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

艾伦非常喜欢数学的这种超脱世俗之外的特点。G.H.哈代从另一个角度阐释这种特点：

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是一个素数，不是因为我们觉得如此，也不是因为我们希望如此，而是它本来就是如此，数学的事实就是如此。

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.

哈代本人是一个纯数学家，他研究的数学分支，不仅超脱世俗，还超脱了物理世界。数字具有非物质性，纯数学的关键在于绝对化的逻辑推理。

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，剑桥也很重视应用数学，但并不是把数学应用到工业、经济或者其它有用的社会科学领域，英国的大学没有把学术与实际利益相结合的传统。它是指数学和物理的结合，一般来说，是最基础而理论化的物理。牛顿在研究引力定律的过程中发展了微积分，而在20年代，也有一段类似的繁荣时期，量子理论的研究需要新的工具，而这工具意外地在纯数学的发展中被发现了。在这方面，由于爱丁顿等人（比如还有P.A.M.狄拉克）的贡献，剑桥的地位不逊于量子论的起源地──哥廷根。