雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(52)
But in 1914 Hardy's collaborator J.E. Littlewood had shown that this was not so, for there existed some point where the simple assumption would underestimate the cumulative total of primes.
Then in 1933 a Cambridge mathematician, S. Skewes, had shown19 that if the Riemann Hypothesis were true, a crossover point would occur before which,
隨後在1933年，劍橋的一位數學家S.斯奇烏斯表明，如果黎曼猜想是成立的，那麼就會在之前找到一個轉折點。Hardy commented, was probably the largest number ever to serve any definite purpose in mathematics.
哈代評論說，這個數可能是有用的數學研究中出現過的最大的數注。
It could be asked whether this enormous bound might be reduced, or whether one could be found that did not depend upon the truth of the Riemann Hypothesis, and these were the problems that Alan now undertook.
人們現在要問，這個巨大的範圍是否有可能縮小，或者說，是否有可能不依賴於黎曼猜想的正確性而找到一個範圍。這就是艾倫現在要研究的問題。One new departure at Cambridge was his acquaintance with Ludwig Wittgenstein, the philosopher.
艾倫在劍橋的另一個收穫，是認識了哲學家路德維希·維特根斯坦。He would have seen Wittgenstein before at the Moral Science Club, and Wittgenstein (like Bertrand Russell) had received a copy of Computable Numbers.
他以前也許在道德科學俱樂部見過維特根斯坦，維特根斯坦（他喜歡伯特蘭·羅素）已經讀過了《可計算數》。But it was in this summer of 1937 that Alister Watson, the King's Fellow, introduced them and they met sometimes in the botanical gardens.
1937年夏天，國王學院的研究員艾力斯特·沃特森爲他們引見，他們時常會在植物園見面。Watson had written a paper on the foundations of mathematics for the Moral Science Club, in which he made use of the Turing machine.
沃特森圍繞圖靈機的概念，給道德科學俱樂部寫了一篇關於數學基礎的論文。Wittgenstein, whose first work had been as an engineer, always liked practical, down-to-earth constructions and would have approved of the way that Alan had made a vague idea so definite.
維特根斯坦是工程師出身，他很喜歡實踐，他想要通過一種實體的構建，來證明艾倫的想法。Curiously, the failure of the Hilbert programme had also meant the end of the point of view advanced by Wittgenstein in his first phase, in the Tractatus Logico-Philosophicus, that every well-posed problem could be solved.
有趣的是，希爾伯特計劃的失敗，終結了維特根斯坦前期的信念，在他的《邏輯哲學論》中，他認爲所有表述清楚的問題都是可解的。
