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“You should try it. You just have to apply for a grant.”

She shook her head sadly.

“I’ve tried, I’ve already tried, but it seems it’s too late. They’d never admit it, of course, but they prefer to give them to younger women. I’m almost twenty-nine,” she said, as if that were the start of old age. She added, bitterly: “Sometimes I’d give anything to get away from here.”

I gazed at the ivy-clad houses, the spires on top of medieval cupolas, the crenellated towers in the distance.

“Get away from Oxford? I can’t imagine a more beautiful place.”

A look of futility dulled her eyes.

“Yes, maybe…if you didn’t have to look after an invalid all the time and spend your days doing something that lost all meaning long ago.”

“Don’t you like playing the cello?” I found this surprising, and interesting. I looked at her, trying to see what lay beneath the surface.

“I hate it,” she said, and her eyes grew dark. “I hate it more every day, and it’s getting harder and harder to hide. Sometimes I’m scared that it shows when I play, that the conductor or one of my colleagues will realise how much I detest each note. But at the end of every concert the audience claps and nobody seems to notice anything. Isn’t that funny?”

“I’d say you’re safe. I don’t think hatred has its own special vibration. In that sense, music is as abstract as maths: it doesn’t make moral distinctions. As long as you follow the score, I don’t imagine there’s any way of detecting it.”

“Follow the score…that’s what I’ve done all my life,” she sighed. We were at the front door now and she put her hand on the doorknob. “Don’t take any notice of me,” she said, “I’ve had a bad day.”

“But the day isn’t over yet,” I said. “Is there anything I can do to improve it?”

She smiled sadly and took the cello from me.

“Oh, you’re such a Latin man,” she murmured, as if that were something she should be wary of. Still, before she shut the door, she allowed me a last glimpse of her blue eyes.

Two weeks passed. Summer was slowly starting, with mild evenings and very long sunsets. On the first Wednesday in May, on my way home from the Institute, I stopped at a cash machine to get money for my rent. I rang Mrs Eagleton’s doorbell and, as I waited, a man came up the winding path to the house. He was tall and took large strides, and he looked preoccupied. I peered at him out of the corner of my eye as he came to a stop beside me. He had a wide, high forehead and small, deep-set eyes, and a noticeable scar on his chin. He must have been in his mid-fifties, but a kind of contained energy in his movements made him seem still young. There was a brief moment of awkwardness as we both waited at the closed door, until he asked, in a deep, melodious Scottish accent, if I had rung the bell. I said I had and rang for a second time. I said perhaps my first ring had been too brief. As I spoke the man gave me a friendly smile and asked if I was Argentinian.

“So you must be Emily’s graduate student,” he said, switching to perfect Spanish with-amusingly-a Buenos Aires accent.

Surprised, I said that I was and asked him where he had learned Spanish. He arched his eyebrows, as if looking into the distant past, and said he’d learned it many years ago.

“My first wife was from Buenos Aires.” He held out his hand. “I’m Arthur Seldom.”

At that time few names could have provoked more admiration in me. The man with the small, pale eyes holding out his hand was already a legend among mathematicians. I’d spent months studying his most famous work, the philosophical extension of Godel’s theorem from the thirties, for a seminar. He was considered one of the four leading minds in the field of logic, and you just had to glance at the varied titles of his work to see that he was a rare case of mathematical genius. Beneath that high, serene forehead some of the most profound ideas of the century had fallen into place. On my second visit to the bookshops in town I had tried to get hold of his latest book, a popular work explaining logical series, and found, to my surprise, that it had been sold out for a couple of months. Someone mentioned that, since the book’s publication, Seldom had disappeared from the conference circuit and apparently nobody dared venture a guess as to what he was working on now. In any case I didn’t even know he lived in Oxford, and I certainly never would have expected to bump into him at Mrs Eagleton’s front door. I told him I’d expounded on his theorem at a seminar and he seemed pleased by my enthusiasm. But he was obviously worried about something as he kept glancing at the door.

“Mrs Eagleton should be in, shouldn’t she?” he said.

“I would have thought so,” I said. “There’s her electric wheelchair. Unless someone’s taken her out by car.”

Seldom rang the bell again and listened at the door. He went to the window that looked on to the hall, and peered inside.

“Is there a back door?” And then, in English, he said: “I’m worried something might have happened to her.”

I could tell from his face that he was deeply alarmed, as if he knew something that stopped him concentrating on anything else.

“We could try the door,” I said. “I don’t think they lock it during the day.”

Seldom turned the handle and the door opened quietly. We entered without a word, the wooden floorboards creaking beneath our steps. Inside we could hear, like a muffled heartbeat, the stealthy to and fro of a clock’s pendulum. We went through to the sitting room and stopped by the table in the centre. I pointed to the chaise longue by the window looking on to the garden. Mrs Eagleton was lying there, apparently sleeping deeply, her face turned towards the back of the chair. One of her pillows was on the floor, as if it had slipped while she slept. Her bun of white hair was carefully protected by a hairnet and her glasses lay on the little table, beside the Scrabble board. It looked as if she had been playing on her own because the letter racks were both on her side.

Seldom went over to her. As he touched her lightly on the shoulder her head fell heavily to one side. Just then we saw her terrified open eyes and two parallel trails of blood running from her nose to her chin, joining on her neck. Involuntarily I took a step back and had to stop myself from crying out. Seldom, who was supporting her head with his arm, rearranged the body as best he could and muttered something anxiously that I didn’t catch. He picked up the pillow, uncovering a big red stain on the carpet that was almost dry in the centre. He stood for a moment with his arm down by his side, holding the pillow, deep in thought, as if exploring the ramifications of a complex calculation. He looked truly perturbed. I said I thought we ought to call the police and he agreed mechanically.

Three

They said we should wait outside,” said Seldom laconically when he hung up.

We went out to the little porch, making sure not to touch anything. Seldom leaned against the handrail and rolled a cigarette. His hands paused from time to time as he folded the cigarette paper, then compulsively repeated an action, as if they were following the stops and starts of a train of thought that he had to check carefully. He no longer looked overwhelmed, as he had a few moments earlier; instead he seemed to be trying to make sense of something incomprehensible.

Two policemen arrived and stationed themselves silently in front of the house. A tall, grey-haired man with piercing eyes, wearing a dark-blue suit, came up to us. He shook hands with us quickly and asked for our names. He had prominent cheekbones, probably growing sharper with age, and a look of calm but determined authority, as if he was used to taking charge of situations.

“I’m Inspector Petersen,” he said. He indicated a man in green overalls who nodded briefly as he came past. “That’s our forensic pathologist. Would you mind coming inside for a moment? We need to ask you some questions.”