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War all too easily becomes remote to those not engaged in or suffering from it, and in 1914 and ’15 the Tweed Valley was particularly conducive to that point of view. Thompson tried to enlist, was refused and returned to his studies. Donald Verulam left the University for some undisclosed job in the War Office. At school the most obvious effect was the decline in our numbers. By the summer of 1915 most of the rugby team had joined the army or had been recalled to their now-essential jobs in the mills and on the farms. The student body dwindled to just over thirty and economies began to be introduced. The Siddeley-Deasey was sold. The hot-water heating was more often off than on. We got joints of mutton every other day, and then only at weekends. Our diet was supplemented by black pudding, an increase in root vegetables and a regular mincemeat stew of dubious provenance, with a coarse texture and a gamy smell.

As far as Hamish and myself were concerned, the worst consequence of the war was that we were drafted into the rugby team. We were not keen sportsmen, though neither of us was weak or frail, but preference or inclination had no influence on Minto. I was instructed to play center three-quarter, where I was relatively content. I kept out of the scrum, could run quite fast and got rid of the ball as soon as I received it. Hamish was on the wing at first, but then after one match Minto switched him to hooker. He had no aptitude for the position at all, but his shocking acne proved to be a potent disinclination to the opposing front row. Nobody wanted to rub cheeks with Hamish and as a result the binding in the rival scrum was dangerously loose. We got a lot of possession from set play, and with the various talents of the black buns we actually won a few matches.

Hamish and I did not enjoy this extra rugby (regular coaching, a match every Saturday and extra coaching on Sunday if we lost), as it cut heavily into our free time. Normally on a Saturday we would sneak away from the compulsory spectating of the school game and climb Paulton Law, the hill behind the house. There we would sit in the shelter of a dry-stone wall, smoke cigarettes and talk. We talked about everything but, inevitably, Hamish would bring up the subject of mathematics. He did most of the talking. He was already at home in conceptual words I would never penetrate. In fact, I sensed the end of my tether once we started doing quadratic equations. The maths gift was dying on me fast. The terrain ahead seemed shrouded in an opaque mist. By this time Hamish was aged seventeen. I could no longer understand him but I was beguiled by the way his mind worked. Mathematics was for him an entrancing playground. On one of our last Saturday afternoons, I remember, he had become obsessed with the idea that numbers were infinite. He was always fascinated by immensely large numbers. It was a sign of the gulf between us. My brain seemed to seize up at anything over a million.

It was October 1915, I think. The Saturday match had been canceled due to heavy frost. It was a fissile, sharp day. A blue, washed-out sky and hard clear views of the Tweed up as far as Thornielee and downriver to the smoke from the mill chimneys in Galashiels. We sat huddled in our usual spot, smoking Turkish cigarettes and taking sips from a flask of rum that Hamish had smuggled into school.

“Do you remember that time,” he asked, apropos of nothing, “when you said, did prime numbers exist before anyone had thought of them?”

“Did I say that?”

“Yes.… Well, I was thinking. Is maths something we invented or something we discovered? And I thought, we couldn’t have invented something as complicated as maths. The history of maths is a history of exploration. As we go we find out more. It is all there”—he waved at the general scene—“waiting to be found.”

“I suppose so.”

“And what does that tell you about the world?”

I said nothing.

“If maths in some way is already there … who created it?”

“I don’t know.… God?”

“Yes. Maybe. Maybe maths proves God exists.” He looked at me. The cold air was having its usual unfortunate effect on his face, but his eyes were wide with the intensity of his thought. To my astonishment, I suddenly felt a little frightened.

“What I think,” he began slowly, “is that maths is the key to everything.” He paused. “If you go far enough, perhaps you’ll discover the meaning of life.”

I was going to scoff, but I saw that he was caught in a strange fervent mood. He drank from the flask. He was intoxicated, but not as a result of any spiritous liquor. That afternoon he went on to tell me about a mathematician called Georg Cantor, a man, he said, who had organized the infinite. He talked about set theory, transfinite and irrational numbers, and the square root of 2, and the mysteriously potent designation aleph-null that Cantor had devised. He told me many things, most of which I understood not at all, or which promptly slipped my mind, but I will never forget the passion of his monologue. It had a quality that was rare, and, although it may be bizarre to talk about it in association with an abstract academic subject, I can find no better word to describe it than “faith.”

It was shortly after that day on Paulton Law that my uncle Vincent Hobhouse died, not from apoplexy or heart failure as we might reasonably have supposed, but from being run over by a motor bus in Charlbury High Street. I wrote a clumsy but sincere letter of condolence to Aunt Faye. She replied at once, saying how “touched” and “moved” she had been by my sympathy and concern. Perhaps her own bereavement reminded her of mine, but whatever the reason she began to write to me regularly once a week. At first I thought this a little strange, but gradually I grew to look forward to her letters with impatience. I started writing back too, and our correspondence was soon in full spate.

You will understand that, the average seventeen-year-old boy has little or no power over his affections. In my case this impotence was singular. I lived under the sway of my emotions. Even as an adult I find the struggle to resist exhausting. I possessed no resilience then. This sort of nature is both a curse and a blessing. Try to understand me as I was and do not judge too harshly when you hear what happened next.

I have always felt vividly and instantly with no mediating influence of reflection or logic. My nature gives to all my work an impulse and a motive that, however the critics may have carped, they have never denied is my prime and most valuable asset. It is a propensity that has brought me the happiest moments of my life and wreaked terrible devastation. Oonagh was the first to receive my love, and my aunt Faye was the next. She initiated my first adult, equal discourse. I fell in love with her through print. I had not seen her since that day in Waverley Station when she kissed my cheek. Now, those seconds of contact returned — and with what transforming force. I saw her dark, bruised eyes, humid and alive; smelled the odor of her perfume; felt the soft contact of her cheek with mine. I realized, with thrilling hindsight, that I had in fact loved her, unknowingly, since that moment. When the post arrived and was distributed, I held the letter unopened for minutes, my heart clubbing my ribs, my breath painfully constricted. “All my love, Faye.” I derived a hundred nuances from those four bland monosyllables. This was my first blind passion and I celebrated it nightly with physical release.

I began to take more care over the composition of my letters, expanding them from tedious itemization of the school news into what I hoped were stylish intimations of my own character and personality. I told her of Minto’s deepening gloom about the war, of Hamish’s speculations about mathematics as the key to all nature; I whimsically embellished and exaggerated our own roles in the rugby team, as if we were a couple of knowing aesthetes pretending to be bloods for a dare. I presented her with myself stripped of any secondary defining role — child, pupil, nephew. It was a test, in its way, and I took the increasing candor and intimacy of Faye’s replies as a sign that I had passed.