Uncle Petros and Goldbach`s Conjecture

'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.

'Who is that man?' I whispered.

'Take a guess!'

'I haven't the slightest idea – he looks like a street person. Is he mad, or what?'

Sammy giggled. 'That, my friend, is your uncle's nemesis, the man who gave him the pretext for abandoning his mathematical career, none other than the father of the Incompleteness Theorem, the great Kurt Gödel!'

I gasped in amazement. 'My God! That's Kurt Gödel? But, why is he dressed like that?'

'Apparently he is convinced – despite his doctors' total disagreement – that he has a very bad heart and that unless he insulates it from the cold with all those clothes it will go into arrest.'

'But it's warm in here!'

'The modern high priest of Logic, the new Aristotle, disagrees with your conclusion. Which of the two should I believe, you or him?'

On our walk back to the university Sammy expounded his theory: ‘I think Gödel's insanity – for unquestionably he is in a certain sense insane – is the price he paid for coming too close to Truth in its absolute form. In some poem it says that "people cannot bear very much reality", or something like that. Think of the biblical Tree of Knowledge or the Prometheus of your mythology. People like him have surpassed the common measure; they've come to know more than is necessary to man, and for this hubris they have to pay.'

There was a wind blowing, lifting dead leaves in whirls around us. I sighed.

I’ll cut a long story (my own) short:

I never did become a mathematician, and this not because of any further scheming by Uncle Petros. Although his 'intuitive' depreciation of my abilities had definitely played a part in the decision by nurturing a constant, nagging sense of self-doubt, the true reason was fear.

The examples of the mathematical enfants terribles mentioned in my uncle's narrative – Srinivasa Ramanujan, Alan Turing, Kurt Gödel and, last but not least, himself – had made me think twice about whether I was indeed equipped for mathematical greatness. These were men who at twenty-five years of age, or even less, had tackled and solved problems of inconceivable difficulty and momentous importance. In this I'd definitely taken after my uncle: I didn't want to become a mediocrity and end up 'a walking tragedy', to use his own words. Mathematics, Petros had taught me, is a field that acknowledges only its greatest; this particular kind of natural selection offers failure as the only alternative to glory. Yet, hopeful as I still was in my ignorance about my abilities, it wasn't professional failure that I feared.

It all started with the sorry sight of the father of the Incompleteness Theorem padded with layers of warm clothing, of the great Kurt Gödel as a pathetic, deranged old man sipping his hot water in total isolation in the lounge of the Institute for Advanced Study.