Amir Alexander in Scientific American:
In 1842, when the famed German mathematician Carl Gustav Jacobi was invited to speak to a scientific meeting in Manchester, he had a surprise in store for his English hosts. “It is the glory of science to be of no use,” he announced to the startled gathering of physical scientists. The true aim of science is “the honor of the human spirit,” and whether it turns out to be of any practical use matters not at all.
Jacobi made few converts that day. His declaration, he reported to his brother with satisfaction, “caused a vehement shaking of heads,” which was only to be expected from a crowd of men who were devoting their careers to improving industrial processes in the manufacturing capital of Europe. But things were different among Jacobi’s mathematical colleagues, who increasingly came to share his view that mathematical truths stood for themselves, and needed no further justification.
To be sure, no one (including Jacobi) denies that some fields of mathematics have proven extremely useful, and had made modern technology possible. But other fields, including some of the greatest mathematical discoveries ever, seem to serve no practical purpose whatsoever.
It was so from the beginning. The ancient science of geometry, as its name suggests, had its origins in the practical art of land measurement, but by the time Euclid codified it around 300 BCE it had strayed far from its roots.