Uncle Petros and Goldbach

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 ru

(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 Vie

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 a

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 a

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 to 'another place', never specified by her. His house was a true hermitage; with the exception of the a

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 di

“I saw your brother Petros at the club the other day. He demolished me with a Karo-Ca

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 Ca

'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 a

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 reco