by A. N. Myers
There’s something uniquely fulfilling about the proof of a mathematical theorem. It’s an act of divine discovery. It’s like finding a diamond that’s been hidden in the earth since the beginning of time. I remember chatting with a sculptor once who insisted that the beautiful things he created were already there, hidden in the stone, and all he was doing was releasing them. I guess it’s the same with mathematical theorems. You’re making the unreal real and your tools of the trade are your workings, your proofs, as opposed to the hammer and the chisel. I guess by your expression you don’t believe that I can be real either. How could a wizened old woman like me have the answers to all these impossible problems, scribbled down in a yellowing exercise book? You’ve got some choice theories about me, I bet you have! I hope that I’m able to put you straight on one or two of them, for invariably most theories held about people turn out to be wrong.
Let’s start in the year 1947, when I was a lovely young thing of 24 years. I think I was quite an unusual girl at the time, having obtained a mathematics degree from London University, and I was terribly proud of myself for getting through it, against all the odds. On my graduation I imagined I’d find some glamorous job working for the War Office, decoding enemy messages or the like, but when that didn’t work out, I was quite satisfied to take a teaching job at the local grammar school, and that’s what I did for eighteen happy months. I thought my young husband John, away in Burma since the fag end of the war, would be as proud as I was of my achievements. But in my naivety I’d forgotten all about the male ego, and John’s natural conservatism. When he arrived home, he was stick thin and terrifyingly nervous, and it seemed to me almost immediately that his sense of fair play had disappeared with his good health. Within two months of his return, he was working for the Ministry of Food—a job his uncle had wangled for him—and badgering me about resigning my teaching job.
‘Dorothy, I don’t mean to be unkind. But I don’t think it’s fair on us as a couple for you to carry on with this much longer. Your first priority is to our family. Soon, God willing, there will be more than just the two of us. Doesn’t it make sense for you to be getting our home ready for that right now instead of wasting your time on other people’s children?’
‘There’s not a marriage bar on female teachers anymore, John. I think they lifted that a few years ago.’
‘Well, be that as it may, it’s rather selfish for you to carry on schoolmistressing. And it’s not as though we need the money. I’ve got a good job now, and Mr Fazackerley says that I can expect a promotion soon, what with all the extra work we’re having to do.’
I should have told him then and there that I didn’t think I could ever have children—I hadn’t had a period since 1943—but what with his nerves, and the fact that I hated doing anything that would hurt his feelings, I just didn’t. I regret that now, I really do. But I didn’t tell him, and he kept on and on, and within two months I’d handed in my resignation. I cried and cried afterwards. That night John had insisted we went to bed early, ‘to help the baby along’. Well, there wasn’t a baby, there never would be, and as I lay underneath him, desperately wanting to love him again, I was secretly glad of the fact.
* * *
‘I can see you’re missing your teaching,’ said John one day in early 1948 over a copy of The Times. ‘I’m not totally blind, you know. So I’ve fixed something up for you.’
‘Oh?’
‘I’ve told you about Mr and Mrs Fazackerley, haven’t I, their big house in St. Albans? They have a nine-year-old son. Clever little chap, by all accounts, but struggling awfully with his arithmetic. Teachers don’t know what to do with him. I thought it would be a nice thing for you to do a spot of tutoring for him. Get him up to speed, so to speak. And it would be an extra bit of pin money for you, too.’
‘I don’t know, John. I don’t really have experience of teaching the little ones.’
‘Well, I’ve already said you’ll do it,’ he said, vanishing behind his newspaper. ‘I really want to keep Mr Fazackerley sweet, so I’d appreciate it if you gave it a go. And it’s not as though you’re doing much around here, by the looks of it.’ He ran a finger along the sideboard and raised a slightly grimy digit. ‘Be a sport, yes? I said you’d start tomorrow afternoon. I’ll even telephone a cab for you.’
In retrospect, I should have told John to shove his stupid job, but I suppose I was quite pleased to have a chance to teach again, and I genuinely didn’t want to mess things up with Mr Fazackerley for him. So, I said I’d do it. I spent the rest of the evening and the next morning gathering my old teaching materials together and making some rudimentary tutoring plans. Although I had no idea what to expect, or what standard the little fellow was at, I became increasingly excited by the challenge, and before I knew it, I found myself standing on the Fazackerley’s drive, watching the taxi rattle away between the gloomy banks of rhododendrons. It was getting chilly, so I clutched my teaching bag, marched up to the front door, and tugged the bell pull.
As I waited for my new employers to appear, I stood back and examined the property. It was a traditional, albeit slightly shabby, large country house, of the sort occupied by the prosperous middle class, with ivy obscuring half the windows, and a sort of faded grandeur hanging about it. I noticed that the black paint on the door was peeling away, and someone had carved with a knife the legend 48th Canadian Highlanders embarrassed themselves here into the sill above the door, so I knew that soldiers had been billeted here during the war. As I was thinking about ringing the bell again, the door jerked open with a violent squeak, and a tall, olive-skinned woman with bare arms was squinting at me through a fug of cigarette smoke. She tipped her head and plucked the cigarette from her lips.
‘Oh, I almost forgot. You’re Mrs . . . Lampard? The maths tutor?’
‘Yes. Mrs Fazackerley?’ I offered my hand.
She shook it limply. ‘Lillian. I suppose you should come in.’ She bellowed up the stairs, so loud as to make my ears ring. ‘Graham, you little tyke, your teacher’s here!’ She frowned. ‘You know what boys are like, I suppose. God knows what he’s doing up there. I think you’re early? Come a long way?’
I decided that I should only respond to the last of these queries. ‘Not too far. Barnet? I took a cab. The driver’s going to have his dinner at the local inn, then he’ll take me back, hopefully.’
‘Well good luck with that. I know these cabbies. He’ll probably be getting lost or plastered. Barnet. I suppose you’ll know the Musgroves? Of Woodhouse Row?’
‘I’m afraid we don’t.’
‘Oh. Well, your husband works for my husband, doesn’t he? I’d hate to work for Jack. Absolute tyrant.’ Abruptly, she thundered up the stairs, and seconds later returned with a small, mousy haired, reluctant boy in shorts and a grey school blazer.
‘Graham, this is Mrs Lampard. She’s going to try to bang some sums and whatnot into your head. So be good.’ She looked at me askance. ‘I think my husband said something about a guinea for the hour, and your cab fare. Should I pay you now?’
‘Perhaps when I’ve finished?’
She nodded. ‘Graham will escort you up to the school room then.’ She manoeuvred her body so that she was blocking my view of her child, who was hovering on the stairs. ‘You may find that he’s a rather . . . unusual boy,’ she half-whispered. ‘A little giddy at times. Over-imaginative. God knows where he gets that from, his father’s an absolute plank. But he does sometimes insist on spinning the most outrageous stories.’
‘I do not!’ wailed Graham.
‘Be quiet. Anyway, I would take everything he says with a pinch of salt.’ She ground her cigarette out into the mouth of the stuffed deer’s head that was attached to the wall behind me. It glared down at me glassily. I shivered. ‘One hour, then.’
Graham and I were left alone. He grinned at me. He looked younger than his nine years. He reached up a hand. ‘How do you do?’
I shook it. ‘Hello Graham. My name is Mrs Lampard.’
‘I’m Graham Winston Titus Fazackerley.’
Graham led me up a couple of flights of stairs and then onto a pitch dark, musty-smelling landing. I felt a tad discomfited, as I could see precisely nothing. ‘Titus,’ I said, ‘that’s an unusual name.’
I heard Graham fiddling with the bolt on the door. ‘Yes. He was a Roman emperor. He was the emperor when Vesuvius blew up.’ Suddenly the door cracked open, and a splinter of grey light appeared before me. ‘Sorry about the dark. We keep having power cuts. Mother says it’s because of the socialists.’
We entered what the mother had called the school room. It was a large, bleak looking space; I could tell by the rocking horse wallpaper in one of the alcoves that it must have once been a playroom, or a baby’s bedroom, albeit a cheerless one at that. Three or four candles flickered in alcoves, and as we entered, our shadows leapt and wheeled across the grey walls. There were thick heavy curtains all around, behind which I could glimpse dark wooden shutters. The musty aroma was even more pervasive here. It was also surprisingly cold—despite it being a mildish, late autumn evening, it was like walking into a fridge. I decided to keep my coat on. At the end of the room a large chalk board on an easel had been set up, with a supply of chalk on its little shelf, and in front of this was an old-fashioned single seat desk, with a schoolbook, pen and ink pot upon it, as well as a glass of milk and a small plate with three biscuits. I noticed that placed a little way back, by the wall and half hidden by one of the thick curtains, was another desk, and upon this lay a few pieces of paper, and a pen, and a single biscuit. As Graham sat down at the other desk, I nodded at this surprising arrangement.
‘Are we expecting another pupil, Graham?’
‘Oh, that’s just for Peter.’
For a second I thought that there had been some misunderstanding, and I was being expected to teach more than one child. ‘I thought it was just you and I.’
He filled his ink pen without looking up. ‘You don’t need to worry about Peter. You can’t see him. He’ll just listen.’
I remembered what the mother had said about his overactive imagination. ‘Very well,’ I said, unclipping my bag and withdrawing my teaching sheets and stationery. ‘If Peter doesn’t mind, then, we can start by having a little chat and finding out just how much you know already.’
Graham snorted. ‘That won’t take long. My teachers all say I’m a total duffer at sums.’
I have to say that after sitting with Graham for the next ten minutes and posing some of the simplest little maths questions to him I quickly came to the conclusion that his teachers had a point. He was obviously bright, having had all the opportunities of a good education that his upper middle-class background would have afforded. But his comprehension of arithmetic was wretched, a long way behind what I would expect of a boy of his age. He could barely recall his five times table, and could add pairs of two digit numbers with only the severest of struggles. He often wrote his numbers back to front. He didn’t recognise a fraction. Moreover, his difficulties were exacerbated by his poor attention span; he would quite often twist around on his seat to stare, seemingly, at that other desk behind us in the gloom.
‘Graham. Sit forward, and try to concentrate, please.’
‘Sorry, miss. It’s Peter. Being silly.’
I stood up and strode to the other desk. I wrapped the curtain around it. ‘Well, now you can’t see Peter, can you? Please, let’s continue.’
Graham seemed to settle down after this intervention, and we spent the next forty-five minutes revising his times tables, and learning some methods for simple subtraction. Eventually I felt confident enough to set Graham a small test. I gave him some paper and chalked ten simple sums onto the board.
‘I will give you five minutes to do this on your own. Try your very best. I would like to tell your mother that you made good progress today. Let’s see how you get on.’
‘Yes, Mrs Lampard.’
I watched little Graham clutching his pen and scratching away, taking occasional sips of milk from the glass. But once or twice—I don’t know why—I found myself glancing up at that other desk, shrouded by the thick red curtain. Something about it made me feel uneasy and a little afraid. It’s the newness of this situation, I assured myself, the dark, oppressive room, the smell, the cold. But there was something—about the curtain—an anticipation—a sense—like someone was hiding behind it.
‘I’ve finished, Mrs Lampard.’
I picked up the paper. ‘I will mark this at home, dear. You’ve done very well today. I’ll see you next week.’ I felt anxious to leave the house and be on my way home. At that moment I heard the honk of the taxi’s horn outside and saw the beam of the headlamps flickering through the curtain. ‘Let’s hope we have working electric lights by then,’ I added.
I filled my bag and we made to leave the room. As we passed the other desk Graham touched my arm. He reached behind the curtain and presented me with a single sheet of paper. ‘Peter would like you to mark his, too.’
Without looking at it, I crumpled the sheet into my bag. One of the candles had gone out at the back of the room and I was seized with a sense of bewildering nervousness. I reached out and seized Graham’s hand.
‘I think I’ll need you to lead me back downstairs, dear.’
It may have been the current of air as Graham closed the door—it may have been my imagination—but when I glanced back into that schoolroom as we moved to descend the stairs, the curtain by the desk twitched suddenly, as though someone were pushing past it.
* * *
‘Come to bed, Dorothy. I really must insist. It’s nearly twelve and I have to be in the office by eight.’
I was sitting at my dressing table poring over Graham’s test. John was propped up in bed in his pyjamas.
‘Darling,’ I said. ‘Tell me what you think. Give me your opinion, then I’ll come to bed. It doesn’t make sense, that’s all.’
With a groan, John flung back the blankets and slithered out. ‘I thought you said it all went well.’
‘It did. But look at this.’ I showed him Graham’s test paper, with its smudged answers. ‘This is Graham’s. Two out of ten. Not very good. Now, look here.’ I showed John the sheet of paper that Graham had pressed into my hand as we left the room. ‘Graham gave this to me. Said his invisible friend wrote it. See how much neater it is. And not only are all the answers correct—but there’s another ten questions on the next page which I didn’t set. Much harder sums. Look at this one—2410 x 63. He wrote—151,830. Correct answer. 34523 / 43. I worked it out. He got that right, too.’
‘But you said this boy Graham is hopeless.’
‘Well—I didn’t say that—but this is way beyond what I thought he could achieve.’
‘And this was written at the same time? You’re sure?’
‘Darling, I wrote these questions on the board.’
‘There’s only one possibility, isn’t there? This little hound Graham wrote the answers. He’s smarter than you think.’
‘So why would he pretend to be foolish, then?’
‘I don’t know. To rib his parents?’
‘That doesn’t make much sense. And this wasn’t on his desk. He picked it up from the other desk, I’m sure.’
‘Sleight of hand. You said it was dark.’ He placed his hands on my shoulders. ‘Bed?’
I nodded.
As I lay there, and John rolled on top of me, I couldn’t help thinking about that shadowy desk. And as he pulled the blankets over both of us, I was reminded of that thick dark curtain; behind which an imaginary child scribbled out its answers to questions that had never been asked.
* * *
The next week was pretty dreary for me—visiting my mother in Sidcup, a couple of abortive shopping trips, walking the dog, a lot of housework, a little reading—and I was feeling the loss of my teaching job rather acutely. I missed the boys, even the other members of staff—stuffy so-and-sos that they were—but most of all I missed the challenge. Some of the boys were awfully bright and it did me good to work out new ways of stretching them even further. But now—everything seemed so dull, so grey, so meaningless. I began to look forward to travelling to Hertfordshire for my second tutor visit, despite my rather silly superstitions, to get to the bottom of the whole business with the mysterious sums; and I actually found myself counting down the days.
It was Tuesday. I was back in the school room again, with Graham. Mrs Fazackerley had answered the door, as before, and I detected the smell of alcohol on her breath, and she seemed unsteady on her feet, so I congratulated myself on my instincts being correct in this case. I’d brought harder materials on this occasion, more befitting a child of Graham’s genuine ability, and was laying them out before him on the table. I’d wedged Peter’s desk at the back of the room, with its seat against the wall, and confiscated the paper and biscuit that Graham had placed there. The electric lights were working, but their weak glow was no brighter than last week’s candles. The end of the room was almost totally dark, except for the reflection of one of the lamps in a small round mirror. Graham was screwing his face up as he studied the new sums, and I wondered if he needed spectacles.
‘I told you, Miss, I can’t do long sums like this.’ He looked like he might weep. ‘I can’t do any of it. Can’t we do the work from last time again?’
I pulled ‘Peter’s’ papers out of my bag and presented them to him. ‘Well, you managed to do long multiplication last week, didn’t you? I don’t think you’re being entirely honest with me, or your parents.’
‘That isn’t mine. It’s Peter’s.’
I sighed. ‘I don’t see Peter, do you?’
Graham glanced over my shoulder, and I noticed a reluctant smile appear on that thin face. ‘No, miss.’
‘I don’t understand why you would want to pretend to me and your parents that you can’t do these sums, when you obviously can. If all you want is an adult’s attention, well, you’ve got mine.’
‘I’m not lying. I don’t get it at all. Peter, on the other hand—‘
‘Graham—‘
‘He’s terribly good at Maths. He always has been. But now he’s even better. The best in the world, he says, especially since—‘ he looked down at his hands. ‘I shouldn’t say anymore.’
‘No. No, you shouldn’t. Perhaps I should discuss this with your mother.’
‘Please don’t, miss. She’d only get upset.’ He straightened himself in his desk in an attempt to seem more serious and alert. ‘I’ll try really hard tonight. I promise.’
‘And no more Peter talk?’
He nodded. ‘I can’t promise to do long multiplication, but you can give me sums that are a little harder than before, perhaps.’
‘Very well,’ I said. ‘So our journey today shall be from here—‘ I showed him last week’s dismal test paper—‘to here.’ And then I pointed at the efforts attributed to his mysterious friend.
Graham nodded.
For the next half an hour, all was still and serene in the school room. I demonstrated long multiplication to Graham, showed him some tips, and when I saw that he was finding it tough, brought it down a notch. It did seem to me that he really couldn’t do the harder exercises. I wondered if somehow there was another party involved, that I was the victim of a hoax. And then, as I turned my back to Graham to make a simplification on the board to a sum that had confounded him, I heard it.
‘One, five, nine, two, six, five, three, five, eight, nine, seven, nine, three . . .’
A voice, a child’s voice, whispering, somehow muffled and distant, like one heard through a breeze in a wheat field. I became conscious that the temperature of the room had dipped by about ten degrees.
I turned round. Graham had his head down, concentrating valiantly. The room was silent, but for the scratching of his pen nib. ‘Graham, don’t do that.’
He looked up. ‘What, miss?’
‘Reciting numbers. Just concentrate on your sums.’
‘Miss, I’m not saying anything.’
And then I heard that soft, disembodied voice again. It seemed to come from the back of the room. Graham heard it too, lifted his head, opened his mouth as if to say something, then, thinking better of it, returned to his exercises.
‘Four, zero, eight, one, two, eight, four, one, one, one . . .’
‘How are you doing that?’
He shrugged.
The recitation faded and stopped. I ran to the end of the schoolroom, pulled back the curtains one by one.
‘Is there someone hiding there? Hello? Come out! You shouldn’t be here.’
No one. Bare wooden shutters, shadowy corners, a lonely, splintered desk.
Graham was standing next to me. I jumped.
‘I’ve finished, Miss.’ He passed me his completed sums.
‘I think,’ I said, still looking around me, ‘that’ll be all for today. It’s getting too cold to work. Could you get your mother for me, please?’ I was aware that my heart was beating rather hard.
‘Yes, Miss,’ said Graham, and vanished through the door and down the stairs. I stood there alone for few moments in the sombre schoolroom, listening to the wind lean and creak against the shutters, and watching the electric lights blink and stutter, as if struggling to impose themselves against the insistent darkness.
* * *
‘Peter was his brother,’ said Mrs Fazackerley, taking a swig from a large glass of brandy and pulling her knees up to her chest on the sofa. ‘His twin brother.’
‘And Peter,’ I said. ‘Is he . . .’
‘Dead, yes,’ said the mother.
‘Oh. I am so sorry. I suppose you know that . . . that Graham talks about . . . Peter . . . as if he is still here.’
She nodded and bit her lip. ‘We know. They were very close. Obviously, being twins. Jack and I were able to cope with it . . . in our own way . . . but poor Graham found it unbearable, I think. He talks to him . . . all the time. Jack thinks we should get him seen by a doctor, but I’d rather not have him labelled as a fruitcake, so early in his life.’
‘It must have been terrible for him.’
Mrs Fazackerley leaned over the arm of the sofa and filled her glass again awkwardly from the decanter. ‘They were coming back from Wakefield, from evacuation. Two years ago last week. They were at the train station, all ready with their suitcases. Anyway, Peter was reading his book, as usual . . . his Maths primer . . . his teachers thought he was a prodigy, you know? So very, very, bright . . . always with his head in a book, in another world . . . and as he stepped up to get into the carriage, head down, studying like he used to . . . his hand slipped out of Graham’s hand, and he . . . fell between the carriage and the platform—and the train jerked—something to do with the brakes—and he was somehow crushed to death instantly. It happened so quickly. So, very, very quickly, before anyone even knew what was happening. He just slipped, like a fish, down the gap and away from all of us.’
I looked down at my books. I felt suddenly, terribly guilty.
‘He had this strange habit of counting. Reeling off numbers to himself. For hours at a time. We thought that maybe something was . . . I say, are you all right?’
I was shivering, almost uncontrollably. It felt like all the heat of this little room had been sucked out, into the black vacuum beyond the windows. ‘Yes. Graham was doing something similar today. During our lesson.’
Mrs Fazackerley placed her hand on mine. ‘Please, my dear, you must carry on coming to see us, to help us, I implore you. Jack . . . he just stays in London now. I do really think he is afraid of us . . . of Graham and . . . Peter . . . we are all so alone here. But Graham has taken a shine to you, not like his other tutors. I can pay you two guineas if you wish . . .’ she fumbled for her purse. ‘Oh . . . but here’s your taxi. I suppose you’ll have to go. But please, please come to see us next week, won’t you?’
I looked up. Graham was standing at the door, twisting at his grey pullover.
‘Of course,’ I said. I walked to Graham, knelt down and threw my arms around him. ‘Oh, your poor little mite. Of course I’ll help you.’
As I untangled myself, Graham reached into his pocket and drew out a roll of loose papers. ‘I think you left these on the desk,’ he murmured.
I kissed him on the forehead and eased the papers from him. ‘You want me to look at these?’ I said, guessing at their nature.
He nodded. ‘They’re a sort of present.’
‘Well thank you. And I’ll look forward to seeing you again next week.’
* * *
It was two days later, and I had been lying awake in bed for nearly three hours. Earlier, after making love to me, John had whispered that he was ‘certain’ that this time I would conceive, and that all our worries would soon be over, and our little one would soon be on the way. I didn’t say anything, although part of me was desperate to tell him that I was no more capable of giving birth to a child than he was. That same part of me was almost—gleeful—about the power I had over him. All I had to do was to say those magic words, and everything would be smashed. Sometimes I felt them climbing up my throat, clambering over my tongue, my lips; but dying when exposed to the cold air.
As I lay there in the profound dark, while he snored gently next to me, his arm laying across my belly, I thought about those other children in my life, and the story about the little crushed child. I felt a tired sadness slipping over me, enmeshed with pity for that poor family, and a realisation that somehow I had become embroiled in a ghastly private tragedy with which I had no business being involved. Of course there was no ghost—there was no such thing, and I scolded myself for entertaining such silly ideas. So what was behind it? Could it be that Graham, traumatised about the death of his twin, was acting out a fantasy that would allow the brothers to be together again? He was, of course, a bright boy, obviously good at maths, and perhaps this pretence of stupidity made the distinction between him and Peter more acute, and thus the dead twin more real. When I’d explained my theories to John that night, he made some bland and terrible comment about how people should look after their children better, how when we had our child, we would never let strangers take care of it like the Fazackerleys had theirs. I hated him then, and I had secretly blessed my belly for its wonderful sterility.
I drifted off to sleep, and was soon dreaming about chains of numbers, bright like candy sticks, falling through a grey sky. In my dream I was counting them, just like the dead child had done, but the numbers were not sequential—they were arranged in some other way, but my sleeping mind could not divine exactly how.
I woke in the darkness with a start. The numbers were still rolling around my mind. It took a few seconds for me to realise that they were real. I could hear faint counting below me, in the front hall. I sat up. John was snuffling gently next to me. I listened again. I was quite awake. There was someone downstairs, and the mumble had a beat—like an incantation.
I swung my legs out of bed. It was extraordinarily dark, and I could barely make out the shape of the door. I shuffled across the room, creaked it open. Why didn’t I wake John? If there was an intruder, it would be the obvious thing to do. But this felt like it had nothing to do with him. This was about me. This was about a dead child. And there it was again, like a voice caught on the breeze, distant yet close- I heard the number six—and then silence.
I switched on the light and descended the stairs. For some reason I was not afraid at all. The hallway was empty. But someone had been here. The contents of my briefcase were scattered across the hall table, and the empty case flung to the floor. I crossed the hall and marvelled at my papers. Here were my sums, my exercises in preparation for Graham’s lesson, but now they were covered with pencil marks, a dense, childishly worked matrix of numbers and mathematical symbols. I stared at them. They made no sense. They were wildly incoherent, impossibly complex. John couldn’t have done this.
And then I heard John’s terrified wail from our bedroom.
‘Dorothy! Where are you? Please!’
I ran upstairs. John was sitting up in bed, clutching the blanket. ‘There’s someone in here. They touched me. My God, look!’
By the window I perceived the outline of a small child. The light from the hall below spilled around the curtain and touched the edges of the little dark figure, like a halo. And from this black child shape there emerged a rhythmic quavering whisper, and now the numbers were quite distinct.
‘Zero nine two one eight six one one seven three . . .’
‘There’s a damn kid in here! How the hell?’
‘Sssh!’ I crawled forward across the bed, over John, reaching my hand towards the shape. ‘Come here, darling. You don’t have to do that. You can stop.’
‘What’s it saying?’
‘He’s reciting Pi. He’ll go on forever. Ssh, darling . . .’
John switched on the bedroom light. I flinched under the sudden brightness.
The child had gone.
‘What the hell? Where did it go?’
Without saying a word to John, I pulled on my dressing gown and made my way down to the kitchen. He followed me. I placed a kettle onto the gas. Enough water for one.
‘Why aren’t you saying anything?’ said John. ‘There was a bloody kid in our room. Why aren’t you saying anything?’
I set a cup and saucer in front of me.
‘I’m still shaking,’ said John. ‘What a shock. We both saw it. You were speaking to it.’
‘It was the Fazackerley’s child,’ I said.
‘Graham? I don’t understand. How did he—‘
‘Not Graham. The dead one.’
He boggled at me for a few seconds.
‘Then,’ he said, crossing himself, ‘I’ll call the vicar tomorrow. We’ll get the house exorcised. Drive the evil thing back to Hell where it belongs.’
‘He’s not evil. You don’t know anything about it.’
John stared at me as if I was every bit as strange and offensive as our nocturnal visitor. ‘You seem to care far more about other people’s children than you do about ours,’ he said.
‘We don’t have any children.’
‘No. No, we don’t. The only children you seem capable of summoning into our family are dead ones.’
I’d heard the F word used a good few times during my life; by workmen in the street and strangers on the tube; by obnoxious children in school, and once or twice, by John in the midst of his passion. But this was the first time I’d ever uttered the word and now it felt like a glorious release. ‘Oh, just fuck off, John. Just fuck the hell off.’
He looked at me with bemused horror.
That word coming out of my mouth was the strangest visitation of all, and it marked the beginning of the end for us. It was like a great axe coming down, an axe that I’d always known had been there above us, waiting to fall. I can’t remember when I told him I couldn’t have children—it must have been soon afterwards—but within a few days he was gone, back to his mother’s. He just went, one Saturday morning, in his suit, like he was going to work. I watched him through the window, his grey back passing between the privet hedges as he headed for the train station. I never saw him again. Of course, almost immediately he stopped paying the rent, so I packed up and moved back to my parents’ in Cambridge shortly before I was evicted.
The funny thing was, I wasn’t barren after all. Fifteen years later I met a lovely man and fell astonishingly, and delightfully, pregnant.
As I had promised, I continued to visit the Fazackerleys in the months and years that followed. I never told Graham or Lilian about Peter’s visitations. I did, however, tell Graham about the contents of the rolled-up paper he’d given me that second evening.
‘There was this man—a very clever Frenchman—a mathematician—called Pierre De Fermat, and he lived in the 17th Century. Long ago. Well, he had this problem, this puzzle, and he claimed to have solved it—but then he died, and no one could find what he’d written down, and no one ever, ever, was able to solve it again.’
‘What was the puzzle?’
‘It’s this,’ I said, taking out the papers I’d found that night in the hallway, and pointing to Fermat’s conjecture, scrawled at the top of the first page. ‘Now, what is written here over all these pages is very complicated, and I don’t understand it all. But I think it might be the missing proof. If it is, it would be one of the greatest discoveries in mathematics ever.’
Graham nodded sagely. ‘Peter was always good at sums. Maybe he had help on this one, though.’
‘Maybe he did.’
‘He sometimes talks to me at night, between the numbers,’ said Graham, ‘and in my dreams. He told me that since he . . . died . . . he can see things differently. Like all the numbers are there in front of him, all at once, and he can see how they link up, and how they come together to make things work. He says that they are cold and true and kind at the same time. He says they’re beautiful.’
I looked at the proof again. ‘Yes. I can see how he might have said that.’
‘And he wanted you to see them, too.’
* * *
Of course, I never showed the calculations to anybody, at least before now. People would want to know where they had come from, and that would lead to all sorts of questions, and quite frankly this little family had already suffered enough. I put them safe in a drawer for decades. When that chap Wiles figured it out in the 90s it came almost as a relief to me. I wondered how he’d feel if he knew that the proof had been sitting in an old woman’s drawer for nigh on fifty years?
So I went on visiting the Fazackerleys, and I’m pleased to say I made quite a difference to Graham and his maths—he made big improvements, and eventually went on to become a quantity surveyor. He’s still alive, I believe. His poor mother, Lilian, joined her other son a long time ago, though. Liver disease.
As for Peter—well, he continued to visit me throughout my whole life, and I began to love him just like a parent should, while managing to keep it a perfect secret from my new husband and son. The proofs kept coming, of course—I received the latest just the other week—and quite a few of them are entirely unsolved, up to now. I have them here. Maybe you’d like to look at them? All of Landau’s problems . . . Hilbert too . . . and something called the Riemann hypothesis . . . all of them explained by a little dead boy.
Why now? You see, I am dying—I have only a few weeks left—so I’ve decided at long last to show Peter’s proofs to the world. You can take the credit for them if you like. Fame is of no use to me where I am going; hand in hand with Peter, on our journey through the infinite majesty of mathematics—all the way to the end of Pi.
© 2001 A. N. Myers All rights reserved.
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