A Mathematician's Apology

2024-07-11

A Mathematician's Apology is an essay written by famous mathematician G. H. Hardy in 1940. Hardy wrote the essay near the end of his career to serve as an apology to the world from the perspective of Hardy's archetype of a mathematician.

In the essay, Hardy apologizes for mathematics being useless, a sentiment which goes against most people's understanding of the subject. To a physicist, mathematics is the language of our universe. To an engineer, mathematics is certainty. To an architect, mathematics is beauty. Even Hardy would concede these statements, so it surely seems like mathematics is useful. But to a mathematician, mathematics is useless.

What Hardy is trying to say is that mathematics should not be done for the sake of practical application. He argues that any subject's value should not be determined by its usefulness. This is because choosing your actions based on a pragmatic approach decentivizes creativity. Any application that comes out of mathematics should not originate from a will to apply, but to create.

Creativity is another point that Hardy focuses on in the essay. Hardy is quoted as saying "It is a melancholy experience for a professional mathematician to find himself writing about mathematics." This is to say that the reason for mathematics is not to analyze itself. Hardy sees creation as the highest level of thinking, and that "exposition, criticism, [and] appreciation, is work for second-rate minds". Hardy also sees mathematics as best done creatively. This connects to the practice of disregarding application, as well as reveals the true use for mathematics: to create new mathematics.