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So, chess seemed to have been sent to him from heaven. Being by its nature a cerebral game, it has concentration as a necessary requirement. Unless matched with a much inferior opponent, and sometimes even then, the player's attention can only wander at a cost. Petros now immersed himself in the recorded encounters between the great players (Steinitz, Alekhine, Capablanca) with a concentration known to him only from his mathematical studies. While trying to defeat I
The relaxing effect of chess also helped Petros to wean himself from sleeping pills. From then on, if some night he were overcome by fruitless anxiety co
Before his two years of unpaid leave were up, Petros took a momentous decision: he would publish his two important discoveries, the 'Papachristos Partition Theorem' and the other one.
This, it must be stressed, was not because he had now decided to be content with less. There was no defeatism whatsoever concerning his ultimate aim of proving Goldbach's Conjecture. In I
The intellectual peace he had achieved in I
Petros' powerful intuition now told him that the analytic method had all but exhausted itself. The time had come for something new or, to be exact, something old, a return to the ancient, time-honoured approach to the secrets of numbers. The weighty responsibility of redefining the course of Number Theory for the future, he now decided, lay on his shoulders: a proof of Goldbach's Conjecture using the elementary, algebraic techniques would settle the matter once and for all.
As to his two first results, the Partition Theorem and the other, they could now safely be released to the general mathematical population. Since they had been arrived at through the (no longer seemingly useful to him for proving the Conjecture) analytic method, their publication could not threaten unwelcome infringements on his future research.
When he returned to Munich, his housekeeper was delighted to see the Herr Professor in such good shape. She hardly recognized him, she said, he 'looked so robust, so flushed with good health'.
It was mid-summer and, unencumbered by academic obligations, he immediately started to compose the monograph that presented his two important theorems with their proofs. Seeing once again the harvest of his ten-year hard labours with the analytic method in concrete form, with a begi
With the begi
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 I
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.