Uncle Petros and Goldbach

by Apostolos Doxiadis

  'No thanks, Uncle, that won't be necessary.'

  However, it turned out that excuses were necessary. As my ill luck would have it, Father had called the club to ask me to pick something up on the way home and been informed of my absence. Naively, I blurted out the whole truth. As it turned out, this was the worst possible choice. If I'd lied and told him that I played truant from the meeting in Order to indulge in forbidden cigarettes in the park, or even visit a house of ill-repute, he wouldn't have been quite so upset.

  'Haven't I expressly forbidden you to have anything to do with that man?' he yelled at me, getting so red in the face that my mother started pleading with him to think of his blood pressure.

  'No, Father’, I replied truthfully. 'As a matter of fact, you never have. Never!'

  'But don't you know about him? Haven't I told you a thousand times about my brother Petros?'

  'Oh, you've told me a thousand times that he's "one of life's failures", but so what? He's still your brother – my uncle. Was it so terrible to take the poor fellow his letter? And, come to think of it, I don't see how being "one of life's failures" applies to someone with the rank of Professor of Analysis at a great university!'

  "The rank of former Professor of Analysis,’ growled my father, settling the matter of the little 'f.'

  Still fuming, he pronounced the sentence for what he termed my 'abominable act of inexcusable disobedience'. I could hardly believe the severity: for a month I would be confined to my room at all hours except those spent at school. Even my meals would have to be taken there and I would be allowed no spoken communication with himself, my mother, or anybody eise!

  I went to my room to begin my sentence, feeling a martyr for Truth.

  Late that same night, my father knocked softly on my door and entered. I was at my desk reading and, obedient to his decree, didn't speak a word of greeting. He seated himself across from me on the bed and I knew from bis expression something had changed. He now appeared calm, even slightly guilt-ridden. He began by announcing that the punishment he had meted out was 'perhaps a bit too harsh' and thus no longer applied, and subsequently asked my pardon for his manner – a piece of behaviour unprecedented and totally uncharacteristic of the man. He realized that his outburst had been unjust. It was unreasonable, he said – and of course I agreed with him – to expect me to understand something he had never taken the trouble to explain. He had never spoken openly to me about the matter of Uncle Petros and now the time had come for his 'grievous error' to be corrected. He wanted to teil me about his eldest brother. I, of course, was all ears.

  This is what he told me:

  Uncle Petros had, from early childhood, shown signs of exceptional ability in mathematics. In grade school he had impressed his teachers with his ease in arithmetic and in high school he had mastered abstractions in algebra, geometry and trigonometry with unbelievable facility. Words like 'prodigy' and even 'genius' were applied. Though a man of little formal education, their father, my grandfather, proved himself enlightened. Rather than divert Petros to more practical studies that would prepare him to work at his side in the family business, he had encouraged him to follow his heart. He had enrolled at a precocious age at the University of Berlin, from which he had graduated with honours at nineteen. He had earned his doctorate the next year and joined the faculty at the University of Munich as full professor at the amazing age of twenty-four – the youngest man ever to achieve this rank.

  I listened, goggle-eyed. 'Hardly the progress of "one of life's failures",’ I commented.

  'I haven't finished yet,’ warned my father.

  At this point he digressed from his narrative. Without any prompting from me he spoke of himself and Uncle Anargyros and their feelings towards Petros. The two younger brothers had followed his successes with pride. Never for a moment did they feel the least bit envious – after all they too were doing extremely well at school, though in nowhere near as spectacular a manner as their genius of a brother. Still, they had never feit very close to him. Since early childhood, Petros had been a loner. Even when he'd still lived at home, Father and Uncle Anargyros hardly ever spent time with him; while they played with their friends he was in his room solving geometry problems. When he went abroad to university, Grandfather had them write polite letters to Petros ('Dear brother, We are well… etc.'), to which he would reply, infrequently, with a laconic acknowledgement on a postcard. In 1925, when the whole family travelled to Germany to visit him, he turned up at their few encounters behaving like a total stranger, absent-minded, anxious, obviously impatient to get back to whatever it was he was doing. After that they never saw him again until 1940 when Greece went to war with Germany and he had to return.

  'Why?' I asked Father. 'To enlist?'

  'Of course not! Your uncle never had patriotic – or any other, for that matter – feelings. It's just that once war was declared he was considered an enemy alien and had to leave Germany.'

  'So why didn't he go elsewhere, to England or America, to some other great university? If he was such a great mathematician -'

  My father interrupted me with an appreciative grunt, accompanied by a loud slap on his thigh.

  "That's the point,' he snapped. "That's the whole point: he was no longer a great mathematician!'

  'What do you mean?' I asked. 'How can that be?'

  There was a long, pregnant pause, a sign that the critical point in the narrative, the exact locus where the action changes direction from uphill to down, had been reached. My father leaned towards me, frowning ominously, and his next words came in a deep mur-mur, almost a groan:

  'Your uncle, my son, committed the greatest of sins.'

  'But what did he do, Father, teil me! Did he steal or rob or kill?'

  'No, no, all these are simple misdemeanours compared to his crime! Mind you, it isn't I who deem it so but the Gospel, our Lord Himself: "Thou shalt not blaspheme against the Spirit!" Your Uncle Petros cast pearls before swine; he took something holy and sacred and great, and shamelessly defiled it!'

  The unexpected theological twist put me for a moment on guard: 'And what exactly was that?'

  'His gift, of course!' shouted my father. '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 mathemarics. Never! Nothing! Zero!'

  'But why?’ I asked.

  'Oh, because his Illustrious Excellence was engaged with "Goldbach's Conjecture".'

  ‘With what?’

  Father made a distasteful grimace. 'Oh, a riddle of some sort, something of no interest to anyone except a handful of idlers playing intellectual games.'

  ' A riddle? You mean like a crossword puzzle?'

  'No, a mathematical problem – but not just any problem: this "Goldbach's Conjecture" thing is considered to be one of the most difficult in the whole of mathematics. Can you imagine? The greatest minds on this planet had failed to solve it, but your smart aleck uncle decided at the age of twenty-one that he would be the one… Then, he proceeded to waste his life on it!'

  I was rather confused by the course of his reasoning. 'Wait a minute, Father,' I said. 'Is that his crime? Pursuing the solution of the most difficult problem in the history of mathematics? Are you serious? Why, this is magnificent; it is absolutely fantastic!'

  Father glared at me. 'Had he managed to solve it, it might be "magnificent" or "absolutely fantastic" or what have you – although it would still be totally useless, of course. But he didn't!’

  He now got impatient with me, once again his usual seif. 'Son, do you know the Secret of Life?' he asked with a scowl.

  'No,I don't.'

  Before divulging it to me he blew his nose with a trumpeting sound into his monogrammed silk handkerchief.

  'The Secret of Life is always to set yourself attainable goals. They may be easy or difficult, depending on the circum
stances and your character and abilities, but they should always be at-tai-na-ble! In fact, I think I'll hang your Uncle Petros' portrait in your room, with a caption: example to be avoided!'

  It's impossible as I write now, in middle age, to describe the turbulence caused in my adolescent heart by this first, however prejudiced and incomplete, account of Uncle Petros' story. My father had obviously intended it to serve as a cautionary tale and yet for me his words had exactly the opposite effect: instead of steering me away from his aberrant older brother, they drew me towards him as to a brilliantly shining star.

  I was awestruck by what I'd learned. Exactly what this famous 'Goldbach's Conjecture' was I didn't know, nor at that time did I care very much to learn. What fascinated me was that the kindly, withdrawn and seemingly unassuming uncle of mine was in fact a man who, by his own deliberate choice, had struggled for years on end at the outermost boundaries of human ambition. This man whom I'd known all my life, who was in fact my close blood relative, had spent his whole life striving to solve One of the Most Difficult Problems in the History of Mathematics! While his brothers were studying and getting married, raising children and running the family business, wearing out their lives along with the rest of nameless humanity in the daily routines of subsistence, procreation and killing time, he, Prometheus-like, had striven to cast light into the darkest and most inaccessible corner of knowledge.

  The fact that he had finally failed in his endeavour not only did not lower him in my eyes but, on the contrary, raised him to the highest peak of excellence. Was this not, after all, the very definition of the plight of the Ideal Romantic Hero, to Fight the Great Battle Although You Know It To Be Desperate? In fact, was my uncle any different from Leonidas and his Spartan troops guarding Thermopylae? The last verses of Cavafy's poem I had learned at school seemed ideally applicable to him:

  … But greatest honour befits them that foresee,

  As many do indeed foresee,

  That Ephialtes the Traitor will finally appear

  And thus the Persians will at last

  Go through the narrow straits.

  Even before I'd heard Uncle Petros' story, his brothers' derogatory remarks, beyond exciting curiosity, had inspired my sympathy. (This, by the way, had been in contrast to my two cousins' reactions, who bought their fathers' contempt wholesale.) Now that I knew the truth – even this highly prejudiced Version of it -I immediately elevated him to role model.

  The first consequence of this was a change in my attitude towards mathematical subjects at school, which I had found till then rather boring, with a resultant dramatic improvement in my performance. When Father saw on the next report card that my grades in Algebra, Geometry and Trigonometry had shot up to honours level, he raised a perplexed eyebrow and gave me a queer look. It's possible that he even became slightly suspicious, but of course he couldn't make an issue of it. He could hardly criticize me for excelling!

  On the date when the Hellenic Mathematical Society was due to commemorate Leonard Euler's two hundred and fiftieth birthday, I arrived ahead of time at the auditorium, full of expectation. Although high-school maths was of no help in fathoming its precise meaning, the announced lecture's title, ‘Formal Logic and the Foundations of Mathematics', had intrigued me since first reading the invitation. I knew of 'formal receptions' and 'simple logic' but how did the two concepts combine? I'd learned that buildings have foundations – but mathematics?

  I waited in vain, however, as the audience and the Speakers took their places, to see among them the lean, ascetic figure of my uncle. As I should have guessed, he didn't come. I already knew he never accepted invitations; now I'd learned he didn't make exceptions even for mathematics.

  The first speaker, the president of the Society, mentioned his name, and with particular respect:

  'Professor Petros Papachristos, the world-renowned Greek mathematician, will unfortunately be unable to deliver his short address, because of a slight indisposition.'

  I smiled smugly, proud that only I among the audience knew that my uncle's 'slight indisposition' was a diplomatic one, an excuse to protect his peace.

  Despite Uncle Petros' absence, I stayed until the end of the event. I listened fascinated to a brief resume of the honouree's life (Leonard Euler, apparently, had made epoch-making discoveries in practically every branch of mathematics). Then, as the main speaker took the podium and started elaborating on the 'Foundations of Mathematical Theories by Formal Logic', I feil into a charmed state. Despite the fact that I didn't completely understand more than the first few words of what he said, my spirit wallowed in the unfamiliar bliss of unknown definitions and concepts, all symbols of a world which, although mysterious, impressed me from the start as almost sacred in its unfathomable wisdom. Magical, previously unheard-of names rolled on and on, enthralling me with their sublime music: the Continuum Problem, Aleph, Tarski, Gottlob Frege, Inductive Reasoning, Hilbert's Programme, Proof Theory, Riemannian Geometry, Verifiability and Non-Verifiability, Consistency Proofs, Completeness Proofs, Sets of Sets, Universal Turing Machines, Von Neumann Automata, Russell's Paradox, Boolean Algebras… At some point, in the midst of these intoxicating verbal waves washing over me, I thought for a moment I discerned the momentous words 'Goldbach's Conjecture'; but before I could focus my attention the subject had evolved along new magical pathways: Peano's Axioms for Arithmetic, the Prime Number Theorem, Closed and Open Systems, Axioms, Euclid, Euler, Cantor, Zeno, Gödel…

  Paradoxically, the lecture on the 'Foundations of Mathematical Theories by Formal Logic' worked its insidious magic on my adolescent soul precisely because it disclosed none of the secrets that it introduced – I don't know whether it would have had the same effect had its mysteries been explained in detail. At last I understood the meaning of the sign at the entrance of Plato's Academy: oudeis ageometretos eiseto – 'Let no one ignorant of geometry enter'. The moral of my evening emerged with crystal clarity: mathematics was something infinitely more interesting than solving second-degree equations or calculating the volumes of solids, the menial tasks at which we laboured at school. Its practitioners dwelt in a veritable conceptual heaven, a majestic poetic realm totally inaccessible to the un-mathematical hoi polloi.

  The evening at the Hellenic Mathematical Society was the turning point. It was then and there that I first resolved to become a mathematician.

  At the end of that school year I was awarded the school prize for highest achievement in Mathematics. My father boasted about it to Uncle Anargyros – as if he could have done otherwise!

  By now, I had completed my second-to-last year of high school and it had already been decided that I would be attending university in the United States. As the American System doesn't require students to declare their major field of interest upon registration, I could defer revealing to my father the horrible (as he would no doubt consider it) truth for a few more years. (Luckily, my two cousins had already stated a preference that assured the family business of a new generation of managers.) In fact, I misled him for a while with vague talk of plans to study economics, while I was hatching my plan: once I was safely enrolled in university, with the whole Atlantic Ocean between me and his authority, I could steer my course toward my destiny.

  That year, on the feast day of Saints Peter and Paul, I couldn't hold back any longer. At some point I drew Uncle Petros aside and, impulsively, I blurted my intention.

  'Uncle, I'm thinking of becoming a mathematician.'

  My enthusiasm, however, found no immediate response. My uncle remained silent and impassive, his gaze suddenly focused on my face with intense seriousness – with a shiver I realized that this was what he must have looked like as he was struggling to penetrate the mysteries of Goldbach's Conjecture.

  'What do you know of mathematics, young man?' he asked after a short pause.

  I didn't like his tone but I went on as planned: 'I was first in my class, Uncle Petros; I received the school prize!'

  He seemed to consider this info
rmation awhile and then shrugged. 'It's an important decision,’ he said, 'not to be taken without serious deliberation. Why don't you come here one afternoon and we'll talk about it.' Then he added, unnecessarily. 'It's better if you don't tell your father.'

  I went a few days later, as soon as I could arrange a good cover story.

  Uncle Petros led me to the kitchen and offered me a cold drink made from the sour cherries from his tree. Then he took a seat across from me, looking solemn and professorial.

  'So tell me,' he asked, 'what is mathematics in your opinion?' The emphasis on the last word seemed to carry the implication that whatever answer I gave was bound to be wrong.

  I spurted out commonplaces about 'the most supreme of sciences' and the wonderful applications in electronics, medicine and space exploration.

  Uncle Petros frowned. 'If you're interested in applications why don't you become an engineer? Or a physicist. They too are involved with some sort of mathematics.'

  Another emphasis with meaning: obviously he didn't hold this 'sort' in very high esteem. Before I embarrassed myself further, I decided that I was not equipped to spar with him as an equal, and confessed it.

  'Uncle, I can't put the "why" into words. All I know is that I want to be a mathematician – I thought you'd understand.'

  He considered this for a while and then asked: 'Do you know chess?'

  'Sort of, but please don't ask me to play; I can tell you right now I'm going to lose!'

  He smiled. 'I wasn't suggesting a game; I just want to give you an example that you'll understand. Look, real mathematics has nothing to do with applications, nor with the calculating procedures that you learn at school. It studies abstract intellectual constructs which, at least while the mathematician is occupied with them, do not in any way touch on the physical, sensible world.'

  "That's all right with me,’ I said.

  'Mathematicians,’ he continued, 'find the same enjoyment in their studies that chess players find in chess. In fact, the psychological make-up of the true mathematician is closer to that of the poet or the musical composer, in other words of someone concerned with the creation of Beauty and the search for Harmony and Perfection. He is the polar opposite of the practical man, the engineer, the politician or the he paused for a moment seeking something even more abhorred in his scale of values -'… indeed, the businessman.'