A mathematician’s apology

In 1940 a Cambridge don called G.H. Hardy published an essay titled A Mathematician’s Apology. This was not an apology in the sense of saying sorry. It was an apology in the original sense of the word: a robust and combative justification of Hardy’s subject and the way he had lived his life. The little book became a minor classic, and is still in print today. It is complemented very well by a long Foreword written by Hardy’s friend and admirer C.P. Snow, added after Hardy’s death. The Foreword is a kind of mini-biography of Hardy, which also evokes something of the atmosphere of Cambridge and Oxford universities around and between the two world wars. That Oxbridge world lingers in higher education as part of a collective academic unconscious, and so Hardy’s apology is well worth paying attention to.

Hardy put forward his view of academic life with great clarity and precision. He writes as someone exemplifying academic excellence in a specialised subject. At his peak he was, by his own rather precise estimate, the fifth best mathematician in the world. His area of specialisation was number theory, one of the first, most enduring and more highbrow parts of mathematics. For most of his life he lived and worked in Trinity College Cambridge, and that was his home until he died. He did mathematics in the mornings, spent his afternoons at Fenners cricket ground, then had dinner in college. He was an introvert who did not teach, solved no real-life problems, had no administrative duties, never married and is not known to have had any romantic liaisons.

Hardy was the Sadleirian Professor of Pure Mathematics, and he lived and breathed the idea captured in the name of his chair. The adjective ‘pure’ should be understood as having its conventional meaning: pure as in untouched, unsullied, uncontaminated, and, in particular, pure as in not having any connection with the messy world around us. The essence of pure mathematics is that it is not there for any particular purpose. It is there for itself.