To my surprise, this opinion was rewarded with a huge, hearty smile. 'On that, most favoured of nephews, I couldn't agree with you more!'

A month later I returned to the United States to prepare for my Senior year. I now had a new room-mate, unrelated to mathemarics. Sammy had meanwhile graduated and was at Princeton, already deeply involved in the problem that would in due course become his doctoral dissertation – with the exotic title: "The orders of the torsion subgroups of \Omega_{n} and the Adams spectral sequence'.

On my first free weekend I took the train and went to visit him. I found him quite changed, much more nervous and irritable than I had known him in the year of our association. He'd also acquired some kind of facial tic. Obviously, the torsion subgroups of \Omega_{n (whatever they were) had taken their toll on his nerves. We had dinner at a small pizza place across from the university and there I gave him a shortened version of Uncle Petros' story, as I'd heard it from him. He listened without once interrupting for question or comment.

After I was finished, he summed up his reaction in two words: 'Sour grapes.'

'What?'

'You should know – Aesop was a Greek.'

'What's Aesop got to do with it?'

'Everything. The fable of the fox who couldn't reach a yummy bunch of grapes and therefore decided they were unripe anyway. What a wonderful excuse your uncle found for his failure: he put the blame on Kurt Gödel! Wow!' Sammy burst out laughing. 'Audacious! Unheard of! But I have to grant it to him, it is original; in fact it's unique, it should go into some book of records! Never before has there been a mathematician seriously attributing his failure to find a proof to the Incompleteness Theorem!'

Although Sammy's words echoed my own first doubts, I lacked the mathematical knowledge to understand this immediate verdict.

'So, you think it's impossible that Goldbach's Conjecture is unprovable?'

'Man, what does "impossible" mean in this context?' Sammy sneered. 'As your uncle correctly told you, there is, thanks to Turing, no way of telling with certainty that a statement is a priori unprovable. But if mathematicians involved in advanced research started invoking Gödel, no one would ever go near the interesting problems – you see, in mathematics the interesting is always difficult. The Riemann Hypothesis has not yielded to proof after more than a Century? A case of application of the Incompleteness Theorem! The Four Colour Problem? Likewise! Fermat's Last Theorem still unproved? Blame it on evil Kurt Gödel! No one would ever have touched Hilbert's Twenty-three Problems; [14] indeed it's conceivable that all mathematical research, except the most trivial, would come to an end. Abandoning the study of a particular problem because it might be unprovable is like… like…' His face lit up when he found the appropriate analogy. 'Why, it's like not going out in the street for fear that a brick might fall on your head and kill you!'

'Let's face it,' he concluded, 'your Uncle Petros simply and plainly failed to prove Goldbach's Conjecture, like many greater men before him. But because, unlike them, he had spent his whole creative life on the problem, admitting his failure was unbearable. So, he concocted for himself this far-fetched, extravagant justification.'

Sammy raised his soda-glass in a mock toast. 'Here's to far-fetched excuses,' he said. Then he added in a more serious tone: 'Obviously, for Hardy and Littlewood to have accepted him as a collaborator, your uncle must have been a gifted mathematician. He could have made a great success of his life. Instead, he wilfully chose to throw it away by setting himself an unattainable goal and going after a notoriously difficult problem. His sin was Pride: he presumed that he would succeed where Euler and Gauss had failed.'

I was laughing now.

'What's so funny?' asked Sammy.

'After all these years of grappling with the mystery of Uncle Petros,' I said, ‘I’m back to square one. You just repeated my father's words, which I high-handedly rejected as philistine and coarse in my adolescence: "The secret of life, my son, is to set yourself attainable goals." It's exactly what you are saying now. That he didn't do so is, indeed, the essence of Petros' tragedy!'

Sammy nodded. 'Appearances are after all deceptive,’ he said with mock solemnity. 'It turns out the wise elder in the Papachristos family is not your Uncle Petros!'

I slept on the floor of Sammy's room that night, to the familiar sound of his pen scratching on paper accompanied by the occasional sigh or groan, as he struggled to untangle himself from the knots of a difficult topological problem. He left early in the morning to attend a seminar and in the afternoon we met at the Mathematics Library at Fine Hall, as arranged.

'We are going sightseeing,’ he said. 'I have a surprise for you.'

We walked a distance on a long suburban road lined with trees and strewn with yellow leaves.

'What courses are you taking this year?' Sammy asked as we walked towards our mysterious destination.

I started to list them: Introduction to Algebraic Geometry, Advanced Complex Analysis, Group Representation Theory…

'What about Number Theory?' he interrupted.

'No. Why do you ask?'

'Oh, I've been thinking about this business with your uncle. I wouldn't want you getting any crazy ideas into your head about following family tradition and tackling -'

I laughed.''Goldbach 's Conjecture? Not bloody likely!'

Sammy nodded. 'That's good. Because I have a suspicion that you Greeks are attracted to impossible problems.'

'Why? Do you know any others?'

'A famous topologist here, Professor Papakyriakopoulos. He's been struggling for years on end to prove the "Poincare Conjecture" – it's the most famous problem in low-dimensional topology, unproved for more than sixty years… ultra-hyper-difficult!'

I shook my head. 'I wouldn't touch anybody's famous unproved ultra-hyper-difficult problem with a ten-foot pole,’ I assured him.

‘I’m relieved to hear it,' he said.

We had reached a large nondescript building with extensive grounds. Once we had entered, Sammy lowered his voice.

'I got a special permit to come, in your honour,’ he said.

'What is this place?'

'You'll see.'

We walked down a corridor and entered a large, darkish room, with the atmosphere of a slightly shabby but genteel English gentlemen's club. About fifteen men, ranging from middle-aged to elderly, were seated in leather armchairs and couches, some by the windows, reading newspapers in the scanty daylight, others talking in little groups.

We settled ourselves at a little table in a corner.

'See that guy over there?' Sammy said in a low voice, pointing to an old Asian gentleman, quietly stirring his coffee.

'Yes?'

'He is a Nobel Prize in Physics. And that other one at the far end' – he indicated a plump, red-haired man gesturing heatedly as he spoke to his neighbour with a strong accent – 'is a Nobel Prize in Chemistry.' Then he directed my attention to two middle-aged men seated at a table near us. 'The one on the left is Andre Weil -'

'The Andre Weil?'

'Indeed, one of the greatest living mathematicians. And the other one with the pipe is Robert Oppenheimer – yes, the Robert Oppenheimer, the father of the atom bomb. He's the Director.'

'Director of what?'

'Of this place here. You are now in the Institute for Advanced Study, think-tank for the world's greatest scientific minds!'

I was about to ask more when Sammy cut me short. 'Shh! Look! Over there!'

A most odd-looking man had just come in through the door. He was about sixty, of average height and emaciated to an extreme degree, wearing a heavy overcoat and a knitted cap pulled down over his ears. He stood for a moment and peered at the room vaguely through extremely thick glasses. No one paid him any attention: he was obviously a regular. He made his way slowly to the tea and coffee table without greeting anybody, filled a cup with piain boiling water from the kettle and made his way to a seat by a window. He slowly removed his heavy overcoat. Underneath it he was wearing a thick jacket over at least four or five layers of sweaters, visible through his collar.