A Criticism on 'A Mathematicians Apology' by G. H. Hardy

Among the greatest scientists in the world, there are many who consider science, from an idealistic point of view, as an anonymous human achievement, hence, something that mankind should be proud of (contrasting by the way, with many other shames of our species!). This is the point of view which I want to adopt in this article: consider science in a classic and pure context, independent of industrial technology or military motivations. Following this idea, science is evolving naturally as a consequence of the curiosity of the mind on finding out how things in the world around us work, and how they behave: Is it possible that there are general laws? Are there some principles governing the apparent chaos? Is it possible that the apple which falls is part of the same natural phenomenon as the Moon which rotates around the Earth but does not fall?

The search for such kind of answers is rather exciting for these intellects. Two hundred years ago, Laplace explained this exploration in his impressive The System of the World: “One of the strongest passions is the love of truth, in a man of genius” [9, Book V, Chap. IV]. Real scientists do not compete with each other: the challenge is rather to overcome the limitations and ignorance of human beings. Inarguably, some scientific contributions carry more weight than others. But, once scientists view their research as part of an exhilarating scientific voyage, there is no room left for dichotomous attitudes, classifying people as winners or losers. And here starts my criticism of the well-known book of G. H. Hardy (1877Hardy ( -1947)): “A Mathematician’s Apology”. In this book, published for the first time in 1940, he gives his opinion on the mathematical world in twenty-nine short chapters. More recent editions are easier to find and include a foreword by C. P. Snow [5]. Along this article I am going to point out some ideas presented in his book which sound to me either controversial, having prejudice or could be argued in a more respectful and deferential way.

Right from the start, he apologizes for his own criticism, claiming that: “exposition, criticism, appreciation, is work for second-rate minds.” It is a rather surprising beginning (what does he imply about the author of the Exposition du Systême du Monde [9], the masterpiece mentioned above?) We all know about very talented philosophers, critics, writers, artists, even journalists who had been and are still playing a fundamental role in the development of science, arts and humanism in general. So, this comment sounds very pretentious coming from a mathematician.

Still in the first chapter he disdains the speech of Alfred E. Housman (1859Housman ( -1936)), Kennedy Professor of Latin in the University of Cambridge, in his Leslie Stephen lecture on the 9th of May 1933: The Name and Nature of Poetry when, at the very beginning [6, p. 2] he modestly referred to his previous speech years before in the same Senate-House: “In these twenty-two years I have improved in some respects and deteriorated in others, but I have not so much improved as to become a literary critic, nor so much deteriorated as to fancy that I have become one.”

He was reinforcing what he had said in 1911 in the Cambridge Inaugural Lecture The Confines of Criticism, about literary criticism [7, p. 27]. Concerning this quotation, Hardy declares: “. . . deplorable that a great scholar and a fine poet should write like this.” I apologise for wishing to express exactly the same words about Hardy’s declaration.

My disappointment arises specifically from the fact that the book was written by such a great mathematician, who not only left many contributions of his own, but also, the unique occidental mathematician who was considerate enough to recognise the talent of Ramanujan. A quite unusual attitude for that time: help and support bringing to light exceptionally talented people who come from not so (scientifically) prestigious places. For those who are interested in knowing more about the relation between Hardy and Ramanujan, see e.g. the Ranganathan’s book [11], where one finds details of Ramanujan’s meteoric and short carrier, and his depressive and unhealthy life.

Due to the atrocities of the First World War, Hardy had reasons to condemn the application of science in military matters, in particular, to reprobate the fact that some research on applied mathematics was supporting directly those purposes. Needless to say that applied mathematics is much wider than those military purposes (by the way Bertrand Russell knew that, and focused his pacifism in a more directed way, up to the point of being imprisoned for pacifist acts during the war). For some reason related to this, Hardy was very proud for being a pure mathematician (“a real mathematician . . . the purest of the pure” as C. P. Snow described in the Foreword), I would say, almost to the point of treating applied mathematics with prejudice. Nevertheless, ironically, contrasting with this st

This content is AI-processed based on open access ArXiv data.