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 basebalclass="underline" 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 Erdős, 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.”