Uncle Petros and Goldbach

In 1971, I found unexpected assistance in my task.

The military dictatorship that then ruled the country, in a campaign to appear as a benevolent patron of culture and science, proposed to award a 'Gold Medal of Excellence' to a number of rather obscure Greek scholars who had distinguished themselves abroad. The list was short, since most of the prospective honourees, forewarned of the impending distinction, had hastened to exclude themselves; but topmost in it was 'the great mathematician of international fame, Professor Petros Papachristos'.

My father and Uncle Anargyros, in a totally uncharacteristic frenzy of democratic passion, strove to convince him to turn down this dubious honour. Talk of 'that old fool becoming the junta's lackey', 'giving the colonels an alibi', etc., filled our business offices and family homes. At moments of greater honesty the two younger brothers (both old men, by now) confessed to a less noble motive: the traditional reluctance of the businessman to be too closely identified with one political faction for fear of what will happen when another comes to power. Yet I, an experienced Papachristos family observer, could also discern a strong need for them to be proved right in their negative evaluation of his life, also tinged with an element of envy. Father's and Uncle Anargyros' world-view had always been founded on the simple premise that Uncle Petros was bad and they good, a black-and-white cosmology that distinguished between the grasshoppers and the ants, the dilettantes and 'responsible men'. It didn't sit at all well with them that the country's official government, Junta or no Junta, should honour 'one of life's failures', when the only rewards they ever got for their labours (labours, mind you, that also put food on his table) were financial.

I, however, took a different position. Beyond my belief that Uncle Petros deserved the honour (he did, after all, rate some recognition of his life's work, even if it came from the colonels) I had an ulterior motive. So I went to Ekali and, exercising to the full my influence as 'most favoured of nephews', convinced him to overcome his brothers' hypocritical appeals to democratic duty as well as his own misgivings and accept his Gold Medal of Excellence.

The award ceremony – that 'ultimate familial disgrace', according to Uncle Anargyros the late-blooming radical – was held in the main auditorium of the University of Athens. The Rector of the School of Physics and Mathematics, in his ceremonial robes, gave a short lecture on Uncle Petros' contribution to science. Predictably enough he referred almost exclusively to the Papachristos Method for the Solution of Differential Equations, which he lauded with elaborate rhetorical effusions. Still, I was agreeably surprised to hear him also make passing reference to Hardy and Littlewood and their 'appealing to our great fellow-countryman for assistance with their most difficult problems'. While all this was being propounded I stole side-glances at Uncle Petros and saw him blushing red with shame again and again, all the time retreating further into the throne-like, gilded armchair where they had him installed. The Prime Minister (the arch-dictator) then bestowed the Gold Medal of Excellence and afterwards there was a short reception, during which my poor uncle was required to pose for photographs with all the top brass of the Junta. (I have to confess that at this stage of the ceremony I feit a slight dose of guilt about the defining role I had played in his acceptance of the honour.)

When it was all over, he asked me to go back home for some chess, 'for purposes of recovery'. We started a game. I was a good enough player by that time to offer him decent resistance but not so good as to hold his interest after the ordeal he'd been through.

'What did you think of that circus?' he asked me, finally looking up from the board.

'The award ceremony? Oh, it was a bit boring, but I'm still glad you went through with it. Tomorrow it will be in all the newspapers.'

'Yes,’ he said, 'how the Papachristos Method for the Solution of Differential Equations is almost on a par with Einstein's Theory of Relativity and Heisenberg's Uncertainty Principle, one of the crowning achievements of twentieth-century science… How that fool of a Rector carried on! Did you notice, by the way,’ he added with a sour smile, 'the pregnant silence following the "ooohs" and "aaahs" and "ts-ts-ts's" of admiration at my extreme youth when I made the "great discovery"? You could almost hear everybody wondering: But how did the honouree spend the next fifty-five years of his life?'

Any sign of self-pity on his part bothered me inordinately.

'You know, Uncle,’ I provoked him, 'it's not anybody's fault but your own that people don't know of your work on Goldbach's Conjecture. How could they – you've never told! Had you ever written up a report of your research, things would be different.

The story of your quest itself would make a worth-while publication.'

'Yes,’ he sneered, 'a full footnote in Great Mathematical Failures of Our Century.'

'Well,' I mused, 'science advances by failures as well as successes. And anyway, it was a good thing your work in differential equations was acknowledged. I was proud to hear our family name associated with something other than money.'

Unexpectedly, a bright smile on his face, Uncle Petros asked me: 'Do you know it?'

'Do I know what?'

'The Papachristos Method for the Solution of Differential Equations?'

I'd been taken completely unawares and answered without thinking: 'No, I don't.'

His smile went away: 'Well, I expect they don't teach it anymore…'

I feit an upsurge of excitement – this was the chance I was waiting for. Although I had, in fact, ascertained while at university that the Papachristos Method was no longer taught (the advent of electronic calculation had rendered it obsolete), I lied to him, and with great vehemence: 'Of course they teach it, Uncle! It's just that I never took an elective in differential equations.'

'Get paper and pencil then, and I’ll tell you about it!'

I held back a triumphant cry. It was precisely what I'd hoped for when I had convinced him to accept the medaclass="underline" that the honour might reawaken his mathematical vanity and rekindle his interest in his art, enough of it anyway to lure him into a discussion of Goldbach's Conjecture and beyond… to his real reason for abandoning it. Explaining to me the Papachristos Method was an excellent introduction.

I rushed to fetch paper and pencil before he changed his mind.

'You'll have to be a little patient,' he began. 'A lot of water has gone under the bridge since then. Let's see now,’ he murmured and began to scribble. 'Let us assume we have a partial differential equation in the Clairaut form… there! We now take…'

I followed his scribbles and explanations for almost an hour. Although I couldn't completely follow the argument, I showed exaggerated appreciation at every step.

'It's absolutely brilliant, Uncle!' I cried when he'd finished.

'Nonsense.' He brushed my praise aside, but I could see this modesty was not totally sincere. 'Sheer calculation of the grocery-bill variety, not real mathematics!'

The moment I was waiting for had arrived. 'Then talk to me about real mathematics, Uncle Petros. Talk to me about your work on Goldbach's Conjecture!'

He shot me a sideways glance, cunning, inquisitive and at the same time tentative. I held my breath.

'And what, if I may ask, is the purpose of your interest, Mr Almost-Mathematician?'

I had planned my answer to this beforehand, so as to put him in an emotional impasse.