A Doubter's Almanac (28 page)

Of my father’s own particularly stilted genius in the visual arts, I should add, I have few examples. Nearly all of his later drawings were highly ambitious renderings of the hyper-complex intersections of imagined shapes—rotating tesseracts overlapping at their vertices, 3D manifolds spun about planes in 6D space—and all but a handful of these pages have been lost. Nor do any of his portraits of famous mathematicians survive—not in my possession, anyway. In a silver frame on my kitchen wall hangs a single, elaborate depiction of the front of my childhood home, stupendously accurate in its detail up to the top-left corner of the paper, which remains untouched. And next to it is displayed a nearly photographic reproduction of the one misaligned sidewalk square that for as long as I can remember bulged between 1729 Karnum and the driveway to the north. This concrete square was portrayed by my father with mammoth foreshortening of the frost heave in the background and colossal magnification of the thick-capped property stake in the foreground—as though the whole scene were viewed by an ant. The stake lies on
our
side of the raised edge. That was the point of the exercise, which Dad had performed for legal reasons. Our neighbor—the one who liked to spray off our car—had tripped. My father had taken it upon himself to reproduce the facts of the tort, which, while lying on his belly, he did without shame or apology (he was capable of neither). There were no lawsuits in Tapington, of course, but he was very familiar with belligerence and on top of that had once lived in the East. Otherwise, in those days he drew nothing that I remember of the recognizable world, and he never mentioned his depictive talents. It was as if they didn’t exist.

Still, my mother was constantly on the prowl for our abilities.

Anything but math.

The museums were the summertime front in what would eventually become their Fifteen Years’ War. The June that I was eight and Paulie seven, my mother put Bernie in a kennel—my father disliked dogs nearly as much as dogs disliked my father—and drove my sister and me to our aunt’s apartment in Hammond, Indiana. There we stayed for three full weeks without him, my mother delivering us by car every morning to a day camp on Michigan Avenue in Chicago, run by the staff of the Art Institute, then driving back to Hammond to spend the afternoon with her sister, talking about what surely was by then a disintegrating marriage. Along the lakefront in Chicago, two-dozen seven-, eight-, and nine-year-olds sat in front of Georges Seurat’s
Un dimanche après-midi à l’Île de la Grande Jatte,
carefully executing their pointillist imitations, while one of them, using his brush handle as a surveyor’s transit, concentrated on a minimally extrapolated estimate of the number of painted dots (ca. 1.2 million!) on the billboard-sized canvas.

That would be me: Hans Euler Andret.

Failed mathematician.

Volatility Smile

I
’D BEEN NAMED
for mathematicians, of course, and in the fall of my ninth year on earth my father finally grew serious about my education in mathematics. In Dad’s mind, all the other academic disciplines—including the physical sciences, which were his own father’s profession and his own mother’s college major—were irrevocably tainted by their debt to substance. Biology, chemistry, engineering, geology—not to mention all those lesser endeavors that Mom brought home to us in her fraying
GO WOOD DUCKS
!
tote bag—were polluted by their reliance on observation, on the vicissitudes of blood, force, and element. Blunderbusses, all of them. Mathematics, on the other hand, required no concession to the perturbing cant of the world. It was pure logic, streaked with pure imagination. Although I admit that this might be an oversimplification, I maintain that there was something distinctly religious about my father’s devotion to the pure. Mathematics, though invisible, acted and existed everywhere at once, as did the Almighty.

Not even physics could boast such a birthright. My father was nettled all his life, in fact, by the idea that he’d left a university with the greatest mathematics program in the world to teach at a place where the mathematicians had to share a hallway with the physicists. The Fabricus College Department of Mathematics
and
Physics
.
Imagine! I heard him say more than once that the two fields were like cricket and baseball: alike only to those who knew the rules of neither. This was the kind of pronouncement he liked to make at cocktail parties and departmental picnics, if he was dragged into any kind of conversation at all. There were not many people in Tapington, Ohio—not even at Fabricus—who could respond to such a statement with anything more than a nod. In a way, this might have been his problem all along: that human beings would never quite conform to his Occam’s parsing.

The thing is, I had a good time with him. I’m not sure why, knowing what I now do. Maybe it was my mother’s influence—her highly developed penchant for looking at the shinier side of the coin. Things were normal, actually—at least they felt normal to
me
—for most of my childhood.

I remember moments. One afternoon that October, we were sitting under the mulberry tree in our front yard, as we’d done nearly every weekday afternoon that fall, working our way through the foundations of my father’s field. At that point, Dad still hadn’t fully accepted his personal and professional failures—not that I knew of, anyway—and although he’d already been drummed out of Princeton, he was still young and in my mind still a formidable expert on the workings of the world. In the yard, the citrus smell of his cologne was mingling pleasantly with the mild vinegar of the crab apples that lay about on the grass. Paulette was with my mother indoors. On that day, I remember, my father had just led me through a derivation of the fundamental theorem of calculus (James Gregory’s version—he found Isaac Barrow’s less impressive, even if historically superior to both Newton’s and Leibniz’s). This might sound like an outrageous exercise for a boy my age, but I can tell you now that in no way is calculus beyond the grasp of any reasonably talented, if isolated, seventh grader (my sister and I had both skipped three years in school). I could offer other examples—the educational systems of various Eastern cultures, the experience of quite a few homeschooled children, or the statistically reliable presence, in any given year, of dozens of preadolescents among the freshman classes of our great universities—but all that I really need to say is that by that age I’d already mastered every precursor—algebra, geometry, and trigonometry—with no difficulty at all, sitting with my father on a rotted wooden bench beneath a gnarled old mulberry.

I should also add that, among a cohort of future mathematicians, my overall development might actually be considered
slow
. (There were other reasons for this.) By way of example, Paul Erd
ő
s, the great Hungarian savant, could multiply three-digit figures in his head not long after he could walk. In my own case, before I’d even stepped through the doors of a junior high school, my father had explored with me every antecedent of Newton’s and Leibniz’s work, along with all the variously powerful methods that existed for mathematical proof, from the deceptively modest
induction
to the graceful
contraposition
to the thrillingly brutal
reductio ad absurdum
(and even to the reviled
enumeration of cases,
at which computers now excel and about which my father, for his own peculiar reasons, couldn’t speak without his lips puckering, as though around a lemon). I’d learned it all, without particular effort. And I’d thought it all no less normal than his daily breakfast of bacon and bourbon.

“Hans,” he said to me one afternoon, “this idea, this discovery that shapes can be described with incrementally smaller shapes, that anything at all can be approximated in such a simple manner, is what first drew me to mathematics. And it has guided me in much of my thinking since.”

His conversation normally didn’t require response.

“Mathematics is an invented science,” he went on. (This was a peculiarity of his, that he always insisted on the word
mathematics,
when just about every other mathematician I know says
math.
(Although it should also be noted that, like every other mathematician I’ve ever met, he insisted on using the full phrase “the Malosz
conjecture
” or “the Malosz
theorem
” every time he uttered the problem’s name; he would have never, unlike his son, simply called it “the
Malosz.
”)) “But strangely,” he continued, “the inventions of mathematics, which are wholly constructions of the mind, are in turn able to yield other inventions. That is why they often seem more like
discoveries
than
creations
. In fact the distinction remains a debate.” He looked over at me meaningfully, his still-soulful eyes shining vibrantly against the pallor of his cheeks. “I also believe that this is why so many mathematicians feel that they have been privy to the language of God.”

“I’ve heard that,” I offered.

He thought for a moment. “Although I should also say that I’ve thought of it in other ways, too. As the language of the mind, for example. Or even”—here he turned to me more thoughtfully—“as the language of
language
. The underlier of grammar. The skeleton of cognition. The rails on which the train of human advance steams up and down, one hill after the next.”

At that moment, a mulberry twig fell onto the lawn before us.

“Squirrels,” I said, looking up.

He retrieved the bit of wood and turned it over in his hand. Once he was going, it was difficult to stop him. “Mathematics is like carving a wooden doll,” he said, “and then, one day, you watch as your wooden doll gives birth to another wooden doll.”

These words have stayed with me all my life.

We sat there for a time. By that age, I was accustomed to his drifting. I saw the squirrel now, trampolining in the branches. Now and then it shook loose a few leaves, which fell around us. I’ve often wondered if they aim at people.

“In fact,” he suddenly resumed, “this is exactly how you will know whether your wooden doll is alive. If it yields
another
wooden doll.”

Not so many years after that, during the summer when his disease finally became apparent, I remember noticing the altered shape of his belly, which had begun to protrude beyond his belt. He’d taken us to the public pool. By that point, I’d entered a premature adolescence and was already considering Caltech or MIT for my future (or, if for some reason neither saw my potential, perhaps Harvard or Princeton). My father had always been a slender man, practically gaunt. Now his belly resembled a smoothly linear Gaussian curve, slightly downsloped and radially distributed about the nidus of what I would later learn, when I came back from Manhattan to take care of him, was called the umbilical ligament. His gut hung over his swim shorts like a water balloon.

“My God,” I said to him as he sat down near the diving board, “what’s that?”

“Statistical noise,” he answered instantly.

“Fuck you, Dad.”

“Fuck you, Son.”

He smiled. That year, we’d somehow taken to saying this to each other. I was the one who’d started it, but to my surprise he’d kept it up, perhaps because he sensed that the joke of it deflected the serious battle between us that was already on the horizon.

That afternoon, I well remember how he didn’t look like the other middle-aged fathers who were gathered beneath the faded sun umbrellas, their polo shirts amiably protruding. There was nothing roly-poly about Dad’s new belly. Nothing that made him look approachable or paternal. Despite his clever answer, he looked sick. Tall and dashingly thin all the years I knew him, he seemed suddenly to be shedding another, boundaryless person from inside himself—a larger, jiggling, water-inflated homunculus, dusky gray in hue, that had begun pushing itself out of his skin. A wooden doll emerging from another wooden doll.

I was swimming that day with a boy I knew from school, and at one point, as I was crouching to dive, he looked up at me from the water and said, “Your dad’s eyes are yellow.”

“Everybody’s are that color,” I said, “if you look.” Then I dived.

—

I
’M A TEACHER
myself now—high-school geometry, trigonometry, and calculus—and in my job I come across plenty of kids in trouble. It’s not hard to notice the distracted quiet in the loudmouthed jock, the missed homework from the valedictorian, the escalating tardiness from the sleepy cheerleader who wears the same ash-stained blouse to class all week. I’ve made a point to be on the lookout for these kids, for the ones who are smart enough and adept enough to make it into my classes—and smart enough and adept enough, thus, to be ignored by the school’s counselors—but vulnerable enough, if that’s the way you want to think of it, to veer.

Teaching is a noble profession that way. You’re given the opportunity to intervene.

But just in case you think of me in any other way as noble, I should also say that before I became a teacher I first became rich. Moderately rich by the standards of my former field, perhaps, which was statistical arbitrage; but extravagantly rich by the standards of, say, a doctor or a lawyer (and obscenely rich by those of, say, a teacher). Certainly I was already an outlier’s outlier, considering the scant number of years I’d been alive at the time I retired from Physico Partners Capital Management, at an age when plenty of other young men are still carrying coffee upstairs to their bosses. Physico was a hedge fund. PPCM, LLC. For close to a decade, I’d been the mild-mannered wunderkind on their high-frequency trading desk, up there on the top floor of 40 Wall Street (once the tallest building in the world, I should add). I’d started in the days when high-frequency trading was still something of a secret, at least from the public. At Physico, I was set up in my own password-locked execution room, where, in return for a rigorously excised take of four-and-a-half points against the net—which,
not
including my generally staggering bonus, already gave me a payday of a little more than a hundred times what my father earned in a year—I sat at a brilliantly lit desk twelve hours a day, chasing the spread on just about every species of financial instrument then known to man. I chased it on the on-the-run bond issue across all the international exchanges; I chased it on deliverable corn on the CME; I chased it on three-point arbitrage in the Singapore currency markets. Or, to be more accurate, I chased the
shadow
of that spread. Didn’t matter what the underlier was, my specialty was the derivative, which fluttered around the thing itself like the wind around a truck, full of gusts and eddies. That’s what I did: I figured out which gusts and eddies were predictable. When I found one, we fed on it. That’s it. It was all just mathematics. As the great Fischer Black liked to say, the markets
need
noise. We weren’t taking positions in L’eggs stockings or GE for the long hold; it didn’t matter if we were trading on the open exchanges or in the dark pools; it didn’t even matter if we were shorting the very same securities that we had our clients long on; we were just plucking the data points from a proprietary set of statistical curves and taking them to the bank. And it was
my
set of statistical curves.