In a short while I realized that even if I did have their gift (which, after listening to Uncle Petros' story, I began seriously to doubt) I definitely did not want to suffer their personal misery. Thus, with the Scylla of mediocrity on the one side and the Charybdis of insanity on the other, I decided to abandon ship. Although I did, come June, eventually get my BA in Mathematics, Ihad already applied for graduate studies in Business Economics, a field that does not traditionally provide material for tragedy.
Yet, I hasten to add, I've never regretted my years as a mathematical hopeful. Learning some real mathematics, even my tiny portion of it, has been for me the most invaluable lesson of life. Obviously, everyday problems can be handled perfectly well without knowledge of the Peano-Dedekind Axiomatic System, and mastery of the Classification of Finite Simple Groups is absolutely no guarantee of success in business. On the other hand, the non-mathematician cannot conceive of the joys that he's beert denied. The amalgam of Truth and Beauty revealed through the understanding of an important theorem cannot be attained through any other human activity, unless it be (I wouldn't know) that of mystical religion. Even if my education was meagre, even if it meant no more than getting my toes wet on the beach of the immense ocean of mathematics, it has marked my life for ever, giving me a small taste of a higher world. Yes, it has made the existence of the Ideal slightly more believable, even tangible.
For this experience I am forever in Uncle Petros' debt: it's impossible I would have made the choice without him as my dubious role model.
My decision to abandon plans of a mathematical career came as a joyful surprise to my father (the poor man had fallen into deep despair during my last undergraduate years), a surprise made even happier when he learned I would be going to business school. When, having completed my graduate studies and military service, I joined him in the family business, his happiness was at last complete.
Despite this volte-face (or maybe because of it?) my relationship with Uncle Petros blossomed anew after I returned to Athens, every vestige of bitterness on my part totally dissipated. As I gradually settled down to the routines of work and family life, visiting him became a frequent habit, if not a necessity. Our contact was an invigorating antidote to the increasing grind of the real world. Seeing him helped me keep alive that part of the self that most people lose, or forget about, with adulthood – call it the Dreamer or the Wonderer or simply the Child Within. On the other hand, I never understood what my friendship offered him, if we exclude the companionship he claimed not to need.
We wouldn't talk all that much on my visits to Ekali, as we'd found a means of communication better suited to two ex-mathematicians: chess. Uncle Petros was an excellent teacher and soon I came to share his passion (though unfortunately not his talent) for the game.
In chess, I also had the first direct experience of him as a thinker. As he analysed for my benefit the classic great games, or the more recent contests of the world's best players, I was filled with admiration for the workings of his brilliant mind, its immediate grasp of the most complex problems, its analytical power, the flashes of insight. When he confronted the board his features became fixed in utter concentration, his gaze became sharp and penetrating. Logic and intuition, the instruments with which he'd pursued for two decades the most ambitious intellectual dream, sparkled in his deep-set blue eyes.
Once, I asked him why he had never entered official competition.
He shook his head. 'Why should I strive to become a mediocre professional when I can bask in my status as an exceptional amateur?' he said. 'Besides, most favoured of nephews, every life should progress according to its basic axioms and chess wasn't among mine – only mathematics.'
The first time I ventured to ask him again about his research (after the extensive account of his life he had given me, we'd never again mentioned anything mathematicaL both of us apparently preferring to let our sleeping dogs lie) he immediately dismissed the matter.
'Let bygones be bygones and tell me what you see on the chessboard. It's a recent game between Petrosian and Spassky, a Sicilian Defence. White takes Knight to f4…'
More oblique attempts didn't work either. Uncle Petros would not be coaxed into another mathematical discussion – period. Whenever I attempted a direct mention it would always be: 'Let's stick to chess, shall we?'
His refusals, however, didn't make me give up.
My wish to draw him once again to the subject of his life's work was not fired by mere curiosity. Although it was a long time since I had any news of my old friend Sammy Epstein (last time I'd heard of him he was an assistant professor in California), I couldn't forget his explanation of Uncle Petros giving up his research. In fact, I'd come to invest it with great existential significance. The development of my own affair with mathematics had taught me an important lesson: one should be brutally honest with oneself about weaknesses, acknowledge them with courage and chart further course accordingly. For myself I had done this, but had Uncle Petros?
These were the facts: a) From an early age he had chosen to invest all his energy and time in an incredibly, but most probably not impossibly, difficult problem, a decision which I still continued to regard as basically noble; b) As might reasonably have been expected (by others, if not by himself) he had not achieved his goal; c) He had blamed his failure on the incompleteness of mathematics, deeming Goldbach's Conjecture unprovable.
Of this much I was now certain: the validity of his excuse had to be judged by the strict standards of the trade and, according to these, I accepted Sammy Epstein's opinion as final – a final verdict of unprovability a la Kurt Gödel is just not an acceptable conclusion of the attempt to prove a mathematical statement. My old friend's explanation was much closer to the point. It wasn't because of his 'bad luck' Uncle Petros hadn't managed to achieve his dream. The appeal to the Incompleteness Theorem was indeed a sophisticated form of 'sour grapes', meant only to shelter him from the truth.
With the passing of the years, I had learned to recognize the profound sadness that pervaded my uncle's life. His absorption in gardening, his kindly smiles or his brilliance as a chess player couldn't disguise the fact that he was a broken man. And the closer to him I got, the more I realized that the reason for his condition lay in his profound insincerity. Uncle Petros had lied to himself about the most crucial event in his life and this lie had become a cancerous growth that stifled his essence, eating away at the very roots of his psyche. His sin, indeed, had been Pride. And the pride was still there, nowhere more apparent than in his inability to come face to face with himself.
I've never been a religious man, yet I believe there is great underlying wisdom in the ritual of Absolution: Petros Papachristos, like every human being, deserved to end his life unburdened of unnecessary suffering. In his case, however, this had the necessary prerequisite of his admitting the mea culpa of his failure.
The context here not being religious, a priest could not do the job.
The only person fit to absolve Uncle Petros was I myself, for only I had understood the essence of his transgression. (The pride inherent in my own assumption I did not realize until it was too late.) But how could I absolve him if he did not first confess? And how could I lead him to confession unless we started once again to talk mathematics, a thing he persistently refused to do?