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In Defense of Pure Mathematics

After 75 years, Godfrey Harold Hardy’s A Mathematician’s Apology still fuels debate over pure versus applied mathematics.

Daniel S. Silver



(This article is an extended online-exclusive version of the one that appeared in print and digital editions.)

2015-11SilverF1.jpgClick to Enlarge ImageGodfrey Harold Hardy was one of the greatest number theorists of the 20th century. Mathematics dominated his life, and only the game of cricket could compete for his attention. When advancing age diminished his creative power, and a heart attack at 62 robbed his physical strength, Hardy composed A Mathematician’s Apology. It was an apologia as Aristotle or Plato would have understood it, a self-defense of his life’s work.

“A mathematician,” Hardy contended, “like a painter or poet, is a maker of patterns.... The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way.” It was a personal and profound view of mathematics for the layman, unlike anything that had appeared before. The book, which this year reaches the 75th anniversary of its original publication, is a fine and most accessible description of the world of pure mathematics.

Ever since its first appearance, A Mathematician’s Apology has been a lightning rod, attracting angry bolts for its dismissal of applied mathematics as being dull and trivial. The shaft that lit up the beginning of a review in the journal Nature by Nobel laureate and chemist Frederick Soddy was particularly piercing: “This is a slight book. From such cloistral clowning the world sickens.”

Hardy’s opinions about the worth of unfettered thought were strong, but stated with “careful wit and controlled passion,” to borrow words of the acclaimed author Graham Greene. They continue to find sympathetic readers in many creative fields. They were prescient at the time, and remain highly relevant today.

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