A Mathematician's Apology Essays and Criticism

G. H. Hardy

Hardy's Text as an Artistic Treatise and Memoir

Mathematics is an exclusive club that opens its doors to a small number of gifted and often misunderstood individuals. Those who remain outside only have a vague perception of what it means to be a mathematician, and the perception that they do hold is more often than not hindered by an inability to understand exactly what it is that a mathematician does. Conversely, the expert mathematician is almost as ill-equipped as the layperson in trying to convey the beauty and joy of pure mathematics to non-mathematicians; the mathematician’s reliance on abstractions and the specialized vocabulary that define him as a mathematician make him a poor choice to describe and verbalize his field to the layperson. One either grasps the inherent beauty of theorems and numbers, thereby earning entry into the club, or one cannot and remains a perplexed outsider unable to grasp the inscrutable formulas. At least this was the case until G. H. Hardy, one of the foremost mathematicians of the twentieth century, bridged the gap and allowed the non-mathematicians of the world a glimpse into the mind and values of a pure mathematician.

Past his intellectual prime and restricted physically by several years of failing health, Hardy decided to write A Mathematician’s Apology, a book that can be appreciated by the mathematician and non-mathematician alike. The theorems that he outlines are among the most basic in the entire field. They are chosen so that the reader can both readily comprehend the explanations and easily perceive their aesthetic qualities. Hardy writes with the flavor and passion of an art lover about Euclid’s proof of the existence of an infinity of prime numbers and Pythagoras’s proof of the irrationality of the square root of two. The theorems he describes are representative of works of art precisely because they are so simple, which also makes them convenient as perfect examples for the general reader.

Since Hardy writes for an audience in large part comprising non-mathematicians, one must classify his essay with literary rather than mathematical headings. While the cold narrative voice of a mathematician does come forth at times in the prose, so do tones of elitism, disdain, and artistic snobbery, all of which do not normally belong in a mathematical essay. How then should we classify the essay if not as ‘‘mathematical’’? A Mathematician’s Apology is so multifaceted that it seems to transcend pigeonholing or categorizing. Restricting it to any single genre is an error that would cause a very restricted interpretation. For a thorough understanding of Hardy’s intentions, one must read the work as a representative example of various literary genres including the apology, artistic manifesto, and memoir. In each of these genres, Hardy’s elitist, valueladen tone invariably either demands unconditional acceptance or provokes severe disagreement.

A literary apology is a defense or justification for a particular way of life. Hardy, in calling his essay an apology, feels compelled to defend his chosen discipline. The urgency which he brings to the task leads one to believe that he is, at any given moment, trying to convince himself of the arguments. In order to present his belief that mathematics is an art, Hardy returns again and again to the concept of ‘‘utility’’ or ‘‘usefulness.’’ Judging from the disproportionate amount of writing he dedicates to these definitions, the charge that real mathematics has no practical use must have truly bothered him over the years. The disdain Hardy reserves for the widely accepted notions of ‘‘utility’’ and ‘‘useA fulness’’ is a further indication that the core of Hardy’s philosophy resides in these definitions.

Hardy continually splits hairs in defining ‘‘utility’’ or ‘‘usefulness’’ in order to refine a definition that contradicts common sense. After Hardy has finished, the conventional conceptions of ‘‘useful’’ and ‘‘useless’’ have been inverted from what is generally accepted: what we commonly hold to be ‘‘useful’’ applications, such as engineering, geometry, and calculus, are ‘‘trivial’’ and useless to the real mathematician, according to Hardy. Conversely, the ‘‘uselessness’’ of real mathematics is precisely the reason why it is immortal and why one can consider it an art form. Hardy cannot contain his contempt and scorn for applied mathematics, calling it ‘‘school’’ mathematics and referring to its various worldly...

(The entire section is 1844 words.)

Pure Mathematician and the Artist

(Nonfiction Classics for Students)

Mathematics may not be the first pursuit that comes to mind when we speak of the creative process. The artist and the mathematician may seem...

(The entire section is 1548 words.)