The monograph was finished a little after Christmas and it came to about two hundred pages. It was titied, with the usual slightly hypocritical modesty of many mathematicians when publishing important results, 'Some Observations on the Problem of Partitions'. Petros had it typed at the School and mailed a copy to Hardy and Littlewood, purportedly asking them to go over it lest he had slipped into an undetected pitfall, lest some less-than-obvious deductive error had escaped him. In fact, he knew well that there were no pitfalls and no errors: he just relished the thought of the two paragons of Number Theory's surprise and amazement. In fact, he was already basking in their admiration for his achievement.
After he sent off the typescript, Petros decided he owed himself a small vacation before he turned once again full-time to his work on the Conjecture. He de-voted the next few days exclusively to chess.
He joined the best chess club in town, where he discovered to his delight that he could beat all but the very top players and give a hard time to the select few he could not easily overpower. He discovered a small bookshop owned by an enthusiast, where he bought weighty volumes of opening theory and collections of games. He installed the chessboard he'd bought at Innsbruck on a small table in front of his fireplace, next to a comfortable deep armchair upholstered in soft velvet. There he kept his nightly rendezvous with his new white and black friends.
This lasted for almost two weeks. 'Two very happy weeks,’ he told me, the happiness being made greater by the anticipation of Hardy's and Littlewood's doubtless enthusiastic response to the monograph.
Yet the response, when it arrived, was anything but enthusiastic and Petros' happiness was cut short. The reaction wasn't at all what he had anticipated. In a rather short note, Hardy informed him that his first important result, the one he'd privately christened the 'Papachristos Partitions Theorem', had been discovered two years before by a young Austrian mathematician. In fact, Hardy expressed his amazement that Petros had not been aware of this, since its publication had caused a sensation in the circles of number theorists and brought great acclaim to its young author. Surely he was following the developments in the field, or wasn't he? As for his second theorem: a rather more general version of it had been proposed without proof by Ramanujan in a letter to Hardy from India, a few days before his death in 1920, one of his last great intuitions. In the years since then, the Hardy-Littlewood partnership had managed to fill in the gaps and their proof had been published in the most recent issue of the Proceedings of the Royal Society, of which he included a copy.
Hardy concluded his letter on a personal note, expressing his sympathy to Petros for this turn of events. With it there was the suggestion, in the understated fashion of his race and class, that it might in the future be more profitable for him to stay in closer contact with his scientific colleagues. Had Petros been living the normal life of a research mathematician, Hardy pointed out, coming to the international congresses and colloquia, corresponding with his colleagues, finding out from them the progress of their research and letting them know of his, he wouldn't have come in second in both of these otherwise extremely important discoveries. If he continued in his self-imposed isolation, another such 'unfortunate occurrence' was bound to arise.
At this point in his narrative my uncle stopped. He had been talking for several hours. It was getting dark and the birdsong in the orchard had been gradually tapering off, a solitary cricket now rhythmically piercing the silence. Uncle Petros got up and moved with tired steps to turn on a lamp, a naked bulb that cast a weak light where we were seated. As he walked back towards me, moving slowly in and out of pale yellow light and violet darkness, he looked almost like a ghost.
'So that's the explanation,' I murmured, as he sat down.
'What explanation?' he asked absently.
I told him of Sammy Epstein and his failure to find any mention of the name Petros Papachristos in the bibliographical index for Number Theory, with the exception of the early joint publications with Hardy and Littlewood on the Riemann Zeta Function. I repeated the 'burnout theory' suggested to my friend by the 'distinguished professor' at our university: that his supposed occupation with Goldbach's Conjecture had been a fabrication to disguise his inactivity.
Uncle Petros laughed bitterly.
'Oh no! It was true enough, most favoured of nephews! You can tell your friend and his "distinguished professor" that I did indeed work on trying to prove Goldbach's Conjecture – and how and for how longl Yes, and I did get intermediate results – wonderful, important results – but I didn't publish them when I should have done and others got in there ahead of me. Unfortunately, in mathematics there's no silver medal. The first to announce and publish gets all the glory. There's nothing left for anyone eise.' He paused.
'As the saying goes, a bird in the hand is worth two in the bush and I, while pursuing the two, lost the one…'
Somehow I didn't think the resigned serenity with which he stated this conclusion was sincere.
'But, Uncle Petros,’ I asked him, 'weren't you horribly upset when you heard from Hardy?'
'Naturally I was – and "horribly" is exactly the word. I was desperate; I was overcome with anger and frustration and grief; I even briefly contemplated suicide. That was back then, however, another time, another seif. Now, assessing my life in retrospect, I don't regret anything I did, or did not do.'
'You don't? You mean you don't regret the opportunity you missed to become famous, to be acknowledged as a great mathematician?'
He lifted a warning finger. 'A very good mathematician perhaps, but not a great one! I had discovered two good theorems, that's all.'
"That's no mean achievement, surely!'
Uncle Petros shook his head. 'Success in life is to be measured by the goals you've set yourself. There are tens of thousands of new theorems published every year the world over, but no more than a handful per century that make history!'
'Still, Uncle, you yourself say your theorems were important.'
'Look at the young man,' he countered, 'the Austrian who published my – as I still think of it – Partitions Theorem before me: was he raised with this result to the pedestal of a Hubert, a Poincare? Of course not! Perhaps he managed to secure a small niche for his portrait, somewhere in a back room of the Edifice of Mathematics… but if he did, so what? Or, for that matter, take Hardy and Littlewood, top-class mathematicians both of them. They possibly made the Hall of Fame – a very large Hall of Farne, mind you – but even they did not get their statues erected at the grand entrance alongside Euclid, Archimedes, Newton, Euler, Gauss… That had been my only ambition and nothing short of the proof of Goldbach's Conjecture, which also meant cracking the deeper mystery of the primes, could possibly have lead me there…’ There was now a gleam in his eyes, a deep, focused intensity as he concluded: ‘I, Petros Papachristos, never having published anything of value, will go down in mathematical history – or rather will not go down in it – as having achieved nothing. This suits me fine, you know. I have no regrets. Mediocrity would never have satisfied me. To an ersatz, footnote kind of immortality, I prefer my flowers, my orchard, my chessboard, the conversation I'm having with you today. Total obscurity!'