The Mathematician’s Shiva (30 page)

I’m also of an age when intellectual achievements, even those as significant as proofs to nearly impossible problems, take a backseat to friendship and family. I know that in comparison to almost all of my colleagues my “scientific impact” is considerable, but really now, it isn’t much. I can search on Google Scholar and note how many times each article I’ve written has been referenced in the scientific literature. Aside from my mother’s proof, these numbers are paltry, rarely exceeding one hundred. I am a minor footnote, indeed, in the history of science. I take much more comfort and pride in the goings-on of those I know and love. I am lucky and blessed to have a loving wife and stepchildren, and a daughter who forgave me for being absent, and ultimately cruel, during her youth.

Andrea tried to get her mother’s permission to have me call. It never came. A few years ago I called Catherine anyway. She hung up the second she knew I was on the line. I then wrote Catherine a letter asking for her forgiveness but never received a reply. In Christianity, forgiveness is expected when an apology is sincere. I’ve never understood this concept. Apologies are, after all, simply words. They should be weighed in some way against the hurt the offense has caused.

While my transgressions have been generally of a personal nature, my mother, by holding on to a proof for decades out of pure selfishness and egotism, managed to offend the entire mathematical community. She, of course, never apologized to anyone for the trouble she caused. But in an intellectual community, genius always trumps propriety and
menschlichkite
. Bad behavior by leaders in an intellectual field is even, occasionally, celebrated and envied like a rock star’s antics. The rumor mill regarding the publication of my mother’s solution to the Navier-Stokes problem is still actively inventing and recycling narratives. Every once in a while I receive a call from a young professor or Ph.D. student who claims to “want to know the truth.” They sound so disappointed when I tell them that I don’t know what is true and what isn’t.

A few years after the shiva, Yakov Epshtein came to Madison to give a lecture in the math department. Like almost all of my parent’s friends, he was not an idle talker. When he had said at the shiva that he was going to Winnipeg for the express purpose of finding a wife who understood the exquisite delights of Slavic cooking and who would not be deterred by the cold of the American Great Plains, he had meant it. I was not entirely surprised when I received a wedding invitation from him in 2002. I was also not entirely surprised to see how much he had slimmed down by the time of his Madison visit. Married life was treating Yakov well in many ways.

When he came to my office to talk, he extolled the beauty of the world and his wife. A couple of years after the publication of his major proof, he had received an offer of a chaired professorship from the school my mother always detested, the University of Minnesota. Yakov happily accepted. There was now a bit of the contented sage about him. But then he began to reminisce about the shiva, and he narrowed his eyes. “Here’s what I want to know, Sashaleh. All those days. All of us working so hard. It was torture, and yet the problem had already been solved. I can’t get it out of my head. Why?”

“My father said it was my mother’s wish.”

“I don’t believe it. She wasn’t that mean. Not to people she liked, and she liked most of us. Plus, she loved Peter.”

“The Peter thing is a silly rumor.”

“Yeah, right. A silly rumor that’s the truth. You’re trying to ignore my question.”

“OK, I agree with you. My mother couldn’t have predicted you would have crashed the shiva. Back then I wasn’t so sure. But I didn’t know she’d already solved Navier-Stokes. She wouldn’t have wanted the craziness. Not just for the sake of the mathematicians. For everyone, her family especially.”

“So why?”

“I can only guess. My father probably saw all of you wandering around the halls with your stupid plan to solve something in one week that it took my mother thirty years to do, and in a fit of pique he decided to let you carry on with your stupidity.”

“Now that makes some sense,” Yakov said. “Your father could be a handful. But I have a different theory.”

“Which is?”

“Checking your mother’s solution wasn’t easy, especially for someone outside the field like your father. Plus, he was getting old, slowing down. If he faltered, if he felt he couldn’t succeed, we would be there to prop him up. The bastard let us torture ourselves so he could use us as an insurance policy.”

“Don’t speak ill of the dead, Yakov. People do stupid things when they are angry. He didn’t think his actions through clearly, if I am right. He was trying to check my mother’s solution and was being bothered by all of you. Then he had the pleasant distraction of a newly found grandchild and great-grandchild. If my father could have imagined the chaos ahead of time, he would have told everyone the solution was done.”

“You’re probably right about that last part. No one would want to be responsible for such a mess. He wasn’t a bad man. Your father was good to me. Both he and your mother.” Yakov hopped out of his chair with the sprightliness of a middle-aged man who had discovered the benefits of a daily workout. “You have a nice view,” he said. “What’s that place with the green oval field below?”

“The football stadium. Camp Randall.”

“You ever go to see such a thing? Watch young men knock each other over with reckless abandon?”

“No. Never. I don’t understand the purpose of it, actually.”

“See. Your parents raised you the right way. You’re not distracted by nonsense. They’d be proud of you now. Married, thanks to me. Back home with a wonderful wife and a family.”

“I suppose I should thank you for your efforts.”

“Yes, you should. To tell you the truth, that’s why I came to visit your nice little office today. I wanted to hear some belated words of gratitude from the son of Rachela Karnokovitch. You get married. OK, it was a little family ceremony, I understand. That’s your and Jenny’s style. I’m not insulted that I wasn’t invited. But here’s the important thing. Was I right with my advice?”

“You were right, Yakov.”

“Of course I was. Right as rain, as they say. Now, if you don’t have a bottle in your office, it’s time for us to go to a bar and celebrate our good luck and fortune.”

I assumed I’d never know my mother’s side of the story as to why she kept the proof to herself for so long. But then last year, I got a call from the owner of my old family home. He’d found some papers written in a foreign language mixed in with the furnace manual that was attached to the back of the furnace. He thought they might be important. Did I want them?

I was both ecstatic and irritated upon hearing about this find. I was certain that before we sold the house we had combed through every square inch, expertly looking for hidden documents, jewelry, gold coins, and whatnot. What kind of Karnokovitch doesn’t know how to find hidden items of value? I was turning into a lazy American in my middle age.

I went to pick up the papers immediately. Like an impatient schoolboy, I read them before I got back home. It had been ten years since my mother’s funeral and shiva. In a way, my uncle Shlomo had been right. Even after her death, my mother felt the need to say a few more words.

O
ne year when my son was a teen, my family went to the state fair. My son gravitated to the arcade, where he tried his hand, unsuccessfully, at making free throws with a basketball from a very short distance. By happenstance, the Ferris wheel was next to the basketball booth at the arcade. He wanted to take a ride, as did my nephew, who was only three at the time. I looked down from our elevated perch on the wheel and understood instantly why my son, as well as almost all others, had been unsuccessful at making free throws. The rim of the basket was distorted. It was an oval, not a circle, and while the radius of the rim’s width was normal, the radius of its depth was likely barely longer than the radius of the ball. Of course, an arcade player could only discern the rim’s width, and so played a game that he thought was fair, but wasn’t. He had to be almost impossibly perfect in his execution to succeed.

My career in mathematics has been quite like an arcade player shooting baskets. The naïve observer might have seen me at Moscow State University and thought I was evidence that all were welcome in mathematics. But, in fact, as a woman and a Jew, the rim was distorted for me. To succeed I had to be perfect, certainly leagues better than my male and Christian mentors and colleagues.

After I left Russia I continued to work on the Navier-Stokes problem, slowly and, for the most part, steadily making progress. Being a Jew was no longer nearly the obstacle it was in Russia, although, of course, I would still not infrequently run into anti-Semites in my work well into the 1970s. Being a female mathematician was also far less difficult, especially after I reunited with my husband and son and the unwanted advances became less frequent. Still, there were limitations. I note that the first woman to receive the Nobel Prize in physics did so almost one hundred years ago. A woman has yet to win the Fields Medal.

In 1970, when I learned that I would not receive the Fields Medal in my last year of eligibility, I was furious. In the world of mathematics gossip, there are stories about my behavior during that year and the year beyond. Those stories are mostly true. Some of my antics were a bit unnecessary and not productive, but I am extremely proud of one outburst, one that drove a member of the Fields Medal awards committee to tears. I don’t have to state his name. People who need to know already do so. I saw the fear on his face, witnessed the baby tears on his cheeks, watched him bolt out of his chair next to mine in a panic, and felt triumphant.

It took me two years to get over the hurt of being denied my due. Even for me, there was a glass ceiling in mathematics. This shouldn’t have been such a shock, but through my many years of success I had deluded myself into thinking that my talent could overcome any obstacle. I fell hard as a result of my hubris. Still, I had an enviable career. I had excellent students to mentor, and perhaps one of them will receive the award that has been denied to the women of mathematics for so long.

I decided to practice revenge in a calmer way, by living well. I buckled down and finished my work on my career triumph, the Navier-Stokes problem, in 1973. For over thirty years, Navier-Stokes had been a private and exquisite journey. It was the most beautiful of work not only because it was difficult, but also because it was mine, and mine alone. Born in the most unlikely and hostile of places, my work on the Navier-Stokes problem brought out purity and innocence in me that I couldn’t believe I still possessed. It was a gift to live with that problem over those decades. I believe it kept me young.

When I was done I decided that what had heretofore been private would remain private. I no longer had any need for awards and adulation. I knew that I was the best of my generation, and that personal and fair assessment was all I needed. I looked at my competition and knew none possessed the talent to do what I had done. I would assess the young ones coming up and understood that they lacked the necessary talent as well.

Of course, other mathematicians would continue to try to solve the Navier-Stokes problem. Vladimir Zhelezniak, the fiercest of them, wouldn’t follow my approach and engage in a delicate dance with the mathematics. I knew his aggressive style, treating each problem as if it were a death match. What he lacked in intellect Zhelezniak tried to fortify with sheer will. I knew he had been working on the Navier-Stokes problem since the 1950s. Like when he worked on Hilbert’s thirteenth problem, he was doing so with the help of my unfinished work. In this case, he had the drawings I made as a child. It pleased me, the idea that this man who had stolen my ideas once with great success would not have the talent to do so again. I thought of Zhelezniak fruitlessly trying to solve the Navier-Stokes problem year after year, haplessly trying to obtain wisdom from my drawings. I knew that I would not likely outlive him, and entertained the thought of him coming to my funeral in a vain and pathetic search for more material to purloin. It made me smile, and I must say it made me more resolute about keeping my triumph private. This, too, like living well, would be a passive yet perhaps successful final effort to extract revenge.

When the Clay Mathematics Institute formally announced the Millennium Prize for the solution of the Navier-Stokes problem in 2000, I felt wholly vindicated. I had heard rumors about this award for years and I was fortunate to live long enough to see its creation. One million dollars would not have been available to me had I announced my proof when I was young. I wouldn’t be the first woman to win a Fields Medal, but I would be the first to receive a Millennium Prize, albeit posthumously. As is stated in my will, this money will be used to create the Sophie Kowalevski Chair in Mathematics at the University of Wisconsin. The chair will be held by a woman. Perhaps, whatever the number of female mathematicians at my university at any given time, there will be always one more than if I had not won the Millennium Prize.

I look back at my life as others are wont to do when the end is in sight. People commonly express regrets. But when I look back I see the beauty of what I’ve witnessed and done. That’s what I have told people who have asked for advice through the years: focus on what is beautiful and pursue that beauty. We are not perfect vessels, certainly. I am not an exception. But I have no regrets. The love I have given and received has been pure. Driven by loss, I have both used the gift of intellect I possessed and lived my life fully. I will die wholly proud of my life and my accomplishments.

There is a real Navier-Stokes Millennium Prize problem. It has not been solved. Get to work, reader, solve it, and you will be rich. There is no Boussinesq equation problem. The University of Alabama doesn’t have an atmospheric sciences department in Tuscaloosa. Kolmogorov, I was told by one of his former students, loved to jump into ice-cold lakes. So do I. The living mathematicians in this novel are all made up.