雙語暢銷書《艾倫圖靈傳》第3章:思考什麼是思考(16)

Alan responded with joy to the absolute quality of mathematics, its apparent independence of human affairs, which G.H. Hardy expressed another way:10

艾倫非常喜歡數學的這種超脫世俗之外的特點。G.H.哈代從另一個角度闡釋這種特點：

317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

317是一個素數，不是因爲我們覺得如此，也不是因爲我們希望如此，而是它本來就是如此，數學的事實就是如此。

Hardy was himself a 'pure' mathematician, meaning that he worked in those branches of the subject independent not only of human life, but of the physical world itself. The prime numbers, in particular, had this immaterial character. The emphasis of pure mathematics also lay upon absolutely logical deduction.

哈代本人是一個純數學家，他研究的數學分支，不僅超脫世俗，還超脫了物理世界。數字具有非物質性，純數學的關鍵在於絕對化的邏輯推理。

On the other hand, Cambridge also laid emphasis on what it called 'applied' mathematics. This did not mean the application of mathematics to industry, economics, or the useful arts, there being in English universities no tradition of combining high academic status with practical benefits. It referred instead to the interface of mathematics and physics, generally physics of the most fundamental and theoretical kind. Newton had developed the calculus and the theory of gravitation together, and in the 1920s there had been a similar fertile period, when it was discovered that the quantum theory demanded techniques which were miraculously to be found in some of the newer developments of pure mathematics. In this area the work of Eddington, and of others such as P.A.M. Dirac, placed Cambridge second only to G?ttingen, where much of the new theory of quantum mechanics had been forged.

另一方面，劍橋也很重視應用數學，但並不是把數學應用到工業、經濟或者其它有用的社會科學領域，英國的大學沒有把學術與實際利益相結合的傳統。它是指數學和物理的結合，一般來說，是最基礎而理論化的物理。牛頓在研究引力定律的過程中發展了微積分，而在20年代，也有一段類似的繁榮時期，量子理論的研究需要新的工具，而這工具意外地在純數學的發展中被發現了。在這方面，由於愛丁頓等人（比如還有P.A.M.狄拉克）的貢獻，劍橋的地位不遜於量子論的起源地──哥廷根。