Uncle Petros and Goldbach

by Apostolos Doxiadis

  Uncle Petros and Goldbach

  Apostolos Doxiadis

  Amazon.co.uk Review

  "Every family has its black sheep-in ours it was Uncle Petros": the narrator of Apostles Doxiadis's novel Uncle Petros and Goldbach's Conjecture is the mystified nephew of the family's black sheep, unable to understand the reasons for his uncle's fall from grace. A kindly, gentle recluse devoted only to gardening and chess, Petros Papachristos exhibits no signs of dissolution or indolence: so why do his family hold him in such low esteem? One day, his father reveals all:

  Your uncle, my son, committed the greatest of sins… he took something holy and sacred and great, and shamelessly defiled it! The great, unique gift that God had blessed him with, his phenomenal, unprecedented mathematical talent! The miserable fool wasted it; he squandered it and threw it out with the garbage. Can you imagine it? The ungrateful bastard never did one day's useful work in mathematics. Never! Nothing! Zero!

  Instead of being warned off, the nephew instead has his curiosity provoked, and what he eventually discovers is a story of obsession and frustration, of Uncle Petros's attempts at finding a proof for one of the great unsolved problems of mathematics-Goldbach's conjecture.

  If this might initially seem undramatic material for a novel, readers of Fermat's Last Theorem, Simon Singh's gripping true-life account of Andrew Wiles's search for a proof for another of the great long-standing problems of mathematics, would surely disagree. What Doxiadis gives us is the fictional corollary of Singh's book: a beautifully imagined narrative that is both compelling as a story and highly revealing of a rarefied world of the intellect that few people will ever access. Without ever alienating the reader, he demonstrates the enchantments of mathematics as well as the ambition, envy and search for glory that permeate even this most abstract of pursuits. Balancing the narrator's own awkward move into adulthood with the painful memories of his brilliant uncle, Doxiadis shows how seductive the world of numbers can be, and how cruel a mistress. "Mathematicians are born, not made," Petros declares: an inheritance that proves to be both a curse and a gift.-Burhan Tufail

  Review

  If you enjoyed Fermat's Last Theorem, you'll devour this. However, you don't need to be an academic to understand its imaginative exploration of the allure and danger of genius. Old Uncle Petros is a failure. The black sheep of a wealthy Greek family, he lives as a recluse surrounded by dusty books in an Athenian suburb. It takes his talented nephew to penetrate his rich inner world and discover that this broken man was once a mathematical prodigy, a golden youth whose ambition was to solve one of pure maths' most famous unproven hypotheses – Goldbach's Conjecture. Fascinated, the young man sets out to discover what Uncle Petros found – and what he was forced to sacrifice. Himself a mathematician as well as a novelist, Doxiadis succeeds in shining a light into the spectral world of abstract number theory where unimaginable concepts and bizarre realities glitter with a cold, magical and ultimately destructive beauty. (Kirkus UK)

  Apostolos Doxiadis

  Uncle Petros and Goldbach's Conjecture

  Archimedes will be remembered when Aeschylus

  is forgotten, because languages die and mathematical

  ideas do not. 'Immortality' may be a silly word,

  but probably a mathematician has the best

  chance of whatever it may mean.

  G. H. Hardy, A Mathematician's Apology

  One

  Every family has its black sheep – in ours it was Uncle Petros.

  My father and Uncle Anargyros, his two younger brothers, made sure that my cousins and I should inherit their opinion of him unchallenged.

  “That no-good brother of mine, Petros, is one of life's failures”, my father would say at every opportunity. And Uncle Anargyros, during the family get-togethers from which Uncle Petros routinely absented himself, always accompanied mention of his name with snorts and grimaces expressing disapproval, disdain or simple resignation, depending on his mood.

  However, I must say this for them: both brothers treated him with scrupulous fairness in financial matters. Despite the fact that he never shared even a slight part of the labour and the responsibilities involved in running the factory that the three inherited jointly from my grandfather, Father and Uncle Anargyros unfailingly paid Uncle Petros his share of the profits.

  (This was due to a strong sense of family, another common legacy.) As for Uncle Petros, he repaid them in the same measure. Not having had a family of his own, upon his death he left us, his nephews, the children of his magnanimous brothers, the fortune that had been multiplying in his bank account practically untouched in its entirety.

  Specifically to me, his 'most favoured of nephews' (his own words), he additionally bequeathed his huge library which I, in turn, donated to the Hellenic Mathematical Society. For myself I retained only two of its items, volume seventeen of Leonard Euler's Opera Omnia and issue number thirty-eight of the German scientific Journal Monatshefte für Mathematik und Physik. These humble memorabilia were symbolic, as they defined the boundaries of Uncle Petros' essential life-story. Its starting-point is in a letter written in 1742, contained in the former, wherein the minor mathematician Christian Goldbach brings to the attention of the great Euler a certain arithmetical observation. And its termination, so to speak, is to be found in pages 183-98 of the erudite Germanic Journal, in a study entitled 'On Formally Undecidable Propositions in Principia Mathematica and Related Systems', authored in 1931 by the until then totally unknown Viennese mathematician Kurt Gödel.

  Until I reached mid-adolescence I would see Uncle Petros only once a year, during the ritual visit on his name day, the feast of Saints Peter and Paul on the twenty-ninth of June. The custom of this annual meeting had been initiated by my grandfather and as a consequence had become an inviolable obligation in our tradition-ridden family. We journeyed to Ekali, a suburb of Athens today but in those days more of an isolated sylvan hamlet, where Uncle Petros lived alone in a small house surrounded by a large garden and orchard.

  The contemptuous dismissal of their older brother by Father and Uncle Anargyros had puzzled me from my earliest years and had gradually become for me a veritable mystery. The discrepancy between the picture they painted of him and the impression I formed through our scant personal contact was so glaring that even an immature mind like mine was compelled to wonder.

  In vain did I observe Uncle Petros during our annual visit, seeking in his appearance or behaviour signs of dissoluteness, indolence or other characteristics of the reprobate. On the contrary, any comparison weighed unquestionably in his favour: the younger brothers were short-tempered and often outright rude in their dealings with people while Uncle Petros was tactful and considerate, his deep-set blue eyes always kindling with kindness. They were both heavy drinkers and smokers; he drank nothing stronger than water and inhaled only the scented air of his garden. Furthermore, unlike Father, who was portly, and Uncle Anargyros, who was outright obese, Petros had the healthy wiriness resulting from a physically active and abstemious lifestyle.

  My curiosity increased with each passing year. To my great disappointment, however, my father refused to disclose any further information about Uncle Petros beyond his dismissive incantation, 'one of life's failures'. From my mother I learned of his daily activities (one could hardly speak of an occupation): he got up every morning at the crack of dawn and spent most daylight hours slaving away in his garden, without help from a gardener or any modern labour-saving contraptions – his brothers erroneously attributed this to stinginess. He seldom left his house, except for a monthly visit to a small philanthropic institution founded by my grandfather, where he volunteered his services as treasurer. In addition, he sometimes went t
o 'another place', never specified by her. His house was a true hermitage; with the exception of the annual family invasion there were never any visitors. Uncle Petros had no social life of any kind. In the evenings he stayed at home and – here mother had lowered her voice almost to a whisper – 'immersed himself in his studies'.

  At this my attention suddenly peaked. 'Studies? What studies?'

  “God only knows”, answered Mother, conjuring up in my boyish imagination visions of esoterica, alchemy or worse.

  A further unexpected piece of information came to identify the mysterious 'other place' that Uncle Petros visited. It was offered one evening by a dinner-guest of my father's.

  “I saw your brother Petros at the club the other day. He demolished me with a Karo-Cann”, said the guest, and I interjected, earning an angry look from my father: 'What do you mean? What's a Karo-Cann?'

  Our guest explained that he was referring to a particular way of opening the game of chess, named after its two inventors, Messrs Karo and Cann. Apparently, Uncle Petros was in the habit of paying occasional visits to a chess club in Patissia where he routinely routed his unfortunate opponents.

  'What a player!' the guest sighed admiringly. 'If only he'd entered formal competition he'd be a Grand Master today!'

  At this point Father changed the subject.

  The annual family reunion was held in the garden. The grown-ups sat around a table that had been set up in a paved patio, drinking, snacking and making small-talk, the two younger brothers routinely exerting themselves (as a rule, not altogether successfully) to be gracious to the honouree. My cousins and I played among the trees in the orchard.

  On one occasion, having made the decision to seek an answer to the mystery of Uncle Petros, I asked to use the bathroom; I was hoping I would get a chance to examine the inside of the house. To my great disappointment, however, our host indicated a small out-house attached to the toolshed. The next year (by that time I was fourteen) the weather came in aid of my curiosity. A summer storm forced my uncle to open the French windows and lead us into a space that had obviously been intended by the architect to serve as a living room. Equally obviously, however, the owner did not use it to receive guests. Although it did contain a couch, it was totally inappropriately positioned facing a blank wall. Chairs were brought in from the gar-den and placed in a semi-circle, where we sat like the mourners at a provincial wake.

  I made a hasty reconnaissance, with quick glances all around. The only pieces of furniture apparently put to daily use were a deep, shabby armchair by the fire-place with a small table at its side; on it was a chessboard with the pieces set out as for a game in progress. Next to the table, on the floor, was a large pile of chess books and periodicals. This, then, was where Uncle Petros sat every night. The studies mentioned by my mother must have been studies of chess. But were they?

  I couldn't allow myself to jump to facile conclusions, as there were now new speculative possibilities. The main feature of the room we sat in – what made it so different from the living room in our house – was the overwhelming presence of books, countless books everywhere. Not only were all the visible walls of the room, corridor and entrance hall dressed from floor to ceiling with shelves crammed to overflowing, but books in tall piles covered most of the floor area as well. Most of them looked old and overused.

  At first, I chose the most direct route to answering my question about their content: I asked, 'What are all these books, Uncle Petros?'

  There was a frozen silence, exactly as if I had spoken of rope in the house of the hanged man.

  “They are… old”, he mumbled hesitantly, after casting a quick glance in the direction of my father. He seemed so flustered in his search for an answer, however, and the accompanying smile was so wan that I couldn't bring myself to ask for further explanations.

  Once again I resorted to the call of nature. This time Uncle Petros led me to a small toilet next to the kitchen. On my way back to the living room, alone and unobserved, I seized the opportunity I had created. I picked up the top book of the nearest pile in the corridor and flipped hurriedly through the pages. Unfortunately it was in German, a language I was (and still am) totally unfamiliar with. On top of it, most of the pages were adorned with mysterious symbols such as I'd never seen before: "'s and $'s and f’s and Ï's. Among them, I discerned some more intelligible signs, +'s, ='s and ÷'s interspersed with numerals and letters both Latin and Greek. My rational mind overcame cabbalistic fantasies: it was mathematics!

  I left Ekali that day totally preoccupied with my discovery, indifferent to the scolding I received from my father on the way back to Athens and to his hypocritical reprimands about my 'rudeness to my uncle' and 'my busybody, prying questions'. As if it was the breach in savoir-vivre that had bothered him!

  My curiosity about Uncle Petros' dark, unknown side developed in the next few months into something approaching obsession. I remember compulsively drawing doodles combining mathematical and chess symbols in my notebooks during school classes. Maths and chess: in one of these most probably lay the solution to the mystery surrounding him, yet neither offered a totally satisfactory explanation, neither being reconcilable with his brothers' contemptuously dismissive attitude. Surely, these two fields of interest (or was it more than mere interest?) were not in themselves objectionable. Whichever way you looked at it, being a chess player at Grand Master level or a mathematician who had devoured hundreds of formidable tomes did not immediately classify you as 'one of life's failures'.

  I needed to find out, and in order to do so I even contemplated for a while a venture in the style of the exploits of my favourite literary heroes, a project worthy of Enid Blyton's Secret Seven, the Hardy Boys, or their Greek soulmate, the 'heroic Phantom Boy'. I planned, down to the smallest detail, a break-in at my uncle's house during one of his expeditions to the philanthropic institution or the chess club, so I could lay my hands on palpable evidence of transgression.

  As things turned out, I did not have to resort to crime to satisfy my curiosity. The answer I was seeking came and hit me, so to speak, over the head. Here's how it happened:

  One afternoon, while I was alone at home doing my homework, the phone rang and I answered it.

  “Good evening”, said an unfamiliar male voice. I’m calling from the Hellenic Mathematical Society. May I speak to the Professor please?'

  Unthinking at first, I corrected the caller: 'You must have dialled the wrong number. There is no professor here.'

  “Oh, I'm sorry”, he said. 'I should have inquired first. Isn't that the Papachristos residence?'

  I had a sudden flash of inspiration. 'Do you, perhaps, mean Mr Petros Papachristos?' I asked.

  'Yes’, said the caller, 'Professor Papachristos.'

  'Professor'! The receiver nearly dropped from my hand. However, I suppressed my excitement, lest this windfall opportunity go to waste.

  'Oh, I didn't realize you were referring to Professor Papachristos’, I said ingratiatingly. 'You see, this is his brother's home, but as the Professor does not have a telephone' – (fact) – 'we take his calls for him' (blatant lie).

  'Could I then have his address?' the caller asked, but by now I had regained my composure and he was no match for me.

  'The Professor likes to maintain his privacy’, I said haughtily. 'We also receive his mail.'

  I had left the poor man no options. 'Then be so kind as to give me your address. On behalf of the Hellenic Mathematical Society, we would like to send him an invitation.'

  The next few days I played sick so as to be at home at the usual time of mail delivery. I didn't have to wait long. On the third day after the phone call I had the precious envelope in my hand. I waited till after midnight for my parents to go to sleep and then tiptoed to the kitchen and steamed it open (another lesson culled from boys' fiction).

  I unfolded the letter and read:

  Mr Petros Papachristos

  f. Professor of Analysis

  University of Munich


  Honourable Professor,

  Our Society is planning a Special Session to commemorate Leonard Euler's two hundred and fiftieth birthday with a lecture on 'Formal Logic and the Foundations of Mathematics'.

  We would be greatly honoured, dear Professor, if you would attend and address a short greeting to the Society…

  So: the man routinely dismissed by my dear father as 'one of life's failures' was a Professor of Analysis at the University of Munich – the significance of the little 'f.' preceding his unexpectedly prestigious title still escaped me. As to the achievements of this Leonard Euler, still remembered and honoured two hundred and fifty years after his birth, I hadn't the slightest clue.

  The next Sunday morning I left home wearing my Boy Scout uniform, but instead of going to the weekly meeting I boarded the bus for Ekali, the letter from the Hellenic Mathematical Society safely in my pocket. I found my uncle in an old hat and rolled-up sleeves, spade in hand, turning the soil in a vegetable plot. He was surprised to see me.

  'What brings you here?' he asked.

  I gave him the sealed envelope.

  'You needn't have gone to the trouble’, he said, barely glancing at it. 'You could have put it in the mail.' Then he smiled kindly. "Thank you anyway, Boy Scout. Does your father know you've come?'

  'Uh, no,' I muttered.

  'Then I better drive you home; your parents will be worried.'

  I protested that it wasn't necessary, but he insisted. He climbed into his ancient, beat-up VW beetle, muddy boots and all, and we set out for Athens. On the way I attempted more than once to start a conversation on the subject of the invitation, but he switched to irrelevant matters like the weather, the correct season for tree-pruning and scouting.

  He dropped me off at the corner nearest our house. 'Should I come upstairs and provide excuses?'