Apostolos Doxiadis - Uncle Petros and Goldbach

'Mmmm…' I groaned.

'So, have you registered?'

I shook my head wearily.

'Have you at least selected the courses you'll be taking?'

I shook my head once again and he frowned.

'Not that it's any of my business, but don't you think you better turn your attention to these rather urgent matters, instead of sitting there all day staring at the idiot-box?'

As he later confessed, it wasn't merely the urge to assist a fellow human being in crisis that made him assume responsibility – the curiosity to discover the connection between his new room-mate and the notorious mathematical problem was overwhelming. One thing is certain: regardless of his motives, the long discussion I had that evening with Sammy made all the difference to me. Without his understanding and support, I couldn't have crossed the crucial line. And, what's perhaps more important: it's quite unlikely I would ever have forgiven Uncle Petros.

We started our talk in the dining hall, over dinner, and continued through the night in our room, drinking coffee. I told him everything: about my family, my early fascination with the remote figure of Uncle Petros and my gradual discoveries of his accomplishments, his brilliant chess-playing, his books, the invitation of the Hellenic Mathematical Society and the professorship in Munich. About Father's brief resume of his life, his early successes and the mysterious (to me, at least) role of Goldbach's Conjecture in his later dismal failure. I mentioned my initial decision to study mathematics and the discussion with Uncle Petros that summer afternoon, three years back, in his kitchen in Ekali. Finally, I described our 'deal'.

Sammy listened without interrupting once, his small, deep eyes narrowed intently in focus. Only when I reached the end of my narrative and stated the problem that my uncle had required me to solve to demonstrate my potential for mathematical greatness did he burst out, seized by sudden fury.

'What an ass-hole!' he cried.

'My feelings exactly,' I said.

'The man is a sadist,' Sammy went on. 'Why, he's criminally insane! Only a perverted mind could conceive the plot of making a school-kid spend a summer trying to solve Goldbach's Conjecture, and this under the illusion that he had merely been set a challenging exercise. What a total beast!'

The guilt about the extreme vocabulary I had used in my delirious letter to Uncle Petros led me for a moment to attempt to defend him and find a logical excuse for his behaviour.

'Maybe his intentions were not all bad,’ I muttered. 'Maybe he thought he was protecting me from greater disappointment.'

'With what right?' Sammy said loudly, banging his hand on my desk. (Unlike me, he'd grown up in a society where children were not expected as a rule to conform to the expectations of their parents and elders.) 'Every person has the right to expose himself to whatever disappointment he chooses,’ he said fervently. 'Besides, what's all this crap about "being the best" and "golden mediocrities" and whatnot. You could have become a great -'

Sammy stopped in mid-sentence, his mouth gaping in amazement.' Wait a minute, why am I using the past tense?' he said, beaming. 'You can still become a great mathematician!'

I glanced up, startled. 'What are you talking about, Sammy? It's too late, you know that!'

'Not at all! The deadline for declaring a major is tomorrow.'

'That's not what I mean. I've already lost so much time doing other things and -'

'Nonsense,' he said firmly. 'If you work hard you can make up for lost time. What's important is that you recover your enthusiasm, the passion you had for mathematics before your uncle shamelessly destroyed it for you. Believe me, it can be done – and I'll help you do it!'

Day was breaking outside and the moment had come for the fourth and last stage that would complete the mourning process: Acceptance. The cycle had closed. I would pick up my life from where I'd left off when Uncle Petros, through the appalling trick he'd played on me, steered me away from what I then still considered my true course.

Sammy and I consumed a hearty breakfast in the dining hall and then sat down with the list of courses offered by the Department of Mathematics. He explained the contents of each one the way an experienced maitre d' might present choice items on the menu. I took notes, and in the early afternoon I went to the Registrar's office and filed my selection of courses for the semester just beginning: Introduction to Analysis, Introduction to Complex Analysis, Introduction to Modern Algebra and General Topology.

Naturally, I also declared my new field of major concentration: Mathematics.

A few days after the beginning of classes, during the most difficult phase of my efforts to penetrate into the new discipline, a telegram from Uncle Petros arrived. When I found the notice, I had no doubts as to the identity of the sender and initially considered not claiming it at all. However, curiosity finally prevailed.

I made a bet with myself as to whether he would be trying to defend himself, or simply scolding me for the tone of my letter. I opted for the latter and lost. He wrote:

I FULLY UNDERSTAND YOUR REACTION STOP IN ORDER TO UNDERSTAND MY BEHAVIOUR YOU SHOULD ACQUAINT YOURSELF WITH KURT GÖDEL's INCOMPLETENESS THEOREM

At that time I had no idea what Kurt Gödel's Incompleteness Theorem was. Also, I had no desire to find out – mastering the theorems of Lagrange, Cauchy, Fatou, Bolzano, Weierstrass, Heine, Borel, Lebesgue, Tychonoff, et al. for my various courses was hard enough. Anyway, by now I had more or less come to accept Sammy's assessment that Uncle Petros' behaviour towards me showed definite signs of derangement. The latest message confirmed this: he was trying to defend his despicable treatment of me by way of a mathematical theorem! The wretched old man's obsessions were of no further interest to me.

I did not mention the telegram to my room-mate, nor did I give it further thought.

I spent that Christmas vacation studying with Sammy at the Mathematics Library [4].

On New Year's Eve he invited me to celebrate with him and his family at their Brooklyn home. We'd been drinking and were feeling quite merry when he took me aside to a quiet corner.

'Could you bear to talk about your uncle a bit?' he asked. Since that first, all-night session, the subject had never again come up, as if by unspoken agreement.

'Sure I can bear it,' I laughed, 'but what more is there to say?'

Sammy took out of his pocket a sheet of paper and unfolded it. 'It's been a while now since I've been doing some discreet research on the subject,’ he said.

I was surprised. 'What kind of "discreet research"?'

'Oh, don't go imagining anything nefarious; mostly bibliographical stuff.'

'And?'

'And I came to the conclusion that your dear Uncle Petros is a fraud!'

'A fraud?' It was the last thing I would have expected to hear about him and, since blood is thicker than water, I immediately jumped to his defence.

'How can you say that, Sammy? It's a proven fact that he was Professor of Analysis at the University of Munich. He is no fraud!'

He explained: 'I went through the bibliographical indexes of all articles published in mathematical Journals in this Century. I only found three items under his name, but nothing – not one single word – on the subject of Goldbach's Conjecture or anything remotely related to it!'

I couldn't understand how this led to accusations of fraud. 'What's so surprising in that? My uncle is the first to admit that he didn't manage to prove the Conjecture: there was nothing to publish. I find it perfectly understandable!'

Sammy smiled condescendingly.

‘That's because you don't know the first thing about research,’ he said. 'Do you know what the great David Hubert answered when questioned by his colleagues as to why he never attempted to prove the so-called "Fermat's Last Theorem", another famous unsolved problem?'