Toby Lloyd earned his MFA in Fiction from New York University. He has published stories and essays in the Los Angeles Review of Books, Prospect Magazine, The Oxonian Review, and Publicbooks.org. He lives in London and is working on a novel.

1.

There were ten of us in Further Maths and I was third best. Or, in Mr. Damien’s words, eighth worst. Number two was Hideo. He sat to my right and had the ridiculous habit of groaning as he wrote successive lines of an equation, like you could actually hear his mind whir. Hideo was quickest at mental arithmetic and had the best record in spot tests, even beating Mildon. But we weren’t taking our A Levels seriously. When it came to real maths, the sort that keeps you up in the small hours, straight-backed against the pillow, he didn’t get close to William Mildon. Who did? Back when we were thirteen, Mildon told me he could prove that root two was irrational. ‘It’s a proof by contradiction,’ he explained. Genuinely awed, I asked how he came up with it. But he only shrugged. ‘It was bothering me, so I thought it through.’ What can you say? The kid was just wired different. And so, strange as he was, we all sort of looked up to him. All of us except Cruickshank, that is, who as far as I knew didn’t give a single fuck about maths.

First Mildon, then Hideo, and then me. And then everybody else. That was how things stood in our final year of school, the last go-around before our actual real lives would begin. Now, it was the morning of the Senior Maths Challenge, fifteen minutes after registration was supposed to take place.

As usual, Mr. Damien was late. When I got in, also late, Cruickshank was on top of the lockers, flapping and snorting his way through a joke. I’d missed too much to understand the punchline—something about interspecies romance—but it proved a hit with his audience, particularly Amandeep, who struggled for breath. Don’t be misled, no one was laughing with him. Though Cruickshank’s jokes were suitably disgusting, he screwed them up. He always forgot key details and several times mispronounced a climactic pun. The hilarity came from the spectacle of Cruickshank himself, thumping any nearby surface and wheezily giggling, as though he never saw the punchline coming. For him, the school was divided into two groups: the obvious bullies—boys who called him a spastic and slapped his face—and those other subtler bullies that allowed him to believe he was part of the gang. Most guys in Further Maths were in the second camp and kidded themselves they were doing nothing wrong. But me, I stayed out of it. If anything, I felt sorry for him. Growing up, we’d all been like Cruickshank—goofy, bad at sports, and unpopular. It was only now the smart kids were bunched together that new hierarchies emerged, and the former victims could restyle themselves as big shots.

‘Hey man,’ Hideo said as I entered. ‘You missed a classic. Shanks on top form.’

Just then Cruickshank, responding to some animal instinct, leapt down and took his seat at the back of the class. The rest of us soon followed as Mr. Damien marched in and slumped to his chair. For a while he said nothing, just sat catching his breath.

‘Is everyone in? Don’t tell me we have to bother with the register.’

As well as taking us for maths, Mr. Damien was our form tutor. Our intellectual development and emotional well-being were both entrusted to the same mad fuck.

‘Good morning, sir!’ called Amandeep. ‘How are you feeling?’

‘Shut up, Aman. Right. Senior Challenge today, isn’t it? Let’s warm your brains up. Let’s roast those little peanuts. x plus x cubed makes one thousand seven hundred and sixteen. What’s x? Don’t all shout at once. It’s not difficult. Anyone?’

There were about three seconds of silence before Hideo came out with the answer: twelve. ‘Least someone’s awake. Right, who can tell me eleven factorial?’

A few tables over, Tony scratched noisily at his exercise book until Mr. Damien reminded us fiercely that this was a test of our mental arithmetic.

Nearing retirement, Mr. Damien was bad-tempered and often visibly bored. By an agreement with the senior faculty he only taught sixth formers, avoiding younger children altogether. This was for the best. His round face, latticed with broken blood vessels, was not generally beloved, and his classroom manner was, well, let’s say particular. Each lesson, rather than explain the material at hand, he slung an inventive combination of questions and insults at his students, until by the time the hour was up, they felt completely worthless. If you were clever enough, you taught yourself.

The room was arranged so Mr. Damien could reach the board without getting up. With his arm at full stretch, his hand shook and he couldn’t keep a straight line; his numerals sloped drunkenly across the board. Some days he didn’t write at all. Instead he would call a boy to the front to scribe. No one knew his exact age, but he was at least in his sixties. When forced to make some unscheduled movement, like descending the stairs during a fire drill, he would complain this was no job for a fat old man.

That morning, tired of open questions, he began to call on us individually. I was up first.

‘Alan, you are yet to bestow us your wisdom. Not too tired from the weekend’s misadventures, are you?’

‘I’m awake, sir.’

‘Tell me. What’s the second order derivative of tan x?’

‘Hold on, I know this, it’s—’

‘Yes?’

‘Sec x tan x?’

‘Is that a question or an answer?’

‘An answer, sir.’

‘Well, it’s wrong. Shanks, you’ve been rather quiet. For a few happy moments I’d forgotten you existed.’

Seconds later I saw my mistake—the first derivative of tan x being sec squared x, not just plain sec x—but it was too late. Mr. Damien had lost interest.

‘Here’s a question specially for Shanks, then. Nice easy one. What’s seventeen squared?’

‘Can I use my calculator, sir?’

‘I’m trying to test your mind Shanks, not find out if you’ve evolved opposable thumbs.’

‘But sir, I can’t do it in my head.’

‘Yes, you can. Seven sevens are forty-nine, aren’t they Shanky boy, and seven tens are seventy. Ten sevens are also seventy, and ten tens are a hundred. Add ’em up and whaddya get?’ Cruickshank pulled a cross-eyed expression and a few people sniggered.

‘Come on now.’

Cruickshank scratched his head theatrically. Our teacher’s face reddened.

‘Two hundred and eighty-nine,’ he burst out. ‘Incredible, truly incredible. And they let him take Further Maths. Anyone would think you’d done Mr. Statland a favor.’

Mr. Statland was head of maths, a patient man at least a decade younger than Mr. Damien. It was well known that the two got on much better before one was made the other’s boss. Whether Cruickshank was truly unable to do the calculation, or just acting up, I don’t know. He had won some laughs and that was enough. Mr. Damien, meanwhile, was riled.

‘Hideo,’ he said, ‘how’s your mother?’

‘She’s fine, sir.’

‘How about a probability question, then? If I send Mrs. Yanamoto a token of my admiration, a dozen white roses, say, what are the chances she invites me round for a hot cup of saké? Stop smirking, Shanks.’

‘That's not really maths, is it?’ Hideo said.

‘I’ll be the judge of that. I asked you for the odds.’

‘I would say pretty low, sir.’

‘You would say, would you? I hope that isn’t a reference to my weight…’

Mr. Damien could be pretty mean, I’m not denying it, but at least he could laugh at himself.

Like all teachers, he had a cruel nickname. His was Fat Fuck. As a kid, apparently, he was a contender on the tennis court and even considered going pro. Now, every part of him bulged. But despite the monstrousness of personality that seemed enhanced and perhaps even caused by his supreme physical bulk, Mildon, Hideo, and I worshipped him. It was such a relief to have just one teacher who didn’t hide his emotions, who swore under his breath, who would come in late, puffy-eyed, and unshaven without bothering to say sorry. He alone treated us like adults, bringing the whole human package to class each day, not just the shallow anger and recycled jokes of the professional schoolteacher. And we were sure he wasn’t, in his heart, a bad person. He only wanted the best from us.

Now he was writing a seemingly random series of numbers on the whiteboard. No doubt we would be asked to find the formula that linked them.

‘Sir?’ Cruickshank whined.

‘What is it now, Shanks?’

‘What would you bet me that I get a Gold in the paper today?’

Beside me Hideo had stopped listening and was drawing in the bottom corner of his exercise book. After a minute, he lifted his hand and blew pencil filings from the page. A pig with Mr. Damien’s face. It had the same straggly hair and the giveaway buttchin.

. . .

The UKMT Senior Maths Challenge consists of twenty-five multiple choice questions, with possible answers labeled A-E. To discourage guesswork, incorrect answers are penalized. Me, Hideo, and Mildon all expected to score Golds and qualify for The British Maths Olympiad, the first real test of our abilities. Of the others, Tony would probably place into the Kangaroo, a runners-up contest, and Amandeep might scrape a Silver Award. The rest were no-hopers.

On balance, I found the paper easier than the previous year’s. Outside the exam room, I caught up with Hideo.

‘Not bad, was it?’ he asked.

‘Nah, it was fine. Want to hear what I got?’

‘Go on.’

‘A Bad Boy Does Everything. Even Drugs. A Dumb Boy Can’t Count. Can A Dog? Believe Anything, But Don't Believe Everything. Consider Death Eternally Endless.’ Making these acrostics was something we did every year, so we could compare answers.

Hideo was nodding.

‘I like it,’ he said. ‘Although, “Eternally Endless” says the same thing twice. And you got one wrong. You mean, A Bad Boy Does Everything...Dangerous Drugs.’

‘Was that the one about the folded sheet with the holes in it?’

‘No,’ said Mildon. I hadn’t noticed he was walking behind me. ‘It was the one with the graph of y squared equals sine of x squared. And Hideo’s right, the answer was D.’

Mildon and Hideo were never jointly mistaken about something while I alone was correct.

‘Fuck! I remember it now. I put D and then crossed it out and changed it to E. Fuck!’

‘Just one question, mate,’ Hideo said. ‘You’ll still qualify.’

All the same, I was furious. It was a needless error, marks just thrown away. When Cruickshank wandered over, I was in no mood to talk.

‘Why are you smiling?’ I asked.

‘Because I got that one right, bitch.’

Despite Mr. Damien’s protestations, Cruickshank wasn’t quite a moron. But he had a moron’s face. His eyes were too close together, and his uneven teeth were pretty much on permanent display. The idea that he’d beat me was unbearable.

‘Bullshit,’ I said.

‘It’s not bullshit! I nailed the whole test. And I can prove it.’

‘How?’

‘With one of your gayboy little rhymes.’

‘They’re called acrostics, Cruickshank, not rhymes,’ Mildon put in.

‘Same diff. Listen up. A Big, Bulbous Dick Explodes, Drizzling Discus-wide Arseholes, Down By Count Cunt’s Courtyard And Droops Badly…’ Here he paused and looked at me. ‘Alan Bradley's Dick Buttfucks Eleven-year-olds…’

By now the whole set had gathered, laughing. Amandeep repeated some phrases in echoing appreciation.

‘That’s not funny,’ I said. ‘And you’ve just made it up now, based on my answers.’

‘It is funny. Or how come everyone’s laughing?’

‘Yeah man,’ Amandeep said. ‘Fair play to Shanks, he’s pulled it out the bag. “Alan Bradley’s Dick Buttfucks Eleven-year-olds.” That’s some skills!’

Aside from me, Mildon was the only person who looked troubled by what had just come out of Cruickshank’s mouth. Not that he cared about the acrostic.

‘Don’t sulk,’ Hideo said. ‘If Shanks has really done that well, think what the rest of us might do.’

. . .

Four weeks later we got the results. Amandeep got the lowest mark required to bag a Gold. He would be sitting the Kangaroo, and so would Tony, who managed a respectable Silver. Hideo and Mildon both got perfect scores. I got one question wrong, so dropped five marks. Cruickshank got everything he answered right, but left one question blank, so beat me by a single point. The four of us qualified for the Olympiad, along with some dork in the year below.

When he got his result, Cruickshank performed a mad victory dance, rising and falling on bowed legs, while swinging his arms back and forth. And as he danced, he chanted his acrostic. Once again I got to hear how my dick, as if with a will of its own, buttfucks eleven-year-olds. Amandeep and Tony found this hilarious. So did Hideo. Tony even asked Cruickshank to repeat the dance so he could record it on his phone.

2.

‘Ever since I was small boy, I have been fascinated by the beauty of numbers, the way mathematics orders the universe.’ This was the opening line of my personal statement for UCAS. Or it was, until Mr. Damien put a red line through it.

‘You still don’t get it, do you?’ he said.

‘Get what?’

Mr. Damien slid my corrected statement back across his desk and began adding loose rubber bands to a ball in his drawer. In Further Maths we defined relationships. Velocity is the rate of change in displacement, its first differential; acceleration the rate of change of that rate of change, its second differential; and the rate of that change, the third differential, believe it or not, is jerk. Such statements, I thought, brought us nearer to understanding the world we lived in.

Mr. Damien, now finished with his rubber bands, pushed the drawer shut with a deliberate thud. ‘You’re thinking of Physics. Maths has nothing to do with the real world. It’s its own thing.’

Mr. Damien never justified himself when he made pronouncements. ‘He speaks like a priest,’ was how Hideo put it when I told him. ‘Who does he think he is?’

The same week our university applications were due, we began our second statistics module, that branch of maths tantalizingly bound up with predicting outcomes. It was then, amid all our dissections of so-called ‘randomness,’ that Cruickshank started on about his theories. Since his unaccountable success in the Maths Challenge, he’d spoken up more in class, and not just to derail the conversation with idiotic jokes. One time he even disagreed with Mildon on something—an argument about the nature of imaginary numbers. But the theories, now they were something else. In fact, ‘theories’ isn’t even the right word. This shit was insane. Lawrence Cruickshank, incapable of chewing with his mouth closed, had somehow convinced himself that he could outsmart time. He believed he could see into the future.

It was lunch break, a couple weeks before the Olympiad. Amandeep and Tony were debating who would win in a fight, Statland or Damien. Amandeep backed our form tutor, which Tony said was absurd—the man could barely walk. ‘Not now, idiot,’ Amandeep clarified, ‘I mean when he was younger.’ Mildon was bent over his central desk, working on a chess problem. I’d just come from the lunch hall, where I’d sat alone, eating canned pasta heated to the point of structural collapse, before retreating back to the haven of our form room.

‘Mate, you got to hear what Shanks is up to,’ Hideo said. Cruickshank was sitting atop the row of lockers again. ‘I’m going to win the lottery,’ he said.

‘And how are you going to do that?’

Cruickshank folded his arms. ‘Maffs,’ he said. He pronounced it like that on purpose, making it sound as ugly as he could.

‘It’s simple enough,’ Hideo explained. ‘He’s half-listened to some of Fat Fuck’s speeches about probability and decided if a coin toss isn’t truly random, but a dynamic event that can be modeled, then it’s the same thing with lottery numbers. You only need to know certain things—the masses of the balls, the dimensions of the dome, whatever, and you can build a model that will accurately predict the numbers each week.’

‘You hear that?’ Cruickshank said. ‘My massive balls are gonna make me a rich motherfucker.’

It’s hard to say exactly what I found so hateful about him. But every word he spoke, every one of his gestures made me wince. I wonder what proportion of human cruelty can be accounted for by the instinctive loathing that a boy like Cruickshank effortlessly produced in others. Repulsion, just like attraction, must play its role in nature. Or we wouldn’t feel it.

‘I hope someone’s told him he’s a fucking idiot,’ I said.

‘I have,’ Mildon replied, without looking up.

‘Even if you could find all these things out, which—like, how?—there would still be the human element. Each week someone waits for a variable period of time before pressing the button. You’d never know how long the balls have to float and bounce before they were selected.’

‘Nah man, I thought about that. I’ve got a system. It’s all about psychology.’

. . .

The British Maths Olympiad consists of just six questions, which you have three-and-a-half hours to answer. Solutions are scored out of ten with marks available for style. Each year, the top hundred students in the country receive prizes and qualify for the second round. In lower sixth, Mildon alone had squeezed through. This time we were ready. Alongside our ordinary curriculum, we’d been working on past Olympiads since September. Mr. Statland said all four of us had a chance of making the cut. We only had to believe in ourselves and get a good night’s sleep beforehand.

It wasn’t possible to reserve our form room for the length of time required, so the test took place in a disused attic in E-Block. The shelves were half-filled with battered textbooks, no longer in circulation, and the whiteboard was stained with faint orange lettering: the residue of a forgotten lesson.

Mr. Damien looked up at the clock on the wall.

‘We’ll begin at five past,’ he said.

The whole point of the Olympiad is to make students think. The A-Level only tests your memory and ability to plod through calculations. How anyone fails to get the top grade, I never understood. Whereas in the Olympiad, you have to discover the maths as you go. As I read the six questions, one seemed to have a straightforward solution which, fearing a trap, I distrusted; one suggested a means of approach, hard but doable; and the remaining four seemed impossible. Still, I was undaunted. The nice thing about maths, as compared with everyday life, say, is that each problem you’re given, however confusing, has a perfectly satisfying solution lying in wait somewhere, one that doesn’t involve any compromise, or humiliation, or self-sacrifice. I began with the second question.

After an hour, I had managed one full answer and two promising starts. This was little consolation for the constant missteps, or the horror of a question you can’t think how to begin. Now and then I turned away from the paper to look over at my classmates. Hideo never stopped writing. Even in his tiny script, he covered pages and pages, eventually leading him to raise his hand and ask for more paper. Mildon took the opposite approach. He’d stare at the paper for a whole minute, sometimes two, as though studying a photograph. Then, quite deliberately, he wrote down three or four lines of working before stopping once more for reflection. Nothing happened on the page that didn’t first happen in his head. I envied his ability to look with perfect clarity through his mind’s eye. Cruickshank, meanwhile, was floundering. Whenever I looked up, he was either gazing out of the window or doodling chaotically. At one point he appeared to be forcing a solution from origami.

With an hour to go, I was plotting a cubic graph when a screech pulled my attention. It was Cruickshank scraping his chair back. Now he stood up and marched to the front of the room, where he handed his scribbles to Mr. Damien, before stomping out. I can’t imagine it had been much fun for him. At least for the rest of us, the hours of frustration were relieved by a few crystalline moments of illumination.

I returned to my paper. By now I’d turned one promising start into a full-blown solution and followed the other to the bitter end: three pages of working, then a brick wall. There was still one question I thought I might get somewhere with. For a while I just stared at what I’d written. It all seemed perfectly correct, my algebraic reasoning was confident, elegant, and precise. And yet it led me to a proof that five equals six. I glanced up at the clock—thirty minutes left—then back to my desk. Then, on the third or fourth time I checked, I noticed my error. I made the necessary alterations and...suddenly, there it was, the way forward, alluring as a silhouette in a window. It was only a matter of keeping four variables in play long enough for two of them to cancel each other out. With ten minutes to go, I’d managed to grind out an answer that was bloody-minded and unarguable. Wishing to avoid the post-match analysis, I too left early.

3.

It was only a year ago and a bit that I lost my virginity. I’d always had crushes on some of the boys at school, mostly kids on the rugby team. But remember: for the boys in my immediate sphere, a big night was a Star Wars marathon accompanied by a blunt. What I’m saying is, there just weren’t options.

Until summer term of Year 12, that is. Inspired by a conversation I overheard on the bus home one day, I ventured onto chat rooms where I could meet like-minded strangers, hidden by a pseudonym. While I was working up the courage to message someone, I saw an opening gambit challenging users to solve a logic problem and DM the answer. It wasn’t hard hard, but it required a little number theory and took me a moment to figure out. Naturally, this reassured me; whoever this guy was, he was sick of dating dumbasses. (I didn’t know that most guys on here weren’t looking to ‘date’ anybody. Not as I understood the word.) Handsome in a rugged and broken-nosed way, Ryan picked me up in his Volvo just two streets over from my parents’ house, and drove with dipped headlights until we came to a car park in a country lane, empty now the hikers had gone home from their day trips. This is it, I thought, a little afraid and very excited as Ryan bit my neck while unbuttoning my shirt. You’re finally, actually doing it. Though I didn’t believe for a moment he was twenty-two, he was kind enough, and afterwards dropped me home. Others followed. Each time was a little less nerve-wracking than the last, but also less thrilling. There was Andre, who had his ex-wife’s name tattooed on his thigh. Sebastian with the ponytail. And Oliver, who insisted that I never touched him—he only got off on getting other people off, he said. Good guys, mostly. No regrets. Even if I never did learn their real names.

By the autumn of our final year, my weekend liaisons with older men had become routine. Some I saw more than once. One night, I met Thomas in a scummy pub somewhere just outside Lewisham. It was too loud for much small talk, which suited me fine. Thomas bought a couple of pints, which we drank rapidly and without pleasure, before he suggested we go somewhere quieter.

Sitting in the passenger seat, I shivered in the breeze from the open window. Thomas smoked at the wheel.

‘If you’re cold, wind it up,’ he said.

‘I’m fine.’

It was then that I saw Cruickshank on the far side of the road, ambling down the street. His hands were buried in his pockets and he seemed to be shuffling his feet. When he emerged from the shadow between two street lamps, I saw he was kicking something along the pavement in front of him, a can maybe. I had never imagined his life outside the school gates. Why would I? Shanks was a creature of the playground, not someone you socialized with. His whole existence was bound up in the world of exercise books and whiteboards, a place with its own rites and customs, where a smashed plate in the lunch hall received a round of applause from a hundred cheering boys. In school, someone like Cruickshank made sense. He even fit in, just about. But out here on his own, with so many empty weekends yawning before him...what was he doing?

‘You want some music? I can turn the radio on,’ Thomas said.

A few days later, Cruickshank burst into the room waving a lottery ticket. He’d picked three correct numbers out of six.

‘What do you get for that?’ Amandeep asked.

‘Fuck all,’ said Hideo. ‘Well, ten quid.’

‘Baby steps, eh Shanks?’ said Tony.

I wasn’t impressed. As Mildon pointed out, the chances of getting three correct numbers was one in fifty-seven. The average lottery player might expect this result once a year. The fact that Shanks got there in a few weeks was statistically uninteresting.

A couple of weeks later, Cruickshank came in more excited still. This time four balls corresponded to his numbers. He’d won £54. There was a less than one in a thousand chance of this happening. Mildon’s eyes narrowed. He was thinking.

. . .

When the Olympiad scores came through, Mr. Damien told the class he was going to announce them out loud. ‘First up, Hideo, who—’ ‘Sir! You can’t! It’s not fair.’

Hideo was the only one who tried to stop him. The rest of us were too curious, and shouted our friend down.

‘Snot fair,’ Mr. Damien mimicked.

Hideo got twelve out of sixty. We all tried to be nice about it, but it wasn’t good. I got twenty-seven. Although I didn’t qualify for the next round, even Mr. Damien said it was respectable. Mildon got forty-nine and Cruickshank got fifty-one. Each score was met by a round of applause, even Hideo’s, but Cruickshank got whoops and cheers. I couldn’t tell if we were still mocking him.

After registration, the classroom emptied as students made their way to lessons. I had a free period, and so lingered after the others. Hideo approached. He looked broken.

‘Everyone has off days,’ I began.

‘I don’t care about that,’ he said. ‘I knew I’d fucked it. We need to talk about Shanks.’

‘Yes. Do you think he’s been pretending all along?’

‘All along?’

‘That he’s no good. Not only did he beat Mildon, he left an hour early. That’s mental. He must be one of the top four or five young mathematicians in the country.’

Hideo looked at me like I’d just told him the earth was only a few thousand years old. ‘Alan,’ he said. ‘I saw his paper. He didn’t even attempt the questions, just drew a lot of ugly pictures.’

I remembered looking over at him in the test, how I had never seen him do anything that looked like maths.

‘What are you saying?’

‘It’s easy enough to see how he did it in the Challenge. Did you notice who he was next to?’

I’d sat behind him. I could picture him now, dropping his pencil repeatedly and each time leaning over towards Mildon’s desk to pick it up.

‘Does William know?’ I asked.

‘Shouldn’t think so. He’s good with numbers, sure, but he’s also a dumb shit.’

‘But what about his BMO score? You can’t copy on the Olympiad, you’d be spotted a mile off. Besides, we all sat so far apart.’

Apart from the two of us, the room was empty. Still, we kept our voices down. ‘What happened to our papers after we handed them in?’

‘I don’t know,’ I said. ‘I left early, remember.’

‘Fat Fuck took them. And he was the one who sent them off to the examiners. No one else touched them. He must have tampered with Cruickshank’s paper. Man, I’m sure he got a real kick out of doing a test meant for teenagers. To get fifty-one, you’d have to solve all six questions.’

‘But he doesn’t even like Shanks!’

‘You sure?’ Hideo asked. ‘Look, do you remember in Year 11, we had that Christmas quiz, and Damien rigged it by giving Charlie Hodges all the answers beforehand?’

‘It’s not the same. That quiz was just a bit of fun. What did it matter who won?’

‘What does any of it matter to that vicious prick? How many times does he have to tell you that he doesn’t give a bollocks whether you pass your exams before you’ll believe him? Here’s a thought: Fat Fuck is not a kind man pretending to be a bastard, just a bastard being a bastard. How funny to show us all up like this! He doesn’t care about honesty, and he definitely doesn’t care about us—’

‘He cares about maths, though,’ I said.

‘No, he doesn’t. You want to know what he really cares about? Power. It would be just the same if he was a football coach or choir master. He’d still just use his authority to belittle everybody. It’s what he gets off on.’

‘I don’t know, man. He’d be risking his job.’

‘Ask Shanks.’

‘Ask Shanks what?’

‘Ask him how he did it. Tell him to write out the solutions for you. See what he says.’

. . .

We had double maths later that day and for once I loathed every minute. The teacher I knew was gone. In his place an imposter, the petty bully that Hideo described. Every one of his quips annoyed me. Cruickshank’s clowning grated as ever. Even Mildon, with his cool lucidity, wound me the fuck up. If there’s one thing that a mathematical education teaches you, it’s that a single false assumption invalidates all your conclusions. It might be something tiny, a misplaced decimal point, say. And everything you thought should follow was wrong. Line after line of plausible nonsense until you end up at five equals six.

When the bell rang for lunch, Mr. Damien got up and headed for the staffroom, while the rest of us stayed put. Most of the class brought food from home. Cruickshank began holding forth again. And people listened. The Olympiad result was the final evidence they needed to take his crazy ideas seriously.

‘The way I see it, man’s no different from a plastic ball. Just another object moving around until he stops.’

I asked if he was still going on about the lottery.

‘Keep up, mate, he’s well past that,’ Tony said. ‘Shanks has his eyes on bigger things now. He reckons he can predict when a person’s gonna die.’

‘I’m a prophet, brother. This shit’s Old Testament now.’

‘Oh come on,’ I said. ‘This is literally insane.’

‘I agree with Alan,’ said Mildon. ‘It’s a very basic category error.’

No one paid him any attention. Cruickshank sat on Mr. Damien’s desk with his knees tucked under his chin and his shoes resting on the table-top—a bold move, he’d be flayed alive if he was caught—and the others formed a horseshoe around him.

‘Go on, tell us how long I’ve got?’ said Tony.

Someone else asked if Mickey Andrews, the school’s champion rower, would die any time soon. ‘His girlfriend’s fit!’

‘Nah, nah, nah, let’s stay closer to home,’ said Amandeep. ‘Which of us here is gonna die first?’

Cruickshank considered this.

‘Alan,’ he said. ‘The boy’s doomed. He gets up to some dangerous things at the weekend, I can tell you. Unless you’re counting Fat Fuck, that is, who’s gonna piss out his last piss any day now.’

Everyone stared at me. Amandeep told me I should get cracking on my will. Tony wanted to know if I had a bucket list.

‘Will’s all sorted,’ I said. ‘But if I really don’t have long left, there’s something I’d like to tell Shanks.’

‘What’s that, battyboy?’

I didn’t say anything while the room was still murmuring and laughing.

‘I’m waiting,’ Cruickshank said. I remained silent until the other boys settled down, eager to hear where this was going.

‘Shanks, everything you think is a lie.’

‘What are you chatting about?’

‘No, no, listen to me. No one in this room likes you. No one. Every single day we laugh at you. You’re a clown.’

‘Shut your mouth,’ he said, and spat on the carpet.

‘When was the last time you saw anyone on the weekend? Who invites you over to their house?’

Mildon, who hated conflict, said something like ‘steady on.’ Amandeep tried to disagree,

‘Cruickshank’s safe enough—’ he began.

‘Tell him that I’m wrong then! Have him over this weekend!’ Both Mildon and Amandeep were silent. To my own surprise, I’d lost control of my voice and was shouting at him now. ‘Ask them, Shanks, ask them who your best friend is. Go on.’

Nobody said a word. Not even Cruickshank, who’d never been quiet for a full minute in all the time I’d known him. He glanced around the room, hoping to catch a friendly face. Surely there was someone who would stick up for him, someone who really did like his jokes, who’d been on his side all along. If not Hideo or Amandeep, then Tony maybe? Or Mildon, perhaps? One by one, the members of the Further Maths set averted their eyes. At last Cruickshank knew what the situation of his life really was. His eyes were shining. How pathetic it would be if he cried.

But I wasn’t done yet.

‘What’s more, Shanks, I know you cheated in the Olympiad.’

‘I didn’t cheat!’

‘Did you think it would impress us? Did you think we would start liking you if you got a high score?’

‘Shut up, Bradley.’

‘Show us! If you really solved all those problems, show us how you did it. There’s a whiteboard, go on.’

Cruickshank kept his seat, defiant. But the class was on my side. However well they’d hid it, nobody liked the oddball shooting up the rankings. Now they wanted to see him brought low.

‘I’ll show you,’ Cruickshank said at last. ‘But not here. Man needs some lunch. You come with me after school, we’ll go round my house, and I’ll show you.’

I agreed. Hideo said he wanted to come, too.

4.

No one had ever been to Cruickshank’s. He lived way out in South London, and it took us over an hour to get there, riding a combination of trains and busses. A ground-floor flat in a cul-de-sac. It was dusky by the time we arrived and Cruickshank pushed his own buzzer.

‘Just letting him know,’ he said, though neither of us had asked.

Before he had a chance to open the door, we were greeted by deep barks from inside the flat. Shanks tried to shout over the dog. ‘Shut up, Bozo!’

‘Your dog’s called Bozo?’ Hideo asked.

‘Everybody’s called bozo.’

Once the door was open, a German Shepherd ran past us, tongue slathering. I never did like dogs. Hideo asked if we should go after it, but Shanks said no, it would come back on its own.

At the end of the landing we came to the flat’s main area, a living room that led through to a kitchen. It’s not that it wasn’t nice. Painted tiles over the sink and a couple of well-worn armchairs gave the place a cozy feeling. But most of the kids I knew were sons of lawyers or doctors and lived in great houses in West London: Chiswick, Richmond, Notting Hill. The interiors always looked somewhere between a display room in Ikea and a private art gallery. Cruickshank’s place, with its cracked surfaces and narrow corridors, was a long way removed. A scholarship boy myself, with parents who taught in the state sector, I knew what it was to listen enviously to breaktime discussions of the skiing at Innsbruck versus Lake Tahoe. Though I don’t remember where I heard it, I was fairly sure Cruickshank lived with just his dad.

While I was looking around, Cruickshank zeroed in on something on the floor by the fridge. Two lumps of shit, one propped up by the other. Only then did I notice the smell.

‘That fucking dog,’ he said to himself. In the cupboard above the sink, he found a roll of paper towels and scooped the shits into a black bin liner. Hideo and I watched without offering to help.

On the far side of the living room, a door opened and a man’s face appeared. He had a beard that had been left to grow and grow, and his eyes were close together, like Cruickshank’s.

‘Who did you bring?’ he said. ‘You’re not meant to bring anyone. Don’t let your friends mess up my house now.’

Behind the man, a flatscreen telly muttered. Cruickshank was spraying fluid from a bright orange bottle. Then he was down on his knees, wiping at the stain.

‘How many times have I told you?’ he said. ‘You have to let the dog out. You lock him up, he craps inside.’

Cruickshank told us to go wait in his room. We heard him argue with his dad as we walked away.

The bedroom was immaculate. No, that doesn’t do it justice. As soon as you entered you could see that everything was arranged according to some obscure scheme. I don’t ever remember standing in a room so intolerant of curves, or where every angle was exactly ninety degrees. The bed was made up in the precise center, and the spines of books along the wall were all an identical height. To one side was Cruickshank’s desk. A small leather-bound notebook. On the cover, the words: ‘Infinities and Bigger Infinities.’

Hideo picked it up and rifled through.

‘Jesus Christ,’ he said.

But my attention was drawn elsewhere. On top of the bookcase, two handheld mirrors faced one other with a sharpened pencil lying between them, and numberless others stretching into their depths. I placed my hand between the two mirrors and observed the multiplication.

‘Dude, this stuff is fucking weird,’ Hideo said. ‘Listen to this. “A proof of personal immortality.” Underneath a bunch of nonsense algebra: “x equals z squared divided by root y, where z is defined as the sum of...something I can’t make out, multiplied by the population of the planet, and y is mean global life expectancy. After that is a so-called proof that motion is impossible. Like Zeno, but without the proper steps. Look at this stuff! It’s mad. Dude, look!’ When I still didn’t answer, Hideo put the book down. I was studying a sheet of lined paper, blu-tacked to the wall. The names of everyone in Further Maths were written in a column. Next to each name were two dates, like on a tombstone. Beside my name the second date was this very year. The image of Cruickshank walking around at night, with hands bunched in his pockets, floated before me.

‘Dude,’ Hideo said again, ‘are you okay?’

There have been three times in my life when I have feared imminent physical violence.

Once when I was eight years old, Bobby Crust told me he was going to beat me up after school, and his friends formed a circle around me when I was trying to leave. Another time I was mugged on my way back from a friend’s birthday; a hooded figure, faceless in memory, snarling. The final time came when I was standing in Cruickshank’s bedroom, waiting for our host to return. The same rush of nerves, an almost dizzy sensation.

‘I’m leaving,’ I said.

‘What are you talking about? We only just got here.’

‘Stay if you like.’

Hideo followed me from the room without protesting further. On the train back he claimed one look at that notebook was enough to see Cruickshank was nuts, but I think he left for the same reason I left. I think he was afraid.

At the door, Cruickshank tried to stop us.

‘But I never showed you my solutions,’ he said.

In the street beyond the patio, there was his dog, a stout black figure skipping leisurely towards us. I said it was fine, we could do it tomorrow. Or whenever, whenever.

5.

We might have learned conclusively whether Cruickshank was a genius or a cheat in the second round of the Olympiad. But he never sat it. The day before, when I got in, everybody was sitting quietly at their desk. Mrs. Scott-Johnson, the deputy head, stood at the front.

‘Come in Alan, sit down.’ For once no one was chattering, and everyone faced the front.

‘I wanted to wait until you were all here before I said anything. This is going to come as quite a shock. The staff were only notified last night.’ She paused. ‘We know you were all very fond of Mr. Damien, and I can only—’

‘He hasn’t bloody gone and died on us, has he?’

No one needed to hear the response to Amandeep’s question to know what the answer was.

Mrs. Scott-Johnson's face twitched, and I wondered if she was annoyed.

‘Amandeep, this is difficult for all of us, so I’ll excuse you. But please in the future watch your language. And yes, I’m afraid Mr. Damien passed away on Saturday morning. There will be a memorial service arranged later in the week in the main hall. Everyone will be welcome to attend. Arrangements for his replacement are currently being discussed.’

‘Miss?’ said Tony.

‘Yes Anthony?’

‘How did he die, Miss?’

‘We don’t know. I think, someone has suggested, that it might have been his heart.’ Double maths was cancelled. In theory, Mr. Statland supervised what was described as a ‘communal sharing and healing session,’ but he busied himself with his marking at the front and left us to get on with things. We told stories about Mr. Damien and gratefully recalled the insults he’d dished out. Now that he was dead, no one had a bad word to say about him. With fondness we remembered the things he’d made us do with our class-time, like when he got us to calculate profit margins of spread betting. And we referred to him affectionately as Fat Fuck, as though he’d always been in on the joke. A few people, in hushed voices, speculated about the cause of his death. Hideo reckoned he topped himself. I didn’t. He was certainly an unhappy man, but I couldn’t believe he’d taken his own life. Not then, in the middle of the school year, with the second stage of the BMO just around the corner.

Only Cruickshank cried. He sobbed like a child, a grotesque wailing noise. It was awful to hear and eventually he was sent home.

‘Strange he should be so upset,’ Mildon said. ‘After all, Mr. Damien was never very nice to him.’

Cruickshank didn’t return to school for several days, by which point the second round Olympiad had been and gone. Nobody mentioned the possibility that he’d cheated again, and nobody mentioned his prediction about Mr. Damien either. Hideo tried to tell the class about that weird afternoon in his house, but it was hard to get across. Everyone just thought it was a funny story about an incontinent dog. He didn’t say anything about the names on the wall, those creepy pairs of dates. When Cruickshank did come back, he was different. He stopped messing around and just quietly got on with his work. He could still be cajoled into telling a joke, now and then, but you could see his heart wasn’t in it. And by summer he was a real introvert, quite sullen even.

It’s July now. Exams are over and school itself, that titanic seven-year block, is finally done. I don’t think I’ll be going in to collect my results next month. I know how I did and you get them in the post regardless. So most of those boys I will probably never see again. Perhaps, in time, I might even miss them. You see people enough and a certain fondness sets in. Don’t you find?