A Mathematician's Apology

by G. H. Hardy
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Last Updated on May 7, 2015, by eNotes Editorial. Word Count: 848

One of Hardy’s principal arguments is that theoretical mathematics, which he refers to as ‘‘real’’ or ‘‘pure’’ mathematics, has similar aesthetic qualities to those of art or poetry. Hardy invests much in his essay defending this position, explaining the beauty of Pythagoras’s and Euclid’s theorems, and comparing the aesthetics of pure mathematics to the simplistic and vulgar exercises that make up applied mathematics.

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Aging, Prime of Life, Depression, and Melancholy
A Mathematician’s Apology was written during the final years of Hardy’s life, shortly after a heart attack and a series of other physical ailments had rendered him mostly sedentary. This theme colors much of the text. Whereas in his prime he could devote his days to intense studies of concepts and vigorous games of cricket, those abilities were long lost to him as he was writing this memoir. Hardy firmly believed that mathematics is a young man’s game. He uses several mathematicians—including Ramanujan, Newton, and others—as examples of geniuses who peaked in their twenties and thirties. By the time of the writing of this memoir, Hardy was in his sixties. This resulted in a melancholic tone that borders on depression. A few years following the publication of the book, Hardy unsuccessfully attempted suicide by taking an overdose of barbiturates.

Creative Process
Throughout A Mathematician’s Apology, Hardy compares the ‘‘real’’ mathematician to the creative artist. He uses poetry and art to make this compariA son. He believes there is an objective ‘‘mathematical reality’’ that exists in the world, which is no different from the ‘‘physical reality,’’ and it is up to the mathematician to discover and describe that reality. The best of pure math can be held as the highest of all art forms.

Genius, Common Man/Everyman
At the expense of being criticized for elitism and snobbery, Hardy distinguishes between those who can perform a single task adequately—of which there are a small minority—and those who can perform a single task in their lives exceptionally, of which there are a significant few. These are the geniuses of the world, and Hardy is proud to have worked alongside those men he considered to be the most ingenious of all time, including Ramanujan and Littlewood.

Despite Hardy’s elitist tendencies and tremendous confidence in his own intellectual abilities and importance, A Mathematician’s Apology is imbued throughout with Hardy’s severe self-doubts about his own worth as a human being and the worth of his contributions to mathematics and to the world. These self-doubts were, undoubtedly, caused in large part by his deteriorating physical state at the time of his writing and also in large part by the accumulation of years of criticism he received for so many of his views. The effects of years of being a ‘‘misunderstood genius’’ appear to have taken their toll, and one of the underlying purposes of writing this memoir is for Hardy to determine for himself if his life has been worthwhile.

Superiority, Egotism/Narcissism, Vanity, Conceit
Hardy admits that A Mathematician’s Apology is an egotistical work. Men—and here Hardy includes himself—who choose to make a career out of mathematics do so in order to achieve a certain status of immortality. And if they sit down to write about their lives or their work, they do so because of their conviction that they have done something remarkable and should be remembered for it. Hardy does not hold back from stating his belief that he has made significant contributions to his field and that he is among the elite of the world in his field. Despite these views, however, his work embraces a certain amount of humility in that he recognizes greater geniuses than himself, and he feels proud to have considered them to be among his colleagues and friends.

Hardy’s famous collaboration with Ramanujan occurred during World War I, a war which Hardy adamantly opposed for both philosophical and practical reasons. Unlike most of his colleagues, Hardy held German society in high regard due to its advances in scientific thought, and he seriously mistrusted the British politicians. As a result, he was one of the few distinguished thinkers of his day, along with Bertrand Russell, who refused to support the war. On a practical level, Hardy thrived through his collaborations, many of which were with colleagues throughout Europe. The war had a tremendously disruptive influence on these efforts and hampered his professional development.

One of the great ironies of A Mathematician’s Apology, written on the eve of World War II, is that Hardy defends the ethics of pure mathematics on the grounds that it is a ‘‘gentle and clean’’ field of study, unlike its counterpart, applied mathematics, which can make claim to its contributions, for instance, to the fields of ballistics. Hardy refuses to admit, or is unable to see, a causal relationship between theoretical math and warfare. He even goes so far as to predict that it would be years before Einstein’s theory of relativity could be applied to any real-life situation.

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