Apostolos Doxiadis - Uncle Petros and Goldbach

The dream's meaning was clear; its bleak symbolism did not need a soothsayer or a psychoanalyst to decipher it: alas, the Incompleteness Theorem applied to his problem. Goldbach's Conjecture was a priori unprovable.

Upon his return to Munich after the year in Cambridge, Petros resumed the external routine he had established before his departure: teaching, chess, and also a minimum of social life; since he now had nothing better to do, he began to accept the occasional invitation. It was the first time since his earliest childhood that preoccupation with mathematical truths didn't occupy the central role in his life. And although he did continue his research awhile, the old fervour was gone. From then on he spent no more than a few hours a day at it, working half-absently at his geometric method. He'd still wake up before dawn, go to his study and pace slowly up and down, picking his way among the parallelograms of beans laid out on the floor (he had pushed all the furniture against the walls to make room). He picked up a few here, added a few there, muttering absently to himself. This went on for a while and then, sooner or later, he drifted towards the armchair, sat, sighed and turned his attention to the chessboard.

This routine went on for another two or three years, the time spent daily at this erratic form of 'research' continuously decreasing to almost nil. Then, near the end of 1936, Petros received a telegram from Alan Turing, who was now at Princeton University:

I HAVE PROVED THE IMPOSSIBILITY OF A PRIORI DECIDABILITY STOP.

Exactly. stop. This meant, in effect, that it was impossible to know in advance whether a particular mathematical statement is provable: if it is eventually proven, then it obviously is – what Turing had managed to show was that as long as it remains unproven, there is absolutely no way of ascertaining whether its proof is impossible or simply very difficult.

The immediate corollary of this, which concerned Petros, was that if he chose to pursue the proof of Goldbach's Conjecture, he would be doing so at his own risk. If he continued with his research, it would have to be out of sheer optimism and positive fighting spirit. Of these two qualities, however – time, exhaustion, ill luck, Kurt Gödel and now Alan Turing assisting – he had run out.

STOP.

A few days after Turing's telegram (the date he gives in his diary is 7 December 1936) Petros informed his housekeeper that the beans would no longer be required. She swept them all up, gave them a good wash and turned them into a hearty cassoulet for the Herr Professor 's dinner.

Uncle Petros remained silent for a while, looking dejectedly at his hands. Beyond the small circle of pale yellow light around us, cast by the single light-bulb, there was now total darkness.

'So that's when you gave up?' I asked softly.

He nodded. 'Yes.'

'And you never again worked on Goldbach's Conjecture?'

'Never.'

'What about Isolde?'

My question seemed to startle him. 'Isolde? What about her?'

'I thought that it was to win her love you decided to prove the Conjecture – no?'

Uncle Petros smiled sadly.

'Isolde gave me "the beautiful journey", as our poet says. Without her I might "never have set out". [13]Yet, she was no more than the original stimulus. A few years after I had begun my work on the Conjecture her memory faded, she became no more than a phantasm, a bittersweet recollection… My ambitions became of a higher, more exalted variety.'

He sighed. 'Poor Isolde! She was killed during the Allied bombardment of Dresden, along with her two daughters. Her husband, the "dashing young lieutenant" for whom she'd abandoned me, had died earlier on the Eastern Front.'

The last part of my uncle's story had no particular mathematical interest:

In the years that followed history, not mathematics, became the determining force in his life. World events broke down the protective barrier which till then had kept him safe within the ivory tower of his research. In 1938, the Gestapo arrested his housekeeper and sent her to what was still in those days referred to as a 'work camp'. He didn't hire anybody to take her place, naively believing that she'd return soon, her arrest due to some 'misunderstanding'. (After the war's end he learned from a surviving relative that she'd died in 1943 in Dachau, just a short distance from Munich.) He started to eat out, returning home only to sleep. When he was not at the university he would hang out at the chess club, playing, watching or analysing games.

In 1939, the Director of the School of Mathematics, by then a prominent member of the Nazi party, indicated that Petros should immediately apply for German citizenship and formally become a subject of the Third Reich. He refused, not for any reasons of principle (Petros managed to go through life unhampered by any ideological burden) but because the last thing he wanted was to be involved once again with differential equations. Apparently, it was the Ministry of Defence that had suggested he apply for citizenship, with precisely this aim in mind. After his refusal he became in essence a persona non grata. In September 1940, a little before Italy's declaration of war on Greece would have made him an enemy alien subject to internment, he was fired from his post. After a friendly warning, he left Germany.

Having, by the strict criterion of published work, been mathematically inactive for more than twenty years, Petros was now academically unemployable and so he had to return to his homeland. During the first years of the country's occupation by the Axis powers he lived in the family house in central Athens, on Queen Sophia Avenue, with his recently widowed father and his newly-wed brother Anargyros (my parents had moved to their own house), devoting practically all his time to chess. Very soon, however, my newborn cousins with their cries and toddler activities became a much greater annoyance to him than the occupying Fascists and Nazis and he moved to the small, rarely used family cottage in Ekali.

After the Liberation, my grandfather managed to secure for Petros the offer of the Chair of Analysis at Athens University, through string-pulling and manoeuvring. He turned it down, however, using the spurious excuse that 'it would interfere with his research'. (In this instance, my friend Sammy's theory of Goldbach's Conjecture as my uncle's pretext for idleness proved completely correct.) Two years later, paterfamilias Papachristos died, leaving to his three sons equal shares of his business and the principal executive positions exclusively to my father and Anargyros. 'My eldest, Petros,’ his will expressly decreed, 'shall retain the privilege of pursuing his important mathematical research,’ i.e. the privilege of being supported by his brothers without doing any work.

'And after that?' I asked, still cherishing the hope that a surprise might be in store, an unexpected reversal on the last page.

'After that nothing,’ my uncle concluded. ‘For almost twenty years my life has been as you know it: chess and gardening, gardening and chess. Oh, and once a month a visit to the philanthropic Institution founded by your grandfather, to help them with the book-keeping. It's something towards the salvation of my soul, just in case there exists a hereafter.'

It was midnight by this time and I was exhausted. Still, I thought I should end the evening on a positive note and, after a big yawn and a stretch, I said: 'You are admirable, Uncle… if not for anything eise, for the courage and magnanimity with which you accepted failure.'

This comment, however, got a reaction of utter surprise. 'What are you talking about?' my uncle said. 'I didn't fail!'

Now the surprise was mine. 'You didn't?'

'Oh no, no, no, dear boy!' He shook his head from side to side. 'I see you didn't understand anything. I didn't fail – I was just unlucky!'