'Quod erat demonstrandum,' I said. "That's exactly it. He's back doing mathematics. In fact, he's back working on Goldbach's Conjecture – ridiculous as that may sound at his age.'

My father shrugged. 'It's ridiculous at any age,’ he said. 'But why worry? Goldbach's Conjecture has already done him all the harm possible. Nothing worse can come of it.'

But I wasn't so sure about that. In fact, I was quite certain that a lot worse things could be in store for us. Goldbach's resurrection was bound to stir up unfulfilled passions, to aggravate deep-buried, terrible, unhealed wounds. His absurd new application to the old problem boded no good.

After work that evening, I drove to Ekali. The ancient VW beetle was parked outside the house. I crossed the front yard and rang the bell. There was no response, so I shouted: 'Open up, Uncle Petros; it's me!'

For a few moments I feared the worst, but then he appeared at a window and stared vaguely in my direction. There was no sign of his usual pleasure at seeing me, no surprise, no greeting – he just stared.

'Good afternoon,’ I said. 'I just came by to say hello.'

His normally serene face, the face of a stranger to life's usual worries, was now marked by extreme tension, his skin pale, his eyes red with sleeplessness, his brow furrowed with concern. He was also unshaven, the first time I'd seen him so. His stare continued absent, unfocused. I wasn't even sure he knew who I was.

'Come on, Uncle dear, please open up for the most favoured,’ I said with a fatuous smile.

He disappeared and after a while the door creaked open. He stood there, blocking my entry, wearing his pyjama bottoms and a wrinkled vest. It was evident he didn't want me to enter.

'What's wrong, Uncle?' I asked. ‘I’m worried about you.'

'Why should you be worried?' he said, now forcing himself to sound normal. 'Everything's fine.'

'Are you sure?'

'Of course I'm sure.'

Then, with a snappy gesture, he beckoned me closer. After quickly, anxiously glancing around, he leaned towards me, his lips almost touching my ear, and whispered: 'I saw them again.'

I didn't understand. 'Who did you see?'

'The girls! The twins, the number 2^100!'

I remembered the strange apparitions of his dreams.

'Well,' I said, trying to sound as casual as possible. ‘If you are once again involved with mathematical research, you are once again having mathematical dreams. Nothing strange about that…'

I wanted to keep him talking so as to (figuratively, but if need be also literally) put a foot in the door. I had to get some sense of how bad his condition was.

'So what happened, Uncle,' I asked, feigning great interest in the matter. 'Did the girls speak to you?'

'Yes,’ he said, 'they gave me a…' His voice quickly trailed off, as if he was afraid he'd said too much.

'A what?' I asked. 'A clue?'

He became suspicious again. 'You mustn't tell,’ he said sternly.

'Mum's the word,' I said.

He had started to close the door. Convinced now that his situation was extremely serious and that the time had come for emergency action, I grasped the knob and started to push. As he felt my force, he tensed up, gritted his teeth and struggled to prevent me from entering, his face contorted to a grimace of desperation. Fearing the effort might be too much for him (he was nearing eighty, after all) I reduced the pressure a bit for a final attempt at reason.

Of all the possible stupid things I could have said to him, I chose this: 'Remember Kurt Gödel, Uncle Petros! Remember the Incompleteness Theorem – Goldbach's Conjecture is unprovable!'

Instantly, his expression changed from despair to wrath. 'Fuck Kurt Gödel,' he barked, 'and fuck his Incompleteness Theorem!' With an unexpected upsurge of strength, he overcame my resistance and slammed the door shut in my face.

I rang the bell again and again, banged the door with my fist and shouted. I tried threats, reasoning and pleading, but nothing worked. When a torrential October rain began to fall I hoped that, mad or not, Uncle Petros might be moved by mercy and let me in. But he wasn't. I left, soaking wet and very worried.

From Ekali I drove straight to our family doctor and explained the Situation. Without altogether ruling out serious mental disturbance (possibly triggered by my unwarranted interference in his defence mechanisms) he suggested two or three organic problems as likelier causes of my uncle's transformation. We decided to go to his house first thing the next morning, force our way in if necessary, and submit him to a thorough medical examination.

That night I couldn't sleep. The rain was getting stronger, it was past two o'clock and I was sitting at home hunched in front of the chessboard, just as Uncle Petros must have been on innumerable sleepless nights, studying a game from the recent world championship. Yet my concern kept interfering and I couldn't concentrate.

When I heard the ringing I knew it was he, even though he'd never yet initiated a call on his newly installed telephone.

I jumped up and answered.

'Is that you, Nephew?' He was obviously all worked up about something.

'Of course it's me, Uncle. What's wrong?'

'You must send me someone. Now!'

I was alarmed. '"Someone"? A doctor you mean?'

'What use would a doctor be? A mathematician, of course!'

I humoured him: 'I'm a mathematician, Uncle; I’ll come right away! Just promise to open the door, so I won't catch pneumonia and -'

He obviously didn't have time for irrelevancies. 'Oh hell!' he grunted and then: 'All right, all right, you come, but bring another one as well!'

'Another mathematician?'

'Yes! I must have two witnesses! Hurry!'

'But why do the witnesses have to be mathematicians?'

Naively, I had thought at first he wanted to write his will.

'To understand my proof!'

‘Proof of what?’

'Goldbach's Conjecture, you idiot – what else!'

I chose my next words very carefully. 'Look, Uncle Petros,' I said, 'I promise to be with you as soon as my car will get me there. Let's be reasonable, mathematicians aren't kept on call – how on earth can I get one at two o'clock in the morning? You'll tell me all about your proof tonight and tomorrow we will go together -'

But he cut me off, screaming. 'No, no, no! There's no time for any of that! I need my two witnesses and I need them now!’ Then he broke down and started sobbing. 'O nephew, it's so… it's so…'

'So what, Uncle? Tell me!'

'Oh, it's so simple, so simple, my dearest boy! How is it possible that all those years, those endless years, I hadn't realized how blessedly simple it was!'

I cut him off. ‘I’ll be there as soon as I can.'

'Wait! Wait! Waaaaa-it!!!' He was now in panic. 'Swear you won't come alone! Get the other witness! Hurry… Hurry up, I implore you! Get the witness! There's no time!'

I tried to appease him: 'Oh, come on, Uncle; there can't be such a rush. The proof won't go away, you know!'

These were his last words: 'You don't understand, dear boy – there's no time left!' His voice then dropped to a low, conspiratorial whisper, as if he didn't want to be overheard by someone close by: 'You see, the girls are here. They are waiting to take me.'

By the time I arrived in Ekali, breaking all speed records, it was too late. Our family doctor (I had picked him up on the way) and I found Uncle Petros' lifeless body slumped on the paving of his little terrace. The torso was leaning against the wall, the legs spread open, the head turned towards us as if in welcome. A flash of distant lightning revealed his features fixed in a wonderful smile of deep, absolute contentment – I imagine it was that which guided the doctor in his instant diagnosis of a stroke. All around him were hundreds of lima beans. The rain had destroyed their neat parallelograms and now they were scattered all over the wet terrace, sparkling like precious jewels.