Fergie Matthews’ Last Theorem

The date is around 520 BC. Fighting for his life, a man is heaved over the side of a boat and dropped into the open water to die. His name is Hippasus of Metapontum. His crime? Telling the world a mathematical secret . . . (T)here was one number that the Pythagoreans found terrifying, the number that might have cost Hippasus his life for revealing its existence to the world . . . The square root of 2 . . . It's what we now call an irrational number, not because it is illogical, but because it can't be represented as a ratio of whole numbers. If you believe that everything is constructed from whole numbers, it is a terrible shock to discover that there is an everyday number . . . that doesn't fit your picture of the world. It's a nightmare—and one from which the Pythagoreans would never really recover.

The Dangerous Ratio, Brian Clegg, University of Cambridge, 2004

November 1983

There’s an untidy pile of books on the coffee table—a new pile of old books. They must belong to the old man. We don’t have old books and we don’t have piles of anything. The coffee table holds a box of tissues, six coasters for drinks and the TV remote. The glass top of the table is a window through which we see the rug with the lilies on it. Now it looks crowded. We keep our books in my room. We line those up in order of height and we throw them out if they get raggedy. Mum says that she likes to keep her school stuff, her class books and her class registers, at school where they belong. “Our house is a tidy house,” Mum often says to me—and I say it back to her after I put my doll back in her box, pretending to be Mum saying it.

“You’ve met Michael, dear,” Mum tells me. She is sitting on the sofa in her Saturday morning sweater. “He teaches with me. Well, in the same school. He teaches math—poor man. I’m glad that I only have to get biology into their heads. At least I stand a chance.”

She smiles at the man on the sofa sitting next to her to let me, and him I guess, know that she’s teasing. I’ve met him before, or someone like him. Hard to tell. Old is old. And this man is ancient. Nose hairs. He sits too close to Mum. He is looking straight ahead—at the mirror and at that picture of a seagull with a fry in its mouth. I’m in the little chair to the side, the one that Mum says that Dad used to sit in to watch TV. I don’t remember that. I like the chair because it has a loose thread on the dark blue cushion which I play with. The thread is white—it comes from one of the diamond shapes in the pattern. I always tuck it down the side so that Mum can’t see it. She would cut it off.

“He’s going to move in after Christmas. Just before your eighth birthday. He’ll be here for your party. Then it will be just like it was before Dad died. But we’re not replacing your dad—just making it like it was before.”

Mum often talks about "before your dad died." I feel sad when she says that because she says it in a sad way. There’s a photo of dead dad, well, Dad before he was dead, on the side table. I know it’s him because Mum often picks the picture up and talks about him as if she’s talking to him. I don’t remember Dad. I only know that I had a dad because Mum goes on about me having one. I don’t want to go back to something that I don’t remember—and I don’t want this old man to move in.

The sofa is in front of the window, which looks out at next door’s hedge. I can see that it has started to rain.

“He’s going to bring a few things over from his house, not much,” she says, glancing toward the man and looking slightly surprised, as if she’d never noticed his nose hairs before. “Just enough to make him comfortable.”

Mum gets up from the sofa and arranges the china horses on the window sill behind the sofa. We usually do this together. We do it every few days. We go around and check the ornaments on every window sill. There’re four windows in the living room. Three brown china horses on one, three beige china dogs on another, two black china cats safely away from the dogs on another, and two china elephants, one blue-spotted and one gray, on the last window. The glass animals are on the glass shelves by the door. Each glass animal has a name. When we do our rounds, Mum picks them up and I dust underneath. I’m not meant to pick them up myself. We tell stories about how Robbie the glass Rabbit has made friends with Lesley the glass Leopard. She tells one story and then I tell the next one.

Right now, she’s only moving the horses. She leaves Tallulah a little bit ahead of Tibbs and Dusty. We always talk about which one is winning when we move the horses. It’s usually Tallulah. Mum says that she likes it when we girls win.

The living room was repainted a few weeks ago. Same cream color. We had to take all the ornaments off the shelves and window sills and put them in boxes. We wrapped them with bubble wrap. When the man was finished and he’d put the furniture back, we put all the animals back in the right places. We both knew exactly where each one was meant to be.

The old man gets up and comes to crouch by my chair. He puts his hand on my shoulder. He smells of soap. That’s not what I expected.

“I’ve been counting,” he says. He has a thin voice—wobbly somehow. Like when I am asked to talk to the class. “Do you know, you’ve got a prime number of horses, the same prime number of dogs, a different prime number of cats and of elephants, and a prime number of glass animals that’s the total of all the other prime numbers plus one? I think that that’s all just wonderful! Now do you know what a prime number is?”

Mum must see me looking at her for help, for a way out. I don’t answer him and I can see that she’s disappointed. She has the look that she has when my cousins come and I don’t want to play with them. She wants me to want what she wants. I smile at her and then she’s OK. "We’re safe as long as we’re together," she always says. We do everything together.

March 1990

I make sure that I’m hardly ever alone with him. I feel compressed, squeezed into something, like trying to wear that coat from two years ago. I’ve put my copy of Seventeen on the coffee table, underneath my homework folder. I’m not meant to read it until I’ve done my homework. Mum knows that I read it—she reads it after me so that we can talk about some of the pop stars, together. We throw it away when we’ve read it.

Mum was doing stuff in the kitchen but has come into the living room. Mum and I used to get the evening meal ready together but I’ve got too much homework these days.

“It’s a bit embarrassing that your stepdad teaches math and you’re so behind,” she says.

Stepdad. Ugh. “At least I’m not in his class. None of my friends like math either. None of us could do the worksheet.”

He’s standing there, the stupid dickwit. He doesn’t say anything. It’s like he’s waiting for something. We can talk about him, in front of him, around him—and he waits, like he’s got his hand up and is asking for permission to speak.

We all leave for school together most days. I hate it. He and Mum walk home from school later than me, still together. He talks then—I’ve seen him talking to Mum about things that require him to wave his arms.

Right now, since Mum came into the room he’s got his concerned look going on. He’s got that one, and a sorry look when he’s not wiped his shoes and his isn’t-that-funny look when he’s trying to persuade me or Mum to give a damn about something he’s going on about and his I-want-you-to-take-this-seriously look when he’s running through one of his lists. His lists. He’s got lists of his lists. Things to do, things to buy, things to watch on TV. He refers to things by their number on the list. Everything is numbered.

Mum’s got some looks too. She has the ‘I’ve got too much for one person to manage’ one on right now. She smiles at me for a second or two and doesn’t look at him as she starts fussing about with cushions and straightening of ornaments. She blows at his pile of books on the coffee table, as if they were ancient and covered in dust. As if they were like him. She doesn’t touch them. She never touches him either.

“I’ll help her, Fergie, while you get on with dinner,” he says in a soft, gooey voice. He’s got his other look on—the ‘I’m just being humble and helpful’ one.

He doesn’t fit. There’s Mum and me, together, in our house, our tidy house with its cream and beige rooms. And there’s him. He’s got books everywhere and he does the Word Search puzzle in the paper even when things need tidying up.

“OK—then maybe you can help her with her biology homework later,” Mum says leaving the room with what’s meant to be a laugh, although I can see that she isn’t happy. I’m not happy—she’s left me with him in the living room.

“The thing is that math isn’t just about homework worksheets—it’s about enjoying the logic of it, seeing the big patterns,” he says in a ‘let’s you and me share a few of our secrets’ sort of way. “Let me show you something, something wonderful.”

He leaves the room and I pick up Seventeen—sliding it out from under the homework folder and holding it at arm’s length so that I can drop it and pretend that I’m not really reading it, although I sort of want him to see that I’d rather be doing just that. He returns with more old books and shows me his name written in old man spidery cursive inside the front cover of one of them. He sits and now we are both on the sofa. Thank God there’s a cushion between us. We are both looking toward the seagull picture, so I don’t need to look at him. He doesn’t even notice my magazine. They’re his school books he tells me. His school books from a hundred years ago.

“I always loved math. I loved the idea that there were just a few small rules and you could follow them and end up with all sorts of big answers.” He’s telling me this because I’m meant to enjoy it also. And if he puts that cheeriness in his voice then that’s going to make it fun for me too. He thinks that’s how it works.

“I’m going to tell you about theorems, the foundations that make the rest of it easy, obvious. It’s like looking underneath and discovering how it all works.”

“Thanks, but I just need to complete the worksheet.”

“Well yes—but I want you to feel a bit excited about the topic—not just wanting to get through the homework. Theorems keep math tidy, like the way that your mum keeps the house. But they keep it tidy because they’re foundations and everything sits neatly on top of them.”

On it goes.

“In the mid-seventeenth century, Pierre de Fermat guessed or somehow worked out that there is a fundamental truth about positive integers, you know, whole numbers greater than zero. No one has ever been able to prove him wrong, but we don’t know why he’s right. It’s like he discovered a secret that he wasn’t meant to know. Fermat’s Last Theorem—it’s magical that it’s true but we don’t know why. Fermat discovered some little spyhole into a wonder of the universe.”

“Look at this,” he says, pretending passion about a page that he’s just flicked to. “You know about Pythagoras and his theorem. Well, you’ve heard of him, I’m sure.”

I nod, trying to neither look stupid or remotely interested.

“Well, in the sixth century BC—oh sorry, BCE—a student of his, Hippasus, discovered that you just can’t divide one whole number into another and come up with the square root of 2. You can’t say that the square root of 2 is one number divided by another. It’s an irrational number. You know—irrational. The decimal places just go on forever. More and more of them—always making you hope that you can capture the number, the idea, in a precise way, but always teasing you by reminding you that they stretch on to infinity, telling you that that number can’t be tidied, or not by us mortals anyway.”

He shows me the sketch of a weird looking guy that’s at the start of some chapter in his book—curly haired, beard and furrowed brow. That’s Hippasus he announces with pride. He sits back, watching and waiting for my delight to emerge.

“He was killed for his discovery, you know.”

I’m nearly interested but saved when Mum comes back in to say that dinner is ready. She sees curly-haired Hippasus in all his long-dead glory.

“Where’s the worksheet? All she needed help with is isosceles triangles. Let’s just get her through the small steps, shall we, before we ask her to digest the history of mathematical concepts. I’ve got a lot to do this evening and I did think that you might help.”

She stops to sigh.

“Sorry dear,” Mum says to me. “As soon as I’ve tidied up you and I can look at the worksheet together,” she adds as if he’s not there.

She’s mad at him. She lines up the china horses. They’re all evenly placed—none in the lead. It’s been a long while since we’ve moved Tallulah to the front. She plumps up the cushions and goes back to the kitchen asking us to come while it’s hot. He looks a bit defeated, lost. He probably thinks that we’re irrational. Nice.

March 1991

We are standing next to the seagull picture. “You don’t get to tell me what time to come home.” I’m trying to hurl the words like they’re in a solid block of ice. I never look at him, so it’s hard to know if he sees that this is the effect that I am hoping to achieve. He’s taller than me, so I don’t look above his head—I look to the sides or to the ground. Eye to eye contact would make him feel like we have a relationship and that’s not what I have in mind.

He’s got a name, but I try not to use that when he’s there. He’s just “you” if it’s just him, or “him” if he’s with Mum.

“I’m asking not telling—11 o’clock is a pretty reasonable time for a fifteen-year-old to be home on a school night,” he says, practically doing acrobatics trying to position himself so that my line of sight has to include him. “And since you weren’t back then, I’m asking a different question now. What were you doing until nearly midnight last night?” he continues in that maddening, pretend-reasonable, pretend-adult, teacher-ish way that he has.

“I was with Nancy. I told Mum and she’s the only one who needs to know.”

He’s caught. It’s delicious. He’d like to scream and shout. He’d like to run to Mum and tell her that her spoiled little entitled daughter was acting up. But he can’t do any of that. He’s got no way in with me and if he steps out of line then he’s got no way in with Mum. He’s here because she lets him be here. Mum can tell him that he should go back to his house whenever she wants. I heard her ask him whether he ever thinks about that. “Oh no—never,” the bastard lied. “I’m here with you now. We’re not going to give up halfway.”

Mum told me that he would never replace my dad, my dead dad. And the bastard learned the same lines and tells the same story. “I’m never going to try and replace your dad, you know,” he said in one of his early ghastly speeches. And then he started getting into my business and trying to be a dad. I don’t remember anything much about my actual dad. The thing is, I don’t need one.

I think that Mum is sorry that she married him. They usually seem like two polite acquaintances, circling around each other, wondering if they’re doing it right. That’s when they’re not arguing about him reading his books, being untidy, and not helping around the house. Well, she argues with him. He doesn’t really argue—just looks super-reasonable. “All you think about is numbers” is her catchphrase. I tried once to ask whether this was what she wanted, and she said that it was just how it was and that she was lucky to have someone to keep her company even though she wished that he wasn’t such a dreamer. Not exactly passion.

June 2011

“There’s going to be a lot less tidying up, that’s for sure.”

He’s died and I feel nothing. I don’t feel sad—that’s for sure—but I don’t feel happy or triumphant either. Nothing. Maybe that’s how I felt when Dad died too—I don’t really know, and I was only four so maybe that’s just how it is when you’re that age. I’d worry for Mum, but she seems more relieved than anything else.

“What will you do if you get scared about being on your own?” I ask her. I hear the clink of glass objects on glass shelves and then the soft scrape of china on a wooden window sill.

“Well, I can call you—although I don’t want you rushing back from London just because your mum’s having a sad evening. There’re people here that I can call. But I’ll be fine. Tell me about the latest boyfriend—well, I suppose that you’re a bit old to call them boys. And did you get that dent on your car fixed?”

She’s right—she’ll be fine. She can lose herself in details. She’s got her ornaments and her cleaning and tidying—she can keep herself busy with all that from here to the grave. Mum asks if I bought that new blouse. She never wonders about anything—it’s always “did you do it or not?” She never asks me how I am or where my life is going. She’s allergic to wondering. Wondering is pretty much all that he did and so she can’t have liked him much. I made his life hell and I wonder whether she did too.

April 2020

She was oddly compliant about going in for rehab. They put screws in rather than do a hip replacement. I could never quite work out why that was. I spoke to the doctor when she was in hospital, but I couldn’t get much further than the bland assertion that it was the right approach “for someone with your mother’s comparative good health and since she doesn’t have much arthritis and since it wasn’t a severe fracture.”

Her room in the rehab facility is almost the same beige as her living room. No glass shelves and only one window. It has an African violet, maybe from the previous occupant, and the begonia that I brought in yesterday on the sill. I’m the only visitor. She says that she has people that she sees—but she never names anyone. She is in a high seat orthopedic chair, blue vinyl, and she is fiddling with a thread that must have come loose from the stitching on the arms.

“He used to go on about theorems. He said that they should be called foundations, or something like that. Remember?”

She’s never been one for reflection. Running through a list of historical moments, asking for confirmation that she has the record right, is as close as she gets. Checking that things happened, never wondering what they were all about. I’m hoping that we’ll move on to the weather and the facility food, safer and simpler topics.

“Theorems, you know,” Mum continues, “He loved math. I used to tell him how us biology teachers had it easy. Fussing with photosynthesis and cutting up frogs—and the kids were always waiting to see when sex was going to come up.”

She pauses, pulling angrily at the thread in an attempt to break it.

“But so messy, he just couldn’t or wouldn’t keep anything straight,” she remembers, looking at me expectantly, daring me to disagree.

“He had such big ideas and he wanted to talk about them. I liked him in the staff room, but he depressed me when we were married. He should have married Fermat.”

“I was never keen on him, as you know,” I reply, raising my eyebrows and trying to look little-girl-naughty so that Mum knows that I’m being funny and not cruel. “But now that you’ve said that you weren’t so keen I feel a bit bad about that.”

It’s like there was a fixed amount of disliking to be done and now that I know that she was doing some of it, I’m thinking that I didn’t need to do so much.

April 2024

“She’s dozing, but I’m sure that she won’t mind if you go in and wake her,” the care assistant says. “It’s tough to lose your mum, maybe it’s tougher losing her gradually like this.”

I’m unclear whether I’m losing her or finding her.

The soft click of the door closing behind me is enough to wake her.

“I bet he hasn’t tidied the kitchen. Him and his books.”

“What? Mum?” I ask, immediately regretting breaking my self-imposed rule of not requiring her to explain or justify her confused, post-nap comments. She looks exasperated, but seeing me, whatever is left of Mum lets go and allows her face to resume its usual resting expression of disappointment.

“Him and that stuff. The books. Our house is a tidy house.”

The confusion that started small and occasional is now large and permanent. There’s more of her confusion than there is of her.

The familiar care assistant comes in after the lightest pretense of a knock. She’s the one that is always on in the afternoons.

“Good afternoon, Mrs. Matthews.”

“I’ve told them a thousand times to call me Fergie,” Mum says to me, as if the care assistant wasn’t there. She pauses, like she needs to recover from a surprising moment of clarity. “But she’s new and so maybe she doesn’t know—and anyway, nice to be asked,” Mum continues.

Was Mum always this high-handed? The care assistant is still here—she’s a sentient human being—why would you talk about her and not to her? Maybe this isn’t the confusion. Maybe this is because she’s always run her life as if everyone around her is just an extra in her play, a hired hand to help her complete the list of mindless tasks that she’s got lined up for the day, or for her life.

I’ve nearly finalized my divorce. I told Mum that we weren’t getting on but I didn’t tell her that we were at the end of the line. Not much point in telling her—she’d be upset but then she’d forget that I told her. My about-to-be-ex was, well I guess still is, a big thinker, with big ideas and no money. I don’t miss the permanent financial terror. I don’t miss the damp socks and sweaty tee shirts that he felt entitled to drop and then not notice. I don’t miss the endless scree of untidiness that he could distribute across cupboards, table tops and window sills.

Mum looks at me suddenly as if she knows something. She really doesn’t. “We’re safe as long as we’re together,” the random firing of some still functioning neural circuit makes her say.

About-to-be-ex has moved out. It was my flat before he came into the picture, and it’s mine again now. I spent more than half my marriage longing to be on my own so that tidiness could be the default in the flat, not something that could only ever be achieved momentarily. I used to tell my friend, my only real friend I think, certainly the only one I can talk to about this sort of stuff, that it wasn’t so much the frustration that he wouldn’t help, the agony for me was that I could never give up the hope that with enough reminders he just might. I won’t miss that forlorn, masochistic hope or his long lectures on the dangers of artificial intelligence and the history of green funerals.

Mr. Math had big ideas too. Mum wanted to trap me in her world of tidy precision. She did trap me. He wanted to help me escape. But Mum and me, we’re the same stuff. The two of us. Always hoping that we can tidy up the square root of 2, that we can get to the end of the decimal places, that we can arrange enough ornaments and people to finish defining our lives.