By making his discovery public, he would also be opening the way into the problem to other mathematicians who would build on it by discovering new results and expand the limits of the field in a way a lone researcher, however brilliant, could scarcely hope. The results they would achieve would, in turn, aid him in his pursuit of the proof to the Conjecture. In other words, by publishing the ‘Papachristos Partition Theorem' (modesty of course obliged him to wait for his colleagues formally to give it this title) he would be acquiring a legion of assistants in his work. Unfortunately there was another side to this coin: one of the new unpaid (also unasked for) assistants might conceivably stumble upon a better way to apply his theorem and manage, God forbid, to prove Goldbach's Conjecture before him.
He didn't have to deliberate long. The danger far outweighed the benefit. He wouldn't publish. The 'Papachristos Partitions Theorem' would remain for the time being his private, well-guarded secret.
Reminiscing for my benefit, Uncle Petros marked this decision as a turning point in his life. From then onwards, he said, difficulties began to pile upon difficulties.
By withholding publication of his first truly important contribution to mathematics, he had placed himself under double time-pressure. In addition to the constant, gnawing anxiety of days and weeks and months and years passing without his having achieved the desired final goal, he now also had to worry that someone might arrive at his discovery independently and steal his glory.
The official successes he had achieved until then (a discovery named after him and a university chair) were no mean feats. But time counts differently for mathematicians. He was now at the absolute peak of his powers, in a creative prime that couldn't last long.
This was the time to make his great discovery – if he had it in him to make it at all.
Living as he did a life of near-total isolation, there was no one to ease his pressures.
The loneliness of the researcher doing original mathematics is unlike any other. In a very real sense of the word, he lives in a universe that is totally inaccessible, both to the greater public and to his immediate environment. Even those closest to him cannot partake ot his joys and his sorrows in any significant way, since it is all but impossible for them to understand their content.
The only community to which the creative mathematician can truly belong is that of his peers; but from that Petros had wilfully cut himself off. During his first years at Munich he had submitted occasionally to the traditional academic hospitality towards newcomers. When he accepted an invitation, however, it was sheer agony to act with a semblance of normality, behave agreeably and make small talk. He had constantly to curb his tendency to lose himself in number-theoretical thoughts, and fight his frequent impulses to make a mad dash for home and his desk, in the grip of a hunch that required immediate attention. Fortunately, either as a result of his increasingly frequent refusals or his obvious discomfort and awkwardness on those occasions when he did attend social functions, invitations gradually grew fewer and fewer and in the end, to his great relief, ceased altogether.
I don't need to add that he never married. The rationale he gave me for this, by which getting married to another woman would mean being unfaithful to his great love, 'dearest Isolde', was of course no more than an excuse. In truth, he was very much aware that his lifestyle did not allow for the presence of another person. His preoccupation with his research was ceaseless. Goldbach's Conjecture demanded him whole: his body, his soul and all of his time.
In the summer of 1925, Petros proved a second important result, which in combination with the 'Partitions Theorem' opened up a new perspective on many of the classical problems of prime numbers. According to his own, exceedingly fair and well-informed opin-ion, the work he had done constituted a veritable breakthrough. The temptation to publish was now overwhelming. It tortured him for weeks – once again, though, he managed to resist it. Again, he decided in favour of keeping his secret to himself, lest it open the way to unwelcome intruders. No intermediate result, no matter how important, could sidetrack him from his original aim. He would prove Goldbach's Conjecture or be damned!
In November of that year he turned thirty, an emblematic age for the research mathematician, practically the first step into middle age.
The sword of Damocles, whose presence Petros had merely sensed all these years hanging in the darkness somewhere high above him (it was labelled: 'The Waning of his Creative Powers') now became almost visible. More and more, as he sat hunched over his papers, he could feel its hovering menace. The invisible hourglass measuring out his creative prime became a constant presence at the back of his mind, driving him into bouts of dread and anxiety. During his every waking moment, he was pestered by the worry that he might already be moving away from the apex of his intellectual prowess. Questions buzzed in his mind like mosquitoes: would he be having any more breakthroughs of the same order as the two first important results? Had the inevitable decline, perhaps unbeknown to him, already started? Every little instance of forgetfulness, every tiny slip in a calculation, every short lapse in concentration, brought the ominous refrain: Have I passed my prime?
A brief visit at about this time from his family (already described to me by my father), whom he hadn't seen in years, was considered by him a gross, violent intrusion. The little time he spent with his parents and younger brothers he felt was stolen from his work, and every moment away from his desk for their benefit he perceived as a small dose of mathematical suicide. By the end of their stay he was inordinately frustrated.
Not wasting time had become a veritable obsession, to the point where he obliterated from his life any activity that was not directly related to Goldbach's Conjecture – all except the two he couldn't reduce beyond a certain minimum, teaching and sleep. Yet he now got less sleep than he needed. Constant anxiety had brought insomnia with it, and this was aggravated by his excessive consumption of coffee, the fuel on which mathematicians run. With time, the constant preoccupation with the Conjecture made it impossible for him to relax. Falling or staying asleep became increasingly difficult and often he had to resort to sleeping pills. Occasional use gradually became steady and doses began to increase alarmingly, to the point of dependency, and this without the accompanying beneficial effect.
At about this time, a totally unexpected boost to his spirits came in the unlikely form of a dream. Despite his total disbelief in the supematural, Petros viewed it as prophetic, a definite omen straight from Mathematical Heaven.
It is not unusual for scientists totally immersed in a difficult problem to carry on their preoccupations into sleep; and although Petros was never honoured by nocturnal visitations from Ramanujan's Namakiri or any other revelatory deity (a fact that should not surprise us, considering his entrenched agnosticism), after the first year or so of his immersion in the Conjecture he began to have the occasional mathematical dream. In fact, his early visions of amorous bliss in the arms of 'dearest Isolde' became less frequent over time, giving their place to dreams of the Even Numbers, which appeared personified as couples of identical twins. They were involved in intricate, unearthly dumbshows, a chorus to the Primes, who were peculiar hermaphrodite, semi-human beings. Unlike the speechless Even Numbers, the Primes often chattered among themselves, usually in an unintelligible language, at the same time executing bizarre dance-steps. (By his admission, this dream choreography was most likely inspired by a production of Stravinsky's Rite of Spring that Petros had attended during his early years in Munich, when he still had time for such vanities.) On rare occasions the singular creatures spoke and then only in classical Greek – perhaps as a tribute to Euclid, who had awarded them infinitude. Even when their utterances made some linguistic sense, however, the content was mathematically either trivial or non-sensical. Petros specifically recalled one such: hapantes protoi perittoi, which means 'All prime numbers are odd', an obviously false Statement. (By a different reading of the word perittoi, however, it could also mean 'All prime numbers are useless', an interpretation which, interestingly, completely escaped my uncle's attention.)