I did not flinch, in fact, but he would not have noticed anyway, preoccupied as he was with the state of his clothes.
“I’ll have to change,” he said. “Bastards.”
“Why don’t you tell Minto? He said we should report bullying.”
He looked at me. “New rat?”
“Yes.”
“Minto would flog them, I suppose, but he always flogs the fellow who clypes as well.”
“Oh.”
“It’s not worth it. You’ll understand when you see how Minto flogs.”
“Why does he flog the victim?”
“Makes sense. He has a quieter life. He knows that when someone does complain it’s really serious.”
He smiled. He had large uneven teeth. He had fair hair and a pale skin that somehow made his acne seem worse. He was an ugly boy.
“What’s your name?”
“Todd.”
“I’m Malahide. Thanks for not slashing on me, Todd.” He paused. “I won’t forget it. Ever.”
It was a strange thing to say. He smiled again and walked off. So began the most important friendship of my life.
Mathematics. Why was I good at it and indifferent to poor in my other subjects? I believe that sort of skill or talent is something to do with the cast of the individual mind, innate, a priori. How could I, whose imagination was first stimulated by unknown stories in an incomprehensible tongue, have a talent for mathematics? The only answer I can supply is precisely because my imagination was stimulated in that way. I went to school clear-eyed, unformed. I remember my first arithmetic class. The rear wall was covered with charts of the multiplication tables.
“Right, Todd. Six-times table.”
“What table, sir?”
Uproar in the class. I was put at a separate desk to learn my tables. The numbers crowded before my eyes. I looked at the nine-times table. I saw at once, with the clarity of instinct, that the integers in the answer to each calculation themselves added up to 9: 9 × 2 = 18, 1 + 8 = 9, 9 × 3 = 27, 2 + 7 = 9. And so on up to 10. I drew my teacher’s attention to this and received my first words of praise.
What made me notice this? What made me see the pattern? And what kind of conjuring trick in that most abstract of worlds is being played here? I am not saying that I felt in some way blessed, but I do consider that some sort of inkling was being offered to me here. Since that first day at school and since that discovery the realm of mathematics was, for me, teeming with promise. What other secrets would I find? What other insights?
It is said that there are two types of mathematicians. Ninety percent see in figures. Ten percent see in pictures. The most brilliant, the most profound, come from that 10 percent. In my own case I think that for a few early years I saw the world of numbers in pictures, that I had the gift up to the age of ten and then, for some reason, it faded into mere proficient numeracy. But the great mathematicians never lose that facility. Perhaps that is why infant prodigies occur only in the worlds of maths, music and chess. These regions can be surveyed pictorially; patterns and shapes can be perceived there. Order can be discerned among randomness, sense separated from contingency. Or at least that is what I used to think. I have abandoned explanations now. Mathematics and physics have led me to greater, more disturbing truths than these, as I shall reveal to you. Sense, order, pattern, meaning … they are all illusions.
Hamish Malahide, of course, was one of those 10 percent. I like to think we all are at birth, but the tabula rasa is quickly scored with confusing hieroglyphics that we never manage to erase again. I was lucky. I had that guileless vision for a few extra years. Hamish never lost it. He was extraordinary. Mathematicians, like artists, tend to have their peak periods. Hamish did also, and as a young man produced the celebrated Malahide Paradoxes I and II. There was a brief refulgence in the 1940s with the discovery of the Malahide Number, but after his twenties the creative power waned, almost like a form of aging. But his perception remained ever vigorous and acute, right to the end of his desperately unhappy life.
At Minto Academy it took me some time to realize his qualities. At school he was a reviled and unpopular figure because of his appalling acne. Even Mrs. Leadbetter, the matron, gave up any pretense of medical impassivity in her vain attempts to keep it under control. She wore cotton gloves when she dabbed the goo and patent lotions on his face, her nostrils tight with disgust. Some of the school wits called him Job and the name stuck. In summer we often went to the Tweed to bathe and Hamish had to swim downstream from the rest of us. Even I, his only friend, had to admit that unclothed he did look repulsive. Consequently I often found myself divided in that role. There were things about him that I found potently intriguing, but if I looked too closely at those vivid encrusted spots my scalp literally began to crawl and my eyes water. But Hamish, with his typical sensitivity, sensed my dilemma. One day he showed me a small pot of ointment.
“What’s that?”
“My mother sent it to me: ‘Dr. Keith Harvey’s Emulsion. Cures Warts, Acne, Lupus, Locomotor — Ataxy and St. Vitus’s Dance.’ She sends me these things once a month.” He smiled. “For my rotten plooks.”
“Oh yes,” I said, as if I had just noticed them. “It must be a …” I could not think of a word—“nuisance” seemed such a grotesque understatement.
“A curse,” he said. “I’ve been cursed, I know.”
The candor was sufficient to remove the awkwardness between us. After that we often spoke about his spots. I even read the Book of Job in the Bible.
“They’ll go,” I said. “My brother had spots — they all went.”
“But what’ll I look like underneath?” he asked with a weird grin. “I can’t imagine what my face’ll be like, clean.”
“Normal … won’t it?”
“I’m not so sure.”
My friendship with Hamish grew as that first term passed. Although we were both maths specialists, he was so far advanced he might have been doing another subject altogether. To take an architectural analogy: while the rest of us were designing cab shelters and public lavatories, Hamish was building Gothic cathedrals. From time to time he spoke about mathematics and I began to gain some insight into the strange and beautiful workings of his mind.
In our class Minto had set us a project to discover all the prime numbers up to 1,000,000. (A prime number, for those of you who do not know, is a number that is not divisible by any other counting number — apart from itself and 1. Eleven is a prime number, so is 19, so is 37.) The project was a long-term one and had been going on for years. Successive generations of schoolboys had been like Minto’s researchers, scrabbling away among the numbers from 1 to 1,000,000, and coming up, like gold prospectors, with the occasional nugget — a prime. As we discovered them we wrote them on a vast wall chart. We were systematically organized by Minto, each one having a few thousand numbers to sift. The project was completed shortly after I arrived. We counted up and had a total of 41,539 primes. Then Minto, with the air of a conjurer producing a rabbit from a hat, showed us a calculation for estimating how many primes lay between any two given numbers. But, interestingly, the figure the calculation produced was sixty-seven numbers out. Checks established that the calculation, while close, was never exactly right.