It was an honour to be elected. I was on the faculty at Inchfield, and seized the opportunity to work under specialist in topologic geometry, Professor Knowlton. Five years later, I was working on a level nearly lateral to his, which earned me the invitation to an informal gathering in his garden. This is where he and a select few would deliberate over nominees for the prestigious Roberts Prize in Mathematics, and who would be awarded its substantial cash prize. Seeing as that year, it was Knowlton\u2019s privilege to judge.<\/p>\n
Having been to Knowlton\u2019s house before once or twice, I\u2019d a cursory acquaintance with his unkempt hedges, substantial brick residence, and an older son who had since entered a foreign university. Knowlton seldom mentioned his younger son, who was mentally deficient.<\/p>\n
We settled at a mosaic table on a piazza, near enough to the French doors that Mrs. Knowlton could handily supply us with coffee and its accompaniments. As I anticipated, Dr. Fuller kicked off the meeting by hammering his preference for a member of his own staff. And though the lad in question had been nominated by someone else, we were gratified when Morris, whose field is probability, grilled Fuller. \u201cYes, yes, of course he\u2019s all those things, but isn\u2019t he also in fact, your godson?\u201d<\/p>\n
The laughter that ensued provided Sorensen an opportunity to introduce his own prot\u00e9g\u00e9, an emeritus in Arizona whose research with Euler circuits had thus far attracted only local attention. Sorensen\u2019s a sucker for obscure underdogs. For example, from an array of composers that including Sorensen, no more than six other human beings have ever heard of, like one would a boutonni\u00e8re, he\u2019ll select his current favorite. He amuses me so much, that I was quite preoccupied when from around the corner came Knowlton\u2019s younger son, to sidle up behind me.<\/p>\n
Slight, and fair haired, Donald was perhaps sixteen at the time. I suppose he chose me because I was the youngest at the table, and because I always greeted him with a smile. He touched my collar and whispered loudly, \u201cMis\u2019er Irving, come with me. I want to show you something.\u201d<\/p>\n
\u201cLater, Donald\u201d I murmured. But his expression, eager to the point of pain, got me off my chair, and excusing myself. However the frowning Knowlton was quick to chastise his son. \u201cDonny, go away. Mr. Irving and I are talking.\u201d<\/p>\n
Donald displayed a particular kind of fear, hurt, and anger which alarmed me. His expression reminded me of a childhood playmate whose father drank. But for the moment reassured by the bland face of Prof. Knowlton, I followed Donald.<\/p>\n
The boy led me back around the corner he\u2019d come from, and via a side-door, in to the house. He then took me up a flight of stairs to his room, which, bare of the expected zoological, mechanical, or academic clutter, was very tidy. And taking from under his bed, a battered spiral notebook, he passed it to me.<\/p>\n
I leafed through the early pages full of penciled numbers, by no means neat, but not illegible. Some basic problems in addition and subtraction. But impatient, he snatched the book and thumbing deeply into it, then handed it back, pointing to an area on the left-hand page. Obedient, I looked only to find before me, his wobbly notation of the Fibonacci Sequence. That plaything of the best minds in each century, encrypted by Nature in cauliflowers and pine cones\u20141, 2, 3, 5, 8, 13, 21\u2026<\/p>\n
Smiling I pointed to the sequence, and when Imurmured its terms, his own face spread with corresponding joy. \u201cYes, one an\u2019 two, then two an\u2019 three, then three an\u2019 five\u2026\u201d<\/p>\n
Noting that his written sequence ended at 89, I pointed to the last terms. \u201cFifty-five and eighty-nine?\u201d Blinking, he grimaced, and pressing fingers, which twitched, to his jaw, he retreated.\u00a0 I waited while, with his skull in both hands, he sat on the smooth white bed.<\/p>\n
\u201cA hun\u2019red and forty-four!\u201d<\/p>\n
I tried to smile, suddenly aching that this devoted mathematician should have to strain so hard to take the first steps of the science. He was still frowning and holding his head, as I continued to leaf through the later pages.<\/p>\n
\u201cA hun\u2019red and forty-four, Mis\u2019er Irving, is twelve twelves,\u201d said Donald. Dismounting from the\u00a0 bed, he took the book, for the purpose of indicating another sequence: 1, 4, 9, 16, 25\u2026<\/p>\n
Again, I was arrested by the point where the sequence stopped.<\/p>\n
\u201cFourteen times fourteen?\u201d I murmured, almost at once regretting that I had. Retrieving the book, with a fresh frown, he retreated to the bed, and began drawing little squares and dotting them. I bent over him to see and realized that he was solving the problem through a crude yet ingenious system of incremental multiplication, similar to a written abacus, which I could only imagine he had invented himself. He seemed to have no notion of the usefulness of place value and columnar operations.<\/p>\n
\u201cA hun\u2019red and ninety-six,\u201d he produced at last, straightening.<\/p>\n
\u201cWho taught you to do this?\u201d<\/p>\n
He blinked.<\/p>\n
\u201cDonald, did your mother teach you to add fourteen fourteens like that?\u201d<\/p>\n
\u201cNo.\u201d<\/p>\n
\u201cThe one, two, three, five, eight, did your mother teach you that? Did anyone teach you that?\u201d<\/p>\n
\u201cNo.\u201d<\/p>\n
\u201cWould you like to have someone teach you about numbers?\u201d<\/p>\n
\u201cNo,\u201d said Donald.<\/p>\n
\u201cHave they tried?\u201d<\/p>\n
\u201cMy math is different,\u201d said Donald.<\/p>\n
I\u2019’m not proud of it, but to be sure that Fuller wasn\u2019t getting anywhere with his prodigy I needed to go back downstairs, and that\u2019s where I went.<\/p>\n
Though Knowlton\u2019s sarcastic appraisal lowered my estimation later, Gening, a statistician for whom I had the greatest respect in those days, was holding the floor when I arrived. In fact, as he laid out the merits of a statistician in Washington, it occurred to me that he possessed all those qualifications himself, only more so. Statistic analysis has never been my strength, and I have, perhaps exaggerated, respect for people who master standard deviation at an earlier age than I did.<\/p>\n
When Donald came up behind me again, his hand touched my collar just at the same moment that Knowlton snapped, \u201cDonald!\u201d Out-of-place against a noble old hawthorn hedge, the boy was wilting before my eyes, which prompted me to rise and, once more, follow him.<\/p>\n
Donald did not take me upstairs, but only out of earshot. \u201cMis\u2019er Irving,\u201d he said, \u201cYou di\u2019n\u2019t stay for what I wanted to tell you. Daddy\u2019s judging the Roberts Prize for math. I want to enter wit\u2019out him knowing. I can\u2019t enter if he knows, you know. It wouldn\u2019t be fair to the others.\u201d<\/p>\n
\u201cDonald, you have to be nominated, you see. That\u2019s what those other mathematicians are here for today, to help your daddy pick somebody good out of the ones that have already been nominated.\u201d<\/p>\n
\u201cBut they haven\u2019t picked yet, have they?\u201d<\/p>\n
\u201cWell, no.\u201d<\/p>\n
\u201cThen couldn\u2019t you nominate me, Mis\u2019er Irving?\u201d<\/p>\n
At this moment Ivy, the Knowltons\u2019 maid, came in. \u201cMr. Irving, Mr. Knowlton begs you not to pay any mind to Donald. He\u2019s been moody all week. Mr. Knowlton\u2019s specially anxious to have your thoughts on the selection.\u201d<\/p>\n
I hadn\u2019t known how much I\u2019d been hoping to hear this until it presented itself.<\/p>\n
\u201cCertainly, Ivy. I\u2019m coming.\u201d<\/p>\n
I had my own definite idea about a candidate, but wouldn\u2019t have brought it up without this encouragement. Silently thankful for Donald\u2019s interruption, I took my iron-filigree chair and began.<\/p>\n
\u201cWhat seems to me,\u201d and gazing at each face, I saw how my sententious tone caught them by surprise, but they remained attentive to me, \u201cis that we\u2019ve an almost equal array of accomplishments before us. Who can say which achievement will really mean more to the science, and to progress. Which will really find its most useful expression, in the future? Burkhardt\u2019s circuits? Pauley\u2019s conchoidal surfaces? Who can tell? What we can estimate now, right here, is the human contribution, the dedication, the labor, that a particular candidate puts into their field. Begin with the expenditure of time. I happen to know that Tillson, for example\u2026\u201d<\/p>\n
Every face turned to the French doors, behind which were sounds of struggle, Ivy\u2019s breathless protests, and Donald\u2019s urgent, partly muffled exclamations.<\/p>\n
\u201cIvy! What\u2019s the boy doing?\u201d demanded Knowlton with an expression of stern distaste.<\/p>\n
\u201cOh, he won\u2019t\u2026 won\u2019t\u2026 stay inside like you asked,\u201d she answered.<\/p>\n
\u201cDonald!\u201d barked Knowlton. \u201cStay inside, for heaven\u2019s sake. Give me half an hour!\u2026 Ivy, tell him I\u2019ll walk with him after\u2026\u201d and raising his watch,\u201cthree, we\u2019ll go to the duck pond at three o\u2019clock.\u201d<\/p>\n
\u201cNo!\u201d Donald\u2019s protest was clearly audible. \u201cI have one thing to say to Mis\u2019er Irving, one thing! Mis\u2019er Irving don\u2019t mind, ask him, he don\u2019t!\u201d<\/p>\n
\u201cDonald,\u201d Knowlton\u2019s voice adopted a tone I would not have defied as a boy, \u201cMr. Irving does mind. He is here on business. No, Irvie, please,\u201d as I must have started to get up and go to the boy. \u201cDonald, this isn\u2019t like you. Why don\u2019t you go upstairs and draw in your sketchbook for awhile?\u201d<\/p>\n
The inner rumpus subsided. Ivy must have persuaded Donald to go upstairs. Frightened that my little opportunity would be lost, I frantically tried to pick up my thread, but picked up something quite unconnected, as in my nervousness, I blurted it out.<\/p>\n
\u201cKnowlton, who teaches Donald his mathematics?\u201d<\/p>\n
The broad, avuncular face was caught with surprise. \u201cDonald? No one! They tried, years ago. Kate tried so hard back then. Hired a specially trained teacher from the elementary school. A tutor from the staff at her own girls\u2019 college, stewed over the times tables with him herself for hours. It was no use. I doubt he can do more than addition on his fingers. We gave up when he turned twelve.\u201d<\/p>\n
I stared into the mosaic tabletop,\u00a0 as I felt my face became bright red. It must have been the sun on my neck that let me feel it. Looking up, I saw what none of the others could. Donald leaning out of a second-floor window, and waving his notebook. He pointed at me, then at himself. and nodded.<\/p>\n
\u201cMr. Irving,\u201d Benedict\u2019s smooth, cultured diction interrupted, \u201cYou were speaking of a \u2018human contribution.\u2019 Permit me to remind you that the true measure of the human contribution of a mathematician is his contribution to humans. The significance of discovery, be it scientific, mathematical, or any sort, lies exactly in the degree to which it can be appreciated and put to use by the human community. That is the purpose of the Roberts Prize. It is a social recognition, paid in hard social and economic currency, awarded in a structured scientific community.\u201d<\/p>\n
I was distracted by Donald disappearing into the window and slamming it shut.<\/p>\n
\u201cSo that,\u201d I rejoined weakly, \u201cif one had to deliberate awarding either Newton or Leibnitz a prize for the discovery of calculus? The criterion wouldn\u2019t be who had worked longer, or harder, or more independently. But only who published, got it out there, for human consumption, first.\u201d<\/p>\n
Benedict seemed taken aback, but soon replied,\u201cIsn\u2019t that, Irving, the only honest way?\u201d<\/p>\n
\u201cBut suppose we found a lost medieval manuscript that described calculus. One that had been lost since it was made, that had never done a soul any good. Would it be a scientific achievement?\u201d<\/p>\n
Knowlton, of all of them, seemed readiest to agree. \u201cBenedict! Think, man! A medieval Newton!\u201d<\/p>\n
I looked up and saw a light, that pensive face regarding me through the window. The head that independently endeavored in a science which I suppose had been a source of torment to him. The head which produced that little system of symbolic multiplication, by a labor I simply couldn\u2019t imagine.<\/p>\n
\u201cNo,\u201d conceded Knowlton, laying his hands on the mosaic tabletop. \u201cYou\u2019re right, Benny. It\u2019s a social enterprise. Art is in the eye of the beholder.\u201d He turned to Fuller. \u201cTell me again about the algorithm Beckridge used.\u201d<\/p>\n
\u201cBother the Roberts Prize,\u201d I grumbled. And it is then, that I left my chair.<\/p>\n","protected":false},"excerpt":{"rendered":"
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