write an story about mathematics,loneliness and philosophy

The Empty Set

Every morning at eight, Professor Elias Venn entered his office, hung his coat on the same brass hook, and wrote something true on the blackboard.

Some mornings it was simple:

On others:

There are infinitely many prime numbers.

He did this before opening his mail.

The habit had begun after his wife left. She had not died, which people sometimes assumed from the way he spoke of her. She lived across the city, above a pharmacy, and had recently taken up swimming.

“I can’t keep being the only uncertain thing in your life,” she had told him.

For months, Elias had tried to understand the sentence as though it were a theorem whose proof she had neglected to provide.

His office faced a courtyard containing a dead fountain and three benches. At lunchtime, students gathered there in arrangements that changed daily but never appeared random. Two became five; five divided into three and two. Someone arrived carrying oranges. Someone left crying and was followed.

Elias ate an apple at his desk.

He was working on a problem concerning the distances between points. The exact problem was difficult to explain, and eventually people stopped asking. This suited him until it didn’t.

One Thursday evening, a cleaner named Mara found him staring at the blackboard.

“You’ve missed a bit,” she said.

He turned.

She pointed to a faint crescent of chalk near the frame.

“Oh.”

“I meant when you wiped it.”

“Yes. I see.”

She emptied his wastebasket. It contained eleven pages covered in calculations and the untouched half of a sandwich.

“Did any of those work?” she asked.

“No.”

“All eleven?”

“They’re attempts at the same thing.”

Mara looked into the bin.

“That seems worse.”

After she left, Elias laughed. The sound startled him in the empty office.

Mara cleaned the mathematics building on Tuesdays and Thursdays. She had once owned a café with her brother. Now her brother lived in Canada, and the café was a shop selling expensive soap.

“People still need coffee,” she said. “Apparently not ours.”

She began taking her break in Elias’s office because he had a kettle and did not ask whether she had always wanted to be a cleaner.

One night she asked what the smallest number was.

“There isn’t one.”

“What about zero?”

“Negative one is smaller.”

“The smallest positive number, then.”

“There isn’t one of those either. Whatever number you choose, divide it by two.”

Mara frowned into her tea.

“So you can keep getting closer to nothing without ever arriving.”

“Yes.”

“I’ve had jobs like that.”

He smiled.

She nodded toward the board. “And people pay you for this?”

“Less enthusiastically than they used to.”

In November, Elias received an invitation to his former wife’s sixtieth birthday.

It was a small card. On the back, she had written:

You would be welcome. No obligation.

He placed it between two books on his desk, leaving only the date visible.

When Mara noticed it, he explained that attending might make the other guests uncomfortable.

“Which guests?”

“I don’t know who’s going.”

“Then you’re getting ahead of yourself.”

“There may be people who think I treated her badly.”

“Did you?”

Elias removed his glasses.

“I thought being faithful was enough.”

Mara waited.

“I never wanted anyone else. I never lied to her. I came home every evening.”

“What happened when you got there?”

He began polishing his glasses, although they were clean.

After a while, Mara took the cups to the sink.

As a young man, Elias had believed mathematics would protect him from solitude.

Not by supplying company. By making company unnecessary.

A proof discovered in an empty room remained a proof. Its validity did not depend on whether anyone admired it, whether its author was loved, whether the world beyond the window had forgotten his name.

He had found dignity in this.

Lately, he wondered whether he had mistaken indifference for generosity.

One evening he asked Mara, “Do you think something can matter if it matters to nobody?”

She was struggling to peel the foil from a yogurt.

“Like what?”

“A beautiful proof no one ever reads.”

“Doesn’t it matter to the person who wrote it?”

“Suppose they’re dead.”

“Were they pleased when they wrote it?”

“Perhaps.”

“Then it mattered.”

“I mean afterward.”

She finally freed the foil. Yogurt spotted her sleeve.

“You do make things difficult to enjoy.”

He nearly objected. Then he looked at her sleeve and passed her a tissue.

The birthday fell on a Saturday.

Elias bought a book of photographs of the sea, remembering too late that his wife had once complained he chose gifts for an earlier version of her.

He went anyway.

At the door, she looked surprised, then pleased, then concerned about where to put his coat. He was grateful for the progression.

Inside were people he knew and people he didn’t. A man with silver earrings was cutting lemons. Someone had brought a dog.

His wife introduced him simply as Elias.

For the first hour, he stood near a bookshelf. He answered questions about the university. He asked a woman about her work and, when she replied, made himself ask another question rather than retreat into thinking what he should say next.

Later, his wife found him in the kitchen.

“I’m glad you came.”

“I nearly didn’t.”

“I know.”

He looked toward the sitting room.

“Are you happy?”

“Much of the time.”

It was an answer he would once have found unsatisfactory.

She touched his wrist.

“And you?”

“I’ve been having tea with someone,” he said.

Her expression changed, and he shook his head.

“No. Not like that. She cleans our building. She used to have a café.”

“What’s her name?”

“Mara.”

“Tell me about her.”

So he did.

The following Thursday, Mara found two pieces of cake beside the kettle.

“How was it?”

“Difficult.”

“That bad?”

“No.”

They ate from paper napkins. Elias told her about the dog, which had stolen a lemon and seemed disappointed by it.

Above them, the blackboard was covered in the week’s unsuccessful work.

Mara studied it while she finished her cake.

“Still not solved?”

“Not yet.”

“Does that bother you?”

“Very much.”

She brushed crumbs into her palm and stood. Her break was over.

At the door she paused.

“Tuesday?”

Elias glanced at the calendar on his desk, though he knew perfectly well that he was free.

“Tuesday.”

After she left, he returned to the problem. He worked until nine, found an error, and crossed out three lines.

Then he put on his coat.

The error would still be there in the morning.