Flight 2901 Prague Delayed 9 P.M. reads the airport display, the one that is announcing arrivals.
It doesn’t matter, I tell myself; I’ve waited for Helena all my life, two more hours aren’t going to make any difference. And you, mother, have you ever waited for somebody with this mixture of patience and impatience?
When I was little, mother, you waited for my father. You waited for him even though you knew he would never, ever come back. Or maybe you didn’t know, did you? Perhaps you pretended not to know, you didn’t want to admit it. You preferred to live in hope. You listened and in a soft voice you sang the sort of music that made you think of my father. I remember our silent walks, the quiet suppers. We remained in silence, like an elderly couple that has said everything they ever needed to say to each other, so who in the end words are no longer necessary.
You sent me to take piano lessons. Why, in fact, didn’t you teach me yourself, if you were a piano teacher? You might have done so if we’d actually had a piano at home. The flats assigned to us by the government got smaller and smaller. During the piano lessons I liked the smooth touch of the keys. I sat next to the mysterious teacher and breathed in her honey scent as her silky hair occasionally brushed against my fingers, which used to happen when we played duets and her fine hair grazed the keyboard. What I most loved about music, apart from the harmony and the theoretical precision, were the scores, those pages full of staves and notes, those complex arrangements that determined the whole feel of the piece.
BE MOVED reads the sign hanging on the wall of the concert hall in the university town where I work. Orpheus first seduced Euridice with music. Later it was his languorous melodies that moved the drunken, unbridled women to kill him by tearing off his head.
Is it a coincidence then that Helena’s a violinist?
Once, I remember starting a new year at school, and as soon as I entered the school I was filled with a feeling of revulsion. Nothing had changed, everywhere the same posters, the color of ripe strawberries, proclaiming eternal friendship with the Soviet Union. The bald pate on the bust of Lenin shimmered in the morning sun. Only one thing had changed: the math teacher. Last year’s, young and irate, had been popular with the girls at school, but the new one seemed old and silly and the girls despised him as a relic from another age. He wore an old-fashioned suit, a white shirt, and a thin tie, his hair was Brilliantined and combed back. He smelled of pipe tobacco and his teeth reminded me of potato peelings. The new math teacher was different from the rest of the teaching staff, maybe because he had lived in Argentina, where, as he put it, he had lived like a monk. Our nickname for him was “The Monk,” everyone made fun of him.
The Monk was quirky: a poet. Math, for him, was a sort of art form, or a musical composition. When he explained the laws that governed mathematics, he never stopped hearing music, like when my piano teacher, whose long hair smelled of honey, played a Mendelssohn sonata. In mathematics, axioms are the basis of everything, and the truth of an axiom is unquestionable, said The Monk. In the same way that a building is constructed on its foundations, the construction of the science of mathematics begins with axioms. This is also true of music: musical compositions are created with the aid of only seven notes. In mathematics, these notes are the axioms. And if the arrangement of musical notes creates different melodies, the configuration of axioms makes new knowledge possible.
“How?” we would ask.
“How?” The Monk would laugh. “Nobody knows that. It is here that the talent of the mathematician lies, his imagination, his gift for hearing a brand new melody,” he’d say, waving his arms about as if he were conducting a one-hundred-and-twenty piece orchestra.
The Monk would open his textbook, then shut it again suddenly, exclaiming, “Yuck! How boring!” Then, in the way a painter filled with inspiration will use wide brushstrokes to fill the canvas with images dictated by his imagination, so The Monk would draw all kinds of parabolas, hyperbolas, and ellipses on the blackboard, which the mathematics textbook could only present in a thoroughly tedious fashion. Back at home, I pored over the textbook, but quickly put it aside. I spent whole hours looking for unusual solutions to mathematical problems. Our new teacher would have explained that what I was looking for were aesthetic solutions. When I showed him my geometrical drawings, The Monk shook his head and made me understand that not everything was a question of aesthetics, but neither was it simply a question of only rational thinking. With this attitude, he instilled in me the ability to analyze according to the rules of the strictest logic. I will never forget how this teacher would run from one end of the long blackboard to the other, sometimes jumping up or squatting down, forever repeating that quote from Einstein about true learning, only sticking in our heads once we had forgotten everything we were taught at school.
Mama, do you remember that small bedside lamp in the room where we lived when I was little? You hung a lace cloth over it, and then that tiny room, which served as both our study and living room, our bedroom and kitchen, would fill with a gentle, golden glow. While I tried to solve mathematical problems, that glimmer of warm light blended with the music of Chopin, Schubert, and the liturgical chants of the Russian Orthodox Church, those albums that you selected and placed on the black platter of the record player. That atmosphere helped me to create a new harmony and a new melody, my own, geometric, mathematical melody. I feared the chaos and instability that surrounded me: while you made me doubt the official ideological dogmas, the teachers worked to make me believe, eliminate any doubts, which they treated as if they were sins. So it was that I grew up surrounded by paradoxes, though I badly needed a feeling of security.
Years later, after the Soviet invasion of our country, when I took advantage of my stay in Yugoslavia to request political asylum from the United States, and they offered me a place as a teaching assistant in a prestigious university, you sent me that piece of cloth, Mama. As if you sensed that death would take you away before we could meet again. I, on the other hand, tried to convince myself that all I wanted in America was to acquire experience and return to you and Helena. Or, if our country continued to be ruled by a foreign power, I would invite both of you over to the United States.
I said goodbye to Helena . . . no, in fact, you can’t really call it a goodbye. Helena vanished. She evaporated like a drop of water on a baking hot stone, like those next to the Bosnia river in Sarajevo.
Looking back, I was simply putting off the time when you could be with me here at the American university. At that time, I had more work than I could cope with. I’d invested myself in a whole new field of research: as a mathematician and engineer, I was becoming interested in electric cars. What’s more, for the first time in my life, I was teaching classes at the university, and I was doing all this in a foreign language that I hadn’t quite mastered.
One day I received a letter from the Czechoslovakian embassy. It informed me that the judicial system had declared me guilty of having abandoned the country illegally, and had sentenced me to jail.
I tried not to think about it too much. The fact is that that letter, when it came down to it, guaranteed that I would never see you again, not you, or my friends, or my city, and, above all, it obliged me to abandon my mother tongue.
At that time I was convinced that my work would make up for the loss of my country, my mother tongue, and a much-loved woman. Now, years later, I can say that I fully subscribe to what Bertrand Russell said about science offering us the causal skeleton of the world, while it leaves out all the colors and variety and singularity of those things which make up the world.
However, I didn’t know that, not back then. I went from one lecture hall to the next, from one class to the next, without looking at the time or even what season we were in. I spent the nights looking for solutions; I can still remember one of them:
u = −(GB)−1 Gƒ
I published the first article based on my research in the IEEE transaction on Power Electronics Journal. I then received a summons from Professor Benjamin Fortner, a celebrated mathematician and world specialist on the theory of differential equations.
“Sit down,” he said in a tiny voice, “you’re probably wondering why I’ve asked you to come. One of my colleagues told me about the article you published in IEEE. You make use of a method that is not in the least bit traditional, and this interests me. I would like to go over certain aspects of the text with you. However, I haven’t got a clue about all that electronic stuff you wrote about.”
Professor Fortner picked up my article and took a close look at it.
“The right-hand side of the equation is a discontinuous function of system coordinates,’” Fortner read aloud. “In the situation you describe, current theories cannot be applied. I’d like to hear how you would go about solving this problem.”
I could scarcely believe that such a prestigious mathematician was unaware of Filippov’s method of solution continuation. And I told him so, adding that I personally found that the solution lays in the convex set.
Fortner replied as if he were a schoolteacher, explaining something that everyone else already understood to a not-very-gifted student.
“Yes, I know Filippov’s method, of course,” Fortner said slowly, disguising his impatience, “but if you look at this piece of research from 1958, you will realize that Filippov developed his method using just one discontinuity surface, whereas you, in your article, employ an arbitrary number! This is why I have some objections to your article, at least those of a formal nature. Of course it is possible that in practice, things might actually work in this way, but in our branch of science one must speak with greater precision. Indeed, I am almost tempted to tell you that you should treat mathematics with more care, with tenderness!”
He added, icily, “Your heuristic approach probably works in engineering, but it is not acceptable for mathematics. Not only that, remember, if you please, that you are teaching in Boston at one of the best mathematical schools in the world.”
He was choking with rage, and I understood that from that moment on, I was not welcome in his study.
I set myself the goal of finding a solution to the problem Fortner had posed; I would wake up in the middle of the night, leap out of bed, and sit down in front of a huge pile of papers, all full of equations. During the day, I got through my classes mechanically; my head bursting with whole waves of calculations, involving all kinds of discontinuity surfaces, differential equations, and coordinate systems. When a friend of mine pulled me out of my office for a beer, I could talk to him of nothing else. I couldn’t contain myself and, with a beer glass in one hand, I grabbed a pencil and filled napkin after napkin with calculations.
And then, one fine morning, I found the solution. I called Benjamin Fortner. The mathematician was busy.
Nonetheless, I went to see him. There was no way I could not.
He looked at me wearily, and sighed.
“Professor, the results of my scientific inquiry are now correct. I will demonstrate this to you using my own method, the method of equivalent control.”
I imagined that Fortner would be left speechless.
The mathematician, however, said with impatience, “What do you expect me to say? I’m glad that after all my objections you didn’t give up, but . . .”
But from the sound of his voice it was clear that he didn’t think my work could be of much interest to him. He glanced fleetingly at the pages on which I had written down my results.
“Leave it here with me,” he said, “I’ll take a look at it later.” Then he pushed my work away, placing it on top of a pile of paperwork.
That mathematician was already thinking about other things, a bit like me when I said goodbye to my students at the end of a class.
A month passed before he called and invited me over to talk. When I knocked on the door of his office, I was ready for yet another show of indifference.
Benjamin Fortner grumbled, “You see . . . how can I put this . . . this work of yours . . .”
He stopped himself, quietly grousing, then continued, “Your work has been a pleasure to read. You proved the theorem confirming the validity of your absolutely universal discontinuity method, because it doesn’t depend on the number of surfaces.”
“So . . .” I said.
He turned his suddenly animated eyes to me, “So I retract my objections.”
“Really?”
“You must publish your findings in a peer-reviewed journal. I will help you.”
An unusual thing happened to me then: not only my engineering colleagues, but the mathematicians too, began to treat me with respect. One day I got a call from the Ford Foundation. They had read my article, and had spoken to professor Fortner. They invited me to give a lecture at their Detroit headquarters.
I noticed that the Ford specialists listened to my conclusions with respectful attention, but without any real interest. Even so, when I explained the relevance of the control of electric automobile motors, they sat up in their seats, craning their necks forward.
Not long afterward I received a letter on Ford Motor Company letterhead. They’d found my lecture stimulating and wanted to invite me back to Detroit to discuss certain matters, they said, that they and I might have in common.
I was greeted by two top-ranking Ford executives. Both wore impeccable navy-blue suits and ties. Those limber, athletic gentlemen had bronzed, closely shaven faces, though one of them had a goldenish hue— probably because he’d spent time at the beach—and the other one was darker—probably because he’d been skiing, even though Detroit is as far from the sea as it is from the mountains. My shabby, gray corduroy jacket, and my unkempt, unstyled hair both indicated that I was a completely different category of human being. We sat down in the meeting room and the two men were cracking jokes and laughing. We were brought some extremely thick sandwiches made with sliced bread, which the rules of etiquette dictated had to be eaten with one’s hands.
“Let’s talk about you maybe working for Ford,” the one with the golden tan said.
“In the future, that is,” the skier clarified.
“Right now would be impossible,” said Golden Tan.
“On the other hand, why not in the future? You could do that for sure! No doubt!” said the skier, laughing and raising his glass of coke.
I didn’t say anything. I waited. They watched me attentively. I remained stubbornly silent. There was nothing to discuss, so I waited to see what would happen next.
Finally I replied, “I’ve never considered leaving the university or my academic work.”
They looked at me like I was some kind of exotic animal.
Golden Tan said, in a low voice, “Think about it carefully, John. We’re not forcing you to do anything, it’s a free country. But do think it over. The best university in the world couldn’t beat the offer we’d be making you.”