The first line of his A Mathematician’s Apology, G.H. Hardy, world renown English mathematician of the late 19th, early 20th century, notes his state of mind at the time of writing as one of melancholy. This is understandable given his sentiment that ”[e]xposition, criticism, appreciation is work for second-rate minds.” Added to the fact that he was pursuing a course that he loathed in others: “If I then find myself writing, not mathematics but ‘about’ mathematics, it is a confession of weakness, for which I may be rightly scorned or pitied by younger and more vigorous mathematicians. I write about mathematics because, like any other mathematician who has passed sixty, I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job.” (G.H. Hardy, A Mathematician’s Apology. Cambridge University Press, Cambridge 2005. pg 63)
What is Hardy apologizing for? He says he is apologizing for mathematics, but is this so? Who is he apologizing to? He answers the latter question: “I shall assume that I am writing for readers who are full, or have in the past been full, of a proper spirit of ambition.” (Ibid pg 77)
Hardy holds ambition in high regard, as it is one of his three highly respectable motives for choosing a field of study: 1) intellectual curiosity; 2) professional pride; 3) ambition, desire for reputation. Whether a chosen field is in service of others, is an afterthought according to Hardy. “It may be fine to feel… that you have added to the happiness or alleviated the sufferings of others, but that will not be why you did it.” (Ibid pg 79) He adds that if anyone told him that alleviating suffering was the motive for choosing his profession, Hardy wouldn’t believe him.
Hardy rates mathematicians as having a ‘fairer chance’ than practitioners in other fields of satisfying intellectual curiosity, pride and ambition. Finally, he justifies mathematics as the most enduring of all fields based on contributions to humanity that have lasted for thousands of years. Therefore those who make major discoveries to such a field would be remembered.
In one of the final sections, Hardy compares mathematicians to painters and poets. All of these practitioners, he says are makers of patterns. “The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful (emphasis in original); the ideas, like the colours or the words, must fit together in a harmonious way.” (Ibid pg 85)
But again, he ranks mathematics at the top. On the other hand, he says, painters make their ideas known with patterns of paints, but usually the ideas they embody are ordinary. Likewise, poets use words to express ideas, but Hardy cites Housman, a poet and one of his contemporaries, as stating that ‘the importance of ideas in poetry is habitually exaggerated.’ (Ibid pg 84)
A Mathematician’s Apology it seems, is less an apology than a defense of Hardy’s chosen field and a lament for his loss of his creative power. Notwithstanding Hardy’s harsh judgement of the population of ’second rate minds’ who choose to appreciate rather than to create and the 90-95 percent of mankind that cannot do anything well, it is very sad to realize that one no longer has one’s former powers.
I have written about this phenomenon in other posts, referring to it as ’identity shift’, which describes events that cause one to re-examine one’s identity. Examples of this include: 1) the onset of a serious illness; 2) loss of a job; 3) marriage; 4) transition from student to worker.
Perhaps the ‘second rate’ professions are actually more enduring during the span of an entire life even though the fruits thereof are not eternal.