The Diophantine Equation

A short story

While waiting for Masha to prepare breakfast, Yury stared glumly out of the window of their tenth-floor flat on Rimsky Korsakov Street. It had been a long cold winter with average temperatures of around -10 C, sometimes plummeting to a bone-chilling -20 C. The sky looked like a slab of concrete, a depressing uniform grey, spreading out to the horizon. It was like being smothered in an army blanket. Down on the ground the snow resembled unappetizing porridge, as dreary and ashen as the sky. Spring was around the corner, although on this lustreless Tuesday in the middle of March, with the whole town cast in gunmetal tints, you would have hardly thought so. The trees were still bare, branches frozen in their leafless winter agony. Ice hung in stalactites from the eaves of buildings. However, the temperature was rising. Yury saw that the red marker on the small thermometer on the outside of the window was hovering around zero. To cap it all, a drizzle was falling, accentuating the general gloom. Great, he thought, the streets will be like ice-rinks. It was a mathematical probability that limbs would be broken or fractured on the slippery mess coagulating on the perilous sidewalks.

Masha was in the kitchen making blinis. She was bustling about, humming a tune. Yury couldn’t quite place it, but it was familiar. Something from one of the old Soviet films she liked to watch?

She came into the living-room and plonked the plate of blinis down on the table. She poured tea, sat down and looked at her husband. He wore his usual non-committal, slightly grumpy expression. She had been to the hairdresser the previous evening and wondered whether he would ever notice. But he didn’t take these things in and a compliment from his lips was as rare as charity on a battlefield. He wasn’t an unkind man, but he was cold, abstracted, withdrawn: a sombre, 38-year-old Russian fellow. The only thing that animated him was mathematics which he taught at Moscow University up on Sparrow Hills.

Masha regarded his crumpled grey suit and sighed.

‘You look like the weather,’ she said, helping herself to a blini and smothering it with sour cream.

Yury drew his attention away from the dismal view and stared at his wife. ‘What?’ he said in an irritated tone of voice.

‘Your suit matches the weather.’

‘Does it?’ he replied, frowning.

‘Yes, so grey! Why don’t you wear something more cheerful? Your blue suit, for example,’ she said, fiddling with a strand of blonde hair and tucking it behind her left ear.

He didn’t answer, merely grunted. Without doubt she was the brighter side of their union, the sunshine peaking from behind dull clouds, and today she was wearing a new dress: blue, the colour of a summer sky. He hadn’t commented on the new addition to her wardrobe. She wondered if she had become invisible to him. She was a good-looking woman and she did her best to look feminine. Her wardrobe was a rainbow of bright colours, a stark contrast to her husband’s monotones. If she was a bird of paradise, Yury was the exact opposite: a drab sparrow; a man going prematurely grey with a long thin face and a professorial pepper and salt beard. Along with her new hair-do, she had been to the manicurist and had had her nails painted a bright fiery red. Not that Yury had noticed any of it, or if he had, he didn’t comment.

They finished their breakfast in silence. The blinis were delicious, his favourite breakfast dish. Masha was a past master at whipping them up, but it didn’t occur to him to tell her how good they were. He was thinking about the unsolved Riemann Hypothesis and the lecture he would be giving later that morning to a bunch of students in a forbidding and echoey lecture hall at the university. He took a last slurp of tea and got up from the table.

‘I have to go, otherwise I’ll be late for my lecture,’ he said.

‘Be careful out there, it’ll be slippery this morning.’

‘A glaringly obvious observation!’ he muttered.

With that he stalked into the hallway and checked the contents of his briefcase. He put on his grey overcoat, stout black boots and clamped his favourite fur hat on his head. Masha was in the kitchen doing the dishes and humming that tune again. What was it? It distracted him for a moment before he called out, gruffly, that he was leaving. There was a muffled response that he didn’t catch. He shrugged his shoulders and walked out of the door.

At the kitchen sink a few tears dripped into and mingled with the dishwater. Masha pulled herself together, dried her eyes on her apron and started attacking the grease on the stove. She reminded herself that she was a strong Russian woman and recalled the famous line by Nekrasov about the Russian woman who could stop a galloping horse and go through a burning building. After hoovering and dusting, she went out shopping for provisions. And so the day passed in housewifely duties, which she completed with her customary diligence and vitality.

Meanwhile, Yury gave his lecture, conducted a couple of seminars and spent the afternoon somberly marking students’ papers. After work, he trudged his usual route to the metro, slipping now and again on the treacherous ice that was melting in the thaw. He cursed the temperature, now one degree above zero. When it happened, he was thinking about the Diophantine equation: x³+y³+z³=k, the sum of three cubes; resolving certain integers had eluded mathematicians for decades. The big bugaboo was the number 42, but, recently, some clever chaps at Bristol University in England had at last solved it, albeit with the aid of a super computer.

Just ahead, high above him, a stalactite of ice was losing its grip on the concrete overhang of a seven-storey building. Yury stopped in his tracks, deep in mathematical cogitation. At that moment, the stalactite, a lethal dagger of ice, came loose and plunged to the pavement. Had Yury not stopped it would have smashed into his skull and killed him. It crashed like a bomb into the pavement just in front of him. A lump of ice, like a piece of shrapnel, ricocheted and struck him on the cheek. He was so startled that he slipped and fell down, clutching his briefcase to his chest as if it were a lifebelt. For a couple of seconds he was dazed, shocked and uncomprehending. He looked at the shattered pieces of the stalactite and realized what a close shave it had been.

As he lay there, he reflected how this event could not be explained mathematically. Maths was deterministic, never random, and yet stopping to ponder the Diophantine equation had saved him. By rights he should be dead, but some inexplicable and timely calculation in his brain, or perhaps divine intervention, had caused him to halt at precisely the right moment to prevent his demise. A message had been sent: STOP!

He reflected that this was chaos theory in action: this unpredictable event in his ordered yet cold life had thrown him. A metaphorical can opener had ripped open his consciousness with startling suddenness. When he picked himself up from the ground, he was a changed man, in some way transfigured, a more grateful man, a man more alive, gripped by a sudden joyfulness and lust for life, all caused by one degree of change in the temperature, a mathematical equation, and a stalactite of ice.

He walked on down the street, glancing up warily from time to time. It had been a nasty moment and it had jolted him out of his complacency. How easily he could have been cancelled out and never seen his wife again, the woman he loved but had taken for granted for too long.

Then, it came to him: at breakfast, Masha had been humming an old song by Klavdiya Shulzhenko called, Что такое любовь (What is it, Love?). She had also had her hair and nails done, which he had churlishly ignored. Ignorant oaf! From now on he decided he would show her the attention she deserved. He came up with a poetic variation of the Diophantine equation: appreciation cubed plus attention cubed plus love cubed equals a happy wife, and therefore, as the saying goes, a happy life.

At the florist near the metro, Yury bought a huge bunch of Masha’s favourite flowers: white lilies. And he decided that he would take her out dinner that very evening and treat her like a lady. He darted into the metro and skipped down the escalators like an eager teenager. He couldn’t wait to get home. On the way, he hummed Shulzhenko’s What is it, Love? He smiled and said to himself, I’ll show her what it is!