell you about not touching her.”

“I didn’t touch her. I just opened the cage and Pascha came out. So then I had to touch her.”

“It’s going to be a lot of work getting Pascha back in,” I said.

“Oh no, it won’t,” Amy said. She reached for the bird with her right hand.

“Be gentle,” Andrea said.

Pascha was still in a good mood. She was bobbing her head now and then as she focused on Amy. Pascha didn’t like big crowds, but having a few people in a room talking softly was something she usually enjoyed.

“I know what to do,” Amy said. “Just what I did when she got out except backwards.” She extended her right hand vertically and Pascha hopped on. Amy walked to the cage and stepped onto the chair that she had evidently placed there to open the cage door earlier, making sure to keep the hand upon which Pascha was perched steady. Standing in front of the black wire cage, Amy raised her arm and slowly guided Pascha through the door. I watched as Pascha hopped off and found her usual perch.

“You can close the door now, Amy.” I said.

“I know, Grandpa.”

“
Dobry ptaszek
,” I said. “That means ‘good bird,’ Amy.”

“Does she speak English at all?”

“No, Amy.”

“I can learn Polish. Say that again, please.” I repeated the phrase. “
Dobry ptaszek
, Pascha,” Amy said. “See. It isn’t that hard.”

DAY 5

A
fter I said good-bye to my daughter and granddaughter, I felt as good as I had felt in decades. I knew what my father thought about these instant additions to our family without even asking him. He looked at the generation beyond me and imagined being a beacon for them, an essential source of wisdom, and an occasional source of financial backing for big-ticket items, like a home.

But I had no such plans. My state of joy wasn’t emanating from a vision of a happy future. I simply felt vindicated, but no, that isn’t quite the right word. In Russian I might say I experienced a
nevoobrazimaya pobeda
, a sense of relief that my past hadn’t been a black mark after all, that it had, not through anything I had actively done, produced something of never-imagined value. I had a daughter with a warm heart who saw the world with clear-eyed realism and a granddaughter who possessed a rare mind capable of focusing on problems that bored or scared mere mortals.

As I write these words, that granddaughter is studying mathematics at Yale. After she won the Woodward Prize—normally awarded by the American Mathematical Society for the best paper published by a graduate student—at the ridiculously young age of sixteen, a fellow freshman clipped out a picture of my granddaughter from the
Yale Daily News
, framed it with makeshift paper Ionic columns and an arch, and pinned the whole thing on the bulletin board outside the math department office. It became an ad hoc temple where students could kneel and pray prior to their calculus and differential equation exams. My granddaughter became, for a time, Yale’s unofficial matron saint of good undergraduate math grades. Of course, I couldn’t have predicted such a future at the time. I was simply joyful over what she was, not what she would become.

I liken my marriage in my twenties to the ill-chosen shot by a basketball player, done without any thought from an impossible angle and motivated by a mix of pure adrenaline and ego, which his coach watches with complete despair as he involuntarily shouts “nooooo.” Then, as the shot miraculously drops through the net, the coach’s cry changes instantly from “nooooo” to “yessss.” My marriage had been a shambles in its motivation and execution. But it had produced something wonderful and miraculous.

Anna came home that night and noticed the difference. “You had a good evening, didn’t you, Sasha?”

“The best.”

“You deserve some luck.”

“Not really. I’ve been a lucky man all along.”

“You think so? Really?”

“Definitely. You look like you had a good evening yourself.”

“It wasn’t bad.” Anna looked down at the Persian carpet. I could still see her smile.

“You don’t want to talk about it, do you.”

“No.”

“You don’t want to jinx it?”

“I’m not superstitious, Sasha.”

“You think you’ve been lucky?”

“I don’t allow myself to be unlucky. I don’t have any complaints. It’s been a good life.”

“I think so, too.”

“I feel good for you, though. A man should have children. Ones he knows about, especially.” Anna reached up to give me a sisterly kiss on the cheek.

Our happiness would not, however, be allowed to last through the night. The phone rang a little before 3:00
A.M.
, never a good sign. It was from the ranger of the Wisconsin Arboretum. “Is this the home of Alexander Karnokovitch?” Not too many people were calling me by my legal name during the shiva. Even if the call had come at a normal hour, I would have sensed that it was important.

“Yes, of course.”

“I’m sorry to call you so late, but I received your number from someone. He was crazy and ranting, but he did come up with this number when I asked if there was someone that I could call for some verification.”

“Big older man? Bushy mustache? Russian accent? Konstantin Otrnlov?”

“He was Russian, yeah. But no, not that name. Zhelezniak. Vladimir Zhelezniak. You know him?”

“Sure I do. Where is he?”

“Let me tell you how I met him, first. He was skiing in the Arboretum. Just in his long johns. Drunk. With a woman. Ms. Virginia Potter, according to her Massachusetts driver’s license. It’s twenty below outside, and he’s skiing after hours in his underwear.”

“That’s what he does. It’s hard to explain. Maybe you knew my mother, Rachela Karnokovitch?”

“Yeah, I figured that you must be related. Nice lady. Sorry to hear about your loss.”

“She used to ski, too.”

“Yeah, I’d see her all the time. Sometimes with your father.”

“She and Zhelezniak, they both had the same mentor in Russia. He believed skiing, especially in the cold, inspired the mind.”

“OK, I get that. But I don’t think your mom ever came out here in her nightgown.”

“Probably not, no.”

“This guy, Zhelezniak, he was out here at two
A.M.
And he was in his underwear. Just about naked. I wouldn’t have noticed except I was coming home late from a date and I saw him and that woman alongside the road. Couldn’t believe it. I pulled over. He started screaming at me. I told him to get in the car. Man, he was sauced, all that alcohol just came off him. She was, too.”

“Can I talk to them now?”

“They wouldn’t cooperate. I’ve never seen anything like that in twenty years. Good skier, though.”

“He’s been skiing for fifty years. Can I talk to Vladimir?”

“Um, no. I mean, he isn’t here. I called the cops. They picked him up. That happened about ten minutes ago. I processed a couple of forms before I’d forget the details of what happened. Then I called you.”

“You had them arrested?”

“Well, yeah. Crazy guy. Screaming. Her, too. I didn’t know what he was saying. Screaming in Russian. Who knows? But that woman. I knew what she was saying. She’s got a mouth on her.”

“She’s a professor of mathematics at Amherst.”

“Yeah. And I have a master’s in forestry from Yale. Big deal. You still need to treat people with respect. I don’t really care who she is and where she’s from, but the names she called me, I don’t care to repeat them here.”

“I’m sorry she was rude. We’ve been under a lot of stress. My mother died. Both those two came here for the funeral. Dear friends. It’s been hard on us, you know.”

“I’m sorry to hear.”

“I hope you don’t press charges. I know they were rude. They should pay a fine, I know. But I hope you’ll consider the circumstances.”

“Well, yeah. I suppose. A nice lady like your mother should have better friends though, sorry to say.”

“Work friends, they were. Essential to her research. Personally, well, you’ve seen what they are like.”

“No joke. Well, they’d have to apologize in person. Especially that woman, Potter. I’ve never been cussed out like that. There’s no need for that kind of language. Plus, there’s still the fine for trespassing. At least one hundred bucks, maybe more.”

“I think it should be more. The Arboretum could always use some extra money, no doubt. I’ll make sure she apologizes tomorrow morning. I promise.”

“Your mom was a Friend of the Arboretum, you know. We appreciated all her support over the years. Good skier, too, just like that Russian dude tonight. Good form even though he was drunk as a skunk. I’ll call the cops and tell them I won’t press charges. But I guess you’re going to have to pick them up, Mr. Karnokovitch.”

“I’ll happily do that. And I promise they’ll come by tomorrow.”

It was freezing outside, colder than I’d experienced in I didn’t know how long. I drove alone in my mother’s Volvo to the police station, and of course hardly anyone was on the road. The police had rounded up an orange prisoner’s outfit so that Zhelezniak wouldn’t be parading around the cop shop in his
kalsony
, although I think that he would have preferred his immodest attire to playing the role of prisoner. Fortunately, Potter had been appropriately attired all along.

“It’s worse than Russia here. A man can’t even ski when he wants. What kind of freedom is that?” Zhelezniak said in the car.

“They treated us like we were common criminals!” Potter said.

Listening to those two bitch and moan after I’d groveled to keep charges from being pressed was more than I could handle. Right then and there I hated them both. Their level of privilege and childishness was stratospheric. I knew that if Anna were with me, she would have launched into a flurry of insults. Maybe because I heard so many of these invectives from Anna, from my parents, and from all those I loved, I’ve always felt that there was no need for me to contribute to the family’s already prodigious lexicon of barbs. That’s not my role.

“How is it going with Hilbert’s twenty-third, anyway?” I asked Zhelezniak in Russian. “You’ve been at it nonstop. Making any progress?”

“That’s not the kind of question you ask a mathematician, Sasha. You should know that. And it’s Hilbert’s sixth, more or less.”

“Six. Twenty-three. Thirteen. Fifteen. Some numbers are more difficult than others. You’ve been working so hard, both of you. Everyone has. And Hilbert’s sixth. Navier-Stokes, whatever you call it. It’s such a difficult problem.”

“Are you being sarcastic, Sasha?”

“Oh no. I know it’s difficult. My mother started to work on this problem when she was eleven years old. That’s when she made her first insight.”

“She told you this?” Zhelezniak asked.

“Sort of, yes. Those two pieces of paper you have been looking at for years now. They are from that time, I’m sure. She even talks about them in her memoirs. They’ve traveled a long way, from the Barents Sea to Moscow and now to the improbable location of Madison, Wisconsin. Sixty years old, those papers are. The drawings and writings of an eleven-year-old girl.”

“Not just any eleven-year-old girl, Sasha.”

“True. And somehow you have to go from those papers to a full-blown proof. That’s a long distance to travel.”

“You’re taunting us, Sasha?”

“No, I’m not. I’m just telling you that I know you won’t succeed.”

“What are you two talking about? I don’t understand a word,” Potter said.

“We were talking about the fine for trespassing. Two hundred dollars each, maybe more. And the fact that you are both going to have to apologize to the Arboretum ranger tomorrow morning.”

“I’m not going to apologize to that dreadful man. He treated me like I was a convicted felon.”

“Yes, you will. You are going to say you were sorry for swearing at him. You are going to pay your fine. Otherwise you will be arrested. And I won’t pick you up next time.”

DAY 5

A
nna, my uncle, and I were in the dining room. My father, daughter, and granddaughter were planning to stop by before they went to the airport. Zhelezniak and Potter were apologizing to the Arboretum ranger and paying their fines. Bruce and Ari Karansky were, according to the rumor mill, discovering their level of compatibility. The absence of these people had temporarily lowered the noise and energy level in my mother’s house. It was almost like a normal shiva. Yakov walked into the dining room, plopped down, and began to devour some
tzimmis
that the rabbi’s wife had sent. “It’s not as good as Jenny’s cooking, but I can understand why the rabbi has been married to this woman for so long,” Yakov said.

“I think it’s more than the food, Yakov. A lot more,” I said.

“Don’t be so sure of yourself, Sasha,” Anna said.

“I think Jenny thought I was crazy,” Yakov said.

“Not really,” I said. “And she’s used to crazy, probably. Her father was in the physics department. Still is. He’s emeritus.”

“Academic brat, just like you. I’m probably not good enough for her, she thinks. And now I’ve scared the
printsessa
away.”

“She’s coming by to bring some dinner tonight. So you must not have been too scary.”

“Really?” Yakov’s mood turned hopeful.

“Yes, really.”

“What is she bringing?”

“I have no idea. I didn’t ask.” Of course, I was lying.

“You didn’t ask? Because of your lack of curiosity I’m going to be thinking about your mystery dinner all day and night. I’ll be a worthless contributor to the problem at hand.”

“You can’t stay for dinner, anyway. Those are the rules. We pray
mincha-maariv
and then all of you have to go. I need some peace and quiet.”

“You’ll have lots of peace and quiet,” Anna said.

“You abandoning me again?”

“Of course,” Anna said.

“We have plans,” my uncle said. “We’re going to meet with Avi’s brother, Shimon, and his wife.”

“A double date?” I asked.

“Have some respect for your elders, Sasha,” my uncle said and gave me the Czerneski death stare even though he knew it had no effect on me.

“Whatever involves that guy can’t be any good,” I said.

“You don’t have any respect for religion, Sasha. For you it’s all mumbo jumbo,” my uncle said.

“And what about you, Anna? Do you have respect for religion?” I asked.

“I don’t know if I do or don’t,” Anna said. “All I know is that some things can’t be explained.”

“I didn’t think you were superstitious,” I said.

“I’m not. It’s just that since your mother died I’ve been having a crazy dream,” Anna said.

“And I’ve been having the same one. Both of us. Your mother is talking to us in our dreams. How do you explain that, Mr. Scientist?”

“What does she say?” I asked.

“I can’t make it out,” my uncle said. “I wish I could. It’s a strange mix. Some Russian, Polish, Hebrew, and languages I don’t even know. Anna can’t make it out, either. It’s like she’s trying to talk to us, but she can’t quite do it,” Shlomo said.

“Maybe it has something to do with mathematics,” Yakov said.

“Yeah, right,” I said. “My mother is trying to give them the solution to Navier-Stokes.”

“Could be,” Yakov said.

“I was joking, Yakov.”

“And I’m not, Sasha,” Yakov said.

“When did you start believing in ghosts?” I asked.

“I don’t believe in ghosts. I believe in opportunities,” Yakov said.

“Reb Ben-Zvi says maybe her soul has risen to be judged and there are complications,” my uncle said.

“Her
yechida
,
chaya
,
neshamah
,
ruach
, and
nefesh
residing in the Garden of Eden, waiting for the world to come.”

“See, you know the names of the souls, Sasha. Don’t make light of them. You’ve never been close to death. You don’t know anything,”

“I still say
Modeh
, thanking God for returning my soul every morning. It’s a beautiful prayer. I’m not a complete heathen,” I said.

“But you don’t believe that your soul rises when you sleep and comes back when you wake. It’s just poetry for you, but I believe it,” Shlomo said. “Your mother’s soul, her
neshamah
, is up on high. It can’t come back down, but maybe it wants to say one last word to us.”

“So you’re going to try to talk to the dead tonight? That’s against the rules, you know,” I said.

“We aren’t going to talk to your mother. Reb Ben-Zvi says there is another way. We’re just going to listen.”

“Listen away, Uncle. I wish you luck. At least Bruce will be here with me,” I said.

“Are you sure?” Anna asked.

“Yeah, he called and said he’d be here in an hour.”

“What about him and that mathematician?” Anna asked.

“Clingy. ‘Very clingy,’” he said.

“Insecure. They all are like that except for your mother. The one in the living room I was married to was like that,” Anna said. She shook her head in judgment.

“I wouldn’t have guessed.”

“Neither did I, obviously.”

“You’ve said hardly a word to him.”

“What is there to say? He was a disappointment from long ago. And now he has ballooned up. Disgusting. I barely recognize him.”

“We should all stay away from mathematicians, Bruce included,” I said.

“You’re being mean to us, Sasha,” Yakov said. “At least do me the courtesy of saving me some of Jenny’s delicious leftovers for tomorrow’s lunch.”

“That I’ll do. You really think you’re going to solve Navier-Stokes during this shiva?”

“It’s our best shot. She ever talk to you about it? What she was working on?”

“She hadn’t published a math paper in ten years, Yakov. She was out of the business.”

“One thing does not mean another. This problem would take a long time to solve. A singular effort. Total concentration would be needed, even for your mother.”

“She was working on the family history, Yakov,” my uncle said. “She was going to turn it into a novel. It was going to be a good one, I know.”

“A multigenerational family saga,” I said.

“Only Slavs know how to do this. What do the Americans have?
Gone With the Wind
? Sentimental trash with no heart. It’s a shallow country,” my uncle said.

“The audiences, too. They watch, but their eyes might as well be closed. They look without comprehension,” Anna said.

“Yet we all came here, didn’t we?” Yakov asked.

“Absolutely,” Shlomo said. “It’s the best place in the world for a smart man to be. All this money, all this opportunity, and only stupid, lazy Americans to compete against. It’s heaven on earth.”

“Your mother flourished here, Sasha,” Yakov said.

“I’m very glad we came, don’t get me wrong. But really, my mother did her best work in Russia,” I said.

“No distractions. Nothing good to do. No fun. So you work. I danced better there, too,” Anna said. She had a faraway, dreamy look, something rare for her.

“When you went with Rachela to visit Russia, and you went to Moscow State with her. Do you know what she did in that office while you were a lookout?” Yakov asked.

“Me? I told you before. It wasn’t my business,” Anna said.

“Probably she had some papers still there. More than just the ones Poponov found,” Yakov said.

“My sister was good at hiding things,” Shlomo said.

“We would like to look for the papers, Sasha,” Yakov said.

“Look for them? Where?”

“In the house.”

“Look away.”

“We’ve already looked. Five days we’ve been here. Looking.”

“I thought so far you were mostly organizing stuff upstairs. It’s a mess up there.”

“Organizing. Looking. What’s the difference? We’ve looked everywhere. Here. In Rachela’s office. We need to look deeper.”

“Deeper?”

“Yes, deeper.”

My uncle seemed keenly interested in this conversation for reasons I couldn’t fathom. “It’s a good idea,” he said.

I looked at my uncle. “What’s a good idea?”

“Look deeper. The walls. The floorboards. Open them up.”

“Are you crazy? You want to tear apart this house to look for some pieces of paper that don’t exist?”

“I don’t give a damn about the papers,” my uncle said. “But your mother. I know my sister. She’s got some money somewhere in here. Cash money.”

“She never told me about any money.”

“She didn’t have to. She knew we’d look.”

“You’re both crazy.”

My father, who had arrived with my newly discovered family, entered the dining room. He looked a bit sad, his usual regal air absent. He’d been drinking already, I could tell, something that was as unusual for him as it was for the rest of my family. In the daytime there was always serious work to be done. But this wasn’t a normal daytime. Even my father was having bouts of melancholy over the loss of my mother.

“Viktor, you knew her better than anyone,” my uncle said. “Where would she hide it?”

“Hide what?”

“The money. The proof. Where would she hide anything?”

Somehow through the fog of alcohol, something clicked in my father. “Oh my god,” he said. He walked upstairs. We followed. In the room of my childhood, we helped my father move a bookcase. Word spread downstairs, and the crowd of mathematicians rushed up the staircase into the hallway. A screwdriver was requested, and the two triplets present descended to the kitchen in a panic to retrieve the tool. As my father lifted the floorboard in the corner of the room next to the clothes closet, there was complete silence.

“Here,” he said. He pulled up a metal ammunition box and handed it to me. The thing weighed about a dozen pounds.

“Open it!” my uncle said.

I did as I was instructed, opened the latch, and yanked on the lid, watching its sticky rubber lining stretch and finally yield. I looked inside. It was full of coins, twenty-ruble pieces from the time of the last tsar.

“In Russia, you could have bought a cow with each one,” my father said.

“Great. I could have a herd of three hundred cattle,” I said.

My uncle was beaming. “I knew it!” he said.

“Where did these come from?” I asked.

“She collected them. It was a long time ago. They weren’t worth much back then. Gold was cheap. And nobody in America or Russia had any interest in tsarist coins. Your mother, underneath it all, was a very sentimental woman,” my father said.

“But what about the proof, Viktor?” Yakov asked.

“There is no proof hidden anywhere, you idiots,” my father said. Disappointment for Slavs is always more poetic and profound, as well as more frequent, than it is for Americans. The collective sigh of the eleven mathematicians in the house, for many of whom English was a second, third, or fourth language, was palpable.

 • • • 

The adrenaline surge caused by our mad search, so surprisingly successful for lucre but so devastatingly unsuccessful in terms of intellectual treasure, had left all of us by the time Zhelezniak, Potter, Bruce, and Ari—our shiva’s lovebirds—returned. Bruce, upon hearing the news, asked to see the coins. I placed them on the kitchen table. A crowd gathered, the way it always does when something that glitters is placed in view. Bruce was sincerely impressed by the bounty.

“That’s easily thirty K right there,” he said. “Way to go, Aunt Rachela.”

“I thought you weren’t good at math,” I said.

“That’s not math. That’s arithmetic. I could always do arithmetic,” Bruce said.

“He does have a good head for numbers,” Uncle Shlomo said. “He got it from me.”

“What are you going to do with it?” Bruce asked.

“I don’t know. Maybe I’ll start a ranch.”

Zhelezniak looked at the coins in the green metal box, picked one up, and rubbed it between his fingers, a rueful expression on his face. “Eighteen ninety-seven. One hundred years ago. The problems were easier to solve then.”

“Only in hindsight,” one of the triplets said. “Important problems are always difficult to solve.”

“Perhaps.”

My granddaughter, Amy, was looking up at Pascha. “Can I take her out, Grandpa?”

“There are too many people around for that, Amy,” I said. “Maybe later, when things quiet down.”

“She can handle Pascha?” Bruce asked.

“Apparently yes,” I said.

“Amy likes Russian food, too,” Yakov noted. “It’s almost like a reincarnation.”

“She does have a gift for math, it’s true,” my father said, and gave her an affectionate pat on the head.

“An
ayzene kepl
,” my uncle said. “I don’t feel so bad anymore. I thought this family was dead. Now look. It keeps going.” He gave my daughter a patriarchal gaze that I didn’t even know he possessed. “Both of you need to have children,” he said. “She in twenty years. You a couple more in the next ten wouldn’t be bad either.”

“I need to find a good man first,” Andrea said.

“It’s true,” said Anna. “So many men. But most aren’t worth even a penny.”

“I’m a good man,” Shlomo said. “There are others, too. Don’t be so pessimistic.”

Zhelezniak looked down at Amy, who was ignoring the conversation and watching Pascha. “She’s been studying?”

“Yes, with Professor Shackleworth,” Andrea said.

“At Berkeley?”

“Yes.”

“He’s a good man. He wouldn’t waste time on someone without talent. She must have a gift.”

“He’s why we’re here now. He had a hunch we were related to Professor Karnokovitch.”

“I’d like to show her some mathematics from her great-grandmother. Would you mind?”

“Zhelezniak, she’s six years old,” I said. “My mother was eleven when she drew those pictures.”

“A gift is a gift, Sasha.”

“You want to show her Rachela’s papers, do you, Vladimir?” my father asked with his thin-lipped smile.

“Of course. What would be the harm?”

“What’s next? You going to show the papers to Pascha, too?” I asked.

“Actually, we already sort of did this,” Peter Orlansky said. He looked up at the cage at Pascha and continued, “
Chcemy zbadac skalowanie funkcji rózniczkowalnej w sposób ciagły.
”