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A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy which defends the pursuit of mathematics for its own sake. Central to Hardy's "apology" – in the sense of a formal justification or defence (as in Plato 's Apology of Socrates) – is an argument that mathematics has value independent of its applications.
- G. H. Hardy, C. P. Snow
- 1940
Professor Hardy distinguishes two questions: (1) What are the motives which lead certain persons to devote themselves to mathematics? And (2) What is the value of their activities?. Professor Hardy's answer to his first question is as follows.
Hardy opens his apology by asserting his belief that in the mere act of ‘‘writing about mathematics’’ he has lowered himself to a level below that of a pure mathematician.
G. H. Hardy is usually known by those outside the field of mathematics for his 1940 essay A Mathematician's Apology, often considered one of the best insights into the mind of a working mathematician written for the layperson.
- Introduction
- Author Biography
- Plot Summary
- Key Figures
- Themes
- Style
- Historical Context
- Critical Overview
- Criticism
- Sources
Godfrey Harold (G. H.) Hardy's A Mathematician's Apology, first published in 1940 in England, is the memoir of the world-renowned mathematician, written in the last few years of his life while he was in failing health. The work is written in the form of an apology, which in literary terms means a defense. In this case, Hardy is defending his career...
Godfrey Harold (G. H.) Hardy was born on February 7, 1877, in Cranleigh, Surrey, England. Both his parents were educators and possessed mathematical skills. Even before learning to speak as a very young child, he demonstrated an extraordinary IQ and performed mathematical computations to amuse himself. After winning a scholarship to Winchester Coll...
Chapters 1-2
Hardy opens his apology by asserting his belief that in the mere act of "writing about mathematics" he has lowered himself to a level below that of apure mathematician. He equates himself in this position to that of an art critic—a profession he considers to be for "second-rate minds"—as opposed to the artist himself. Hardy describes a discussion he had on this subject with British poet A. E. Houseman. In chapter 2, Hardy introduces the questions he proposes to answer throughout the remainder...
Chapters 3-4
Hardy states that most people choose their career path because "it is the one and only thing that [they] can do at all well." Mathematics is a particularly specialized subject, and mathematicians themselves are not noted for their versatility. In chapter 4, he lists several mathematicians whom he considers immortal geniuses, and he points out that most of them reached their intellectual peaks or died before the age of forty. Those men who attempted new careers later in life were largely failu...
Chapters 5-9
Hardy concludes his responses to the questions he posed in chapter 3. As to why one would choose to become a mathematician, Hardy refers to a lecture he gave at Oxford twenty years earlier in which he posited that mathematics is chosen for three reasons. First, it is essentially a "harmless" profession; second, because the universe is so vast, if a few professors wasted their lives doing something at which they excelled, it would be "no overwhelming catastrophe"; and third, there is a "perman...
Niels Henrik Abelwas a Norwegian mathematician (1802-1829) known for the tremendous amount of brilliant work he completed in his brief, twenty-six-year life.
Metaphysician and philosopher F. H. Bradley (1846-1924) is most noted for his Appearance and Reality(1893), which was considered an important philosophical discussion of contemporary metaphysical thought at the time of its publication. He was also known by the influence his writing had on author T. S. Eliot.
German-born physicist Albert Einstein (1879-1955) is considered one of the most brilliant men who ever lived. His theory of relativity, which he introduced in 1915, was revolutionary. It related matter with energy and displaced Newtonian mechanics as the cornerstone of physics by introducing the concept of space-time. In 1921, he received the Nobel Prize. A Jewish pacifist, Einstein immigrated to the United Statesshortly after Hitler came to power.
Aesthetics
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 thebeauty 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.
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 attackand 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...
Topics for Further Study
1. The ethical issues surrounding theoretical research are complex. Hardy called pure mathematics "gentle and clean." However, Einstein's theory of relativity played a direct influence in the development of the first atomic bomb. Research the role Einstein actually played in the development of the atomic bomb. Discuss the letter to President Franklin Delano Rooseveltthat he signed urging the president to expedite its development in order to stop the spread of Nazism. How can you reconcile thi...
Apology
A Mathematician's Apologyis, as the title implies, written in the form of an "apology," or defense. In this case, the author sets out to defend his chosen career: namely, theoretical, or what he calls "pure," mathematics. Although he was generally accepted for his brilliant theoretical insights, which resulted in many remarkable works and collaborations, Hardy's view that theoretical mathematics is an art form, while its counterpart, applied mathematics, is at best an application of trivial e...
Tone
With this book, Hardy set out to address a general audience of both mathematicians and non-mathematicians alike, and as a result he employs a narrative style that could best explain in simple terms his profound and complex array of ideas. To that end, his tone, while often conveying a derogatory and elitist attitude toward his subject matter, never condescends to the reader with lofty diction; anyone with a rudimentary knowledge of mathematics would feel at home and comfortable with Hardy's s...
Since Hardy elucidated a philosophy that stresses the timelessness and immortality of pure mathematics, it is very difficult to contextualize A Mathematician's Apology with respect to a single historical period. Viewed as an autobiographical memoir, A Mathematician's Apologyis a product of a genius who came of age towards the end of the Victorian e...
In his review of A Mathematician's Apology in the Spectator, British author Graham Greene asserts that Hardy's philosophy is akin to the philosophy of an artist. "The real mathematician," accordingto Greene, "must justify himself as an artist." Indeed, Hardy's work is a very successful justification of the mathematician as artist, much in the liter...
David Partikian
Partikian is a freelance writer, editor, and English instructor. In this essay, Partikian suggests that Hardy's text is a multifaceted work that should be appreciated primarily 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...
What Do I Read Next?
1. Copenhagen(1998), a play by Michael Frayn, illustrates the moral issues faced by mathematicians and physicists during World War II. Hardy touches upon many similar subjects in his apology. 2. Mathematics for the Million,by Hardy's contemporary Lancelot Hogben, was originally published in 1937 and republished in 1967. It is an influential work in the field of mathematics and offers a sharp contrast to Hardy's view of applied mathematics as trivial. 3. Hardy's Ramanujan: Twelve Lectures on S...
Catherine Dybiec Holm
Holm is a freelance writer with speculative fiction and nonfiction publications. In this essay, Holm discusses the parallel Hardy draws between the pure mathematician and the artist. 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 to be on different ends of the spectrum. Storytelling, painting, literature, dance—these appear to be the realm of creative artists. Math, on the other hand, is an "austere"...
Dauben, Joseph W., "Mathematics and World War I: The Internal Diplomacy of G. H. Hardy and Gösta Mittag-Leffler as Reflected in Their Personal Correspondence," in Historia Mathematica,Vol. 7, 1980, pp. 261-88. Greene, Graham, "The Austere Art," in Spectator,Vol. 165, December 20, 1940, p. 682. "People Who Count," in Times Literary Supplement,Decemb...
It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathema-ticians have done.
Published in 1940, A Mathematician’s Apology, by G. H. Hardy, is an extended essay on why people study mathematics and how its logical purity, much more than its usefulness in daily life, makes it a worthy pursuit. Hardy was one of the 20th century’s most important mathematicians.
