A quotation by Herbert Turnbull
Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant and what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a2 - b2 but was floored because the examiner unkindly asked for the factors of p2 - q2 .
Quoted in J R Newman, The World of Mathematics (New York 1956).
The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little enquiry into its nature and purpose as a deliberate human activity.
Preface to The Great Mathematicians (London 1929)