Ramanujan's answer came as an unpleasant surprise. 'I have a hunch, you know, that the Conjecture may not apply for some very very big numbers.'
Petros was thunderstruck. Could it possibly be? Coming from him, this comment couldn't be taken lightly. At the first opportunity, after a lecture, he approached Hardy and repeated it to him, trying at the same time to appear rather blase about the matter.
Hardy smiled a cunning little smile. 'Good old Ramanujan has been known to have some wonderful "hunches",' he said, 'and his intuitive powers are phenomenal. Still, unlike His Holiness the Pope, he lays no claim to infallibility.'
Then Hardy eyed Petros intently, a gleam of irony in his eyes. 'But tell me, my dear fellow, why this sudden interest in Goldbach's Conjecture?'
Petros mumbled a banality about his 'general interest in the problem' and then asked, as innocently as possible: 'Is there anyone working on it?'
'You mean actually trying to prove it?' said Hardy. 'Why no – to attempt to do so directly would be sheer folly!'
The warning did not scare him off; on the contrary it pointed out the course he should follow. The meaning of Hardy's words was clear: the straightforward, so-called 'elementary' approach to the problem was doomed to failure. The right way lay in the oblique 'analytic' method that, following the recent great success of the French mathematicians Hadamard and de la Vallee-Poussin with it, had become tres a la mode in Number Theory. Soon, he was totally immersed in its study.
There was a time, in Cambridge, before he made the final decision about his life's work, when Petros seriously considered devoting his energies to a different problem altogether. This came about as a result of his unexpected entry into the Hardy-Littlewood-Ramanujan inner circle.
During those wartime years, J. E. Littlewood had not been spending much time around the university. He would show up every now and then for a rare lecture or a meeting and then disappear once again to God knows where, an aura of mystery surrounding his activities. Petros had yet to meet him and so was greatly surprised when, one day in early 1917, Littlewood sought him out at the boarding-house.
'Are you Petros Papachristos from Berlin?' he asked him, after a handshake and a cautious smile. 'Constantin Caratheodory's Student?'
'I am the one, yes,’ answered Petros perplexed.
Littlewood appeared slightly ill at ease as he went on to explain: he was at that time in charge of a team of scientists doing ballistics research for the Royal Artillery as part of the war effort. Military intelligence had recently alerted them to the fact that the enemy's high accuracy of fire in the Western Front was thought to be the result of an innovative new technique of calculation, called the 'Papachristos Method'.
‘I’m sure you wouldn't have any objection to sharing your discovery with His Majesty's Government, old chap,' Littlewood concluded. 'After all, Greece is on our side.'
Petros was at first dismayed, fearing he would be obliged to waste valuable time with problems that held no more interest for him. That didn't prove necessary, though. The text of his dissertation, which he luckily had with him, contained more than enough mathematics for the needs of the Royal Artillery. Littlewood was doubly pleased since the Papachristos Method, apart from its immediate usefulness to the war effort, significantly lightened his own load, giving him more time to devote to his main mathematical interests.
So: rather than side-tracking him, Petros' earlier success with differential equations provided his entry into one of the most renowned partnerships in the history of mathematics. Littlewood was delighted to learn that the heart of his gifted Greek colleague belonged, as did his, to Number Theory, and soon he invited him to join him on a visit to Hardy's rooms. The three of them talked mathematics for hours on end. During this, and at all their subsequent meetings, both Littlewood and Petros avoided any mention of what had originally brought them together; Hardy was a fanatical pacifist and strongly opposed to the use of scientific discoveries in facilitating warfare.
After the Armistice, when Littlewood returned to Cambridge full-time, he asked Petros to collaborate with him and Hardy on a paper they had originally begun with Ramanujan. (The poor fellow was by now seriously ill and spending most of his time in a sanatorium.) At that time, the two great number theorists had turned their efforts to the Riemann Hypothesis, the epicentre of most of the unproven central results of the analytic approach. A demonstration of Bernhard Riemann's insight on the zeros of his 'zeta function' would create a positive domino effect, resulting in the proof of countless fundamental theorems of Number Theory. Petras accepted their proposal (which ambitious young mathematician wouldn't?) and the three of them jointly published, in 1918 and 1919, two papers – the two that my friend Sammy Epstein had found under his name in the bibliographical index.
Ironically, these would also be his last published work.
After this first collaboration Hardy, an uncompromising judge of mathematical talent, proposed to Petros that he accept a fellowship at Trinity and settle in Cambridge to become a permanent part of their elite team.
Petros asked for time to think it over. Of course, the proposal was enormously flattering and the prospect of continuing their collaboration had, at first glance, great appeal. Continued association with Hardy and Littlewood would no doubt result in more fine work, work that would assure his rapid ascent in the scientific community. In addition, Petros liked the two men. Being around them was not only agreeable but enormously stimulating. The very air they breathed was infused with brilliant, important mathematics.
Yet, despite all this, the prospect of staying on filled him with apprehension.
If he remained in Cambridge he would steer a predictable course. He would produce good, even exceptional work, but his progress would be determined by Hardy and Littlewood. Their problems would become his own and, what's worse, their fame would inevitably outshine his. If they did manage eventually to prove the Riemann Hypothesis (as Petros hoped they would) it would certainly be a feat of great import, a world-shaking achievement of momentous proportions. But would it be his? In fact, would even the third of the credit due to him by right be truly his own? Wasn't it likelier that his part in the achievement would be eclipsed by the fame of his two illustrious colleagues?
Anybody who claims that scientists – even the purest of the pure, the most abstract, high-flying mathematicians – are motivated exclusively by the Pursuit of Truth for the Good of Mankind, either has no idea what he's talking about or is blatantly lying. Although the more spiritually inclined members of the scientific community may indeed be indifferent to material gains, there isn't a single one among them who isn't mainly driven by ambition and a strong competitive urge. (Of course, in the case of a great mathematical achievement the field of contestants is necessarily limited – in fact, the greater the achievement the more limited the field. The rivals for the trophy being the select few, the cream of the crop, competition becomes a veritable gigantomachia, a battle of giants.) A mathematician's declared intention, when embarking on an important research endeavour, may indeed be the discovery of Truth, yet the stuff of his daydreams is Glory.
My uncle was no exception – this he admitted to me with full candour when recounting his tale. After Berlin and the disappointment with 'dearest Isolde' he had sought in mathematics a great, almost transcendent success, a total triumph that would bring him world fame and (he hoped) the cold-hearted Mädchen begging on her knees. And to be complete, this triumph should be exclusively his own, not parcelled out and divided into two or three.