雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(23)
The 'real' mathematics of the 'real' mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Riemann, is almost wholely 'useless' (and this is true of 'applied' as of 'pure' mathematics).
It is not possible to justify the life of any genuine professional mathematician on the ground of the 'utility' of his work.
不能以用途爲標準，來評價真正專業的數學家… The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are, at present at any rate, almost as 'useless' as the theory of numbers.
……在現代，應用數學最偉大的成就，就是相對論和量子力學，而目前無論在哪個層面，這些科目都幾乎和數論一樣沒用。
It is the dull and elementary parts of applied mathematics, as it is the dull and elementary parts of pure mathematics, that work for good or ill.
這是應用數學最基本的部分，也是純數學最基本的部分，正是這個部分，纔是最重要的。In making explicit his response to the growing separation of mathematics from applied science, Hardy attacked the shallowness of the current 'left-wing' Lancelot Hogben interpretation of mathematics in terms of social and economic utility, an interpretation based on the 'dull and elementary' aspects of the subject.
面對數學和應用科學的不斷分化，哈代用這種基本性，來攻擊現行的左派觀點——蘭斯洛特·霍格本從社會和經濟效益來詮釋數學。Hardy spoke more for himself, however, in holding that 'useful' mathematics had in any case worked more for ill than for good, being preponderantly military in application.
哈代說了很多，他堅持認爲，有用的數學在任何情況下都是弊大於利，因爲它總是被用於軍事。He held the total uselessness of his own work in the theory of numbers to be a positive virtue, rather than a matter for apology:
他認爲，數論領域的一切無用研究，都是一種美德，而不是什麼羞愧：No-one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems very unlikely that anyone will do so for many years.
目前還沒有人發現數論有什麼軍事用途，但是這似乎也不會維持很久。Hardy's own near-pacifist convictions stemmed from before the Great War, but no one touched by the Anti-War movements of the 1930s could fail to be unaware of a view that military applications were to be shunned.
在一戰之前，哈代就有着和平主義的堅定思想，但是接觸過30年代反戰運動的人都知道，軍事應用也可以用來避免戰爭。If Alan had now discovered something like a 'warlike purpose' in the play of symbols, he was faced, at least in embryo, with a mathematician's dilemma.
艾倫現在發現了一些東西，比如符號遊戲的軍事用途，他開始陷入數學家的困境了。Behind the off-hand, teasing words to his mother, there lay a serious question.
他用輕鬆的語言對母親訴說，但這背後卻存在着很嚴肅的問題。Meanwhile the English students were brightening the Graduate College life with amusements of their own:
在這個時期，英國的學生們自娛自樂，來使研究生生活更加有趣：
