Abraham Flexner, founding Director of the Institute for Advanced Study, wrote an essay, The Usefulness of Useless Knowledge, for Harper’s magazine in 1939. Princeton University Press has now published a book of the same title, with Flexner's essay and a new companion essay by Robbert Dijkgraaf, Director and Leon Levy Professor at the Institute.
The Flexner essay, although not restricted to Mathematics, can be read as an answer to the question posed here. I haven't read the Dijkgraaf essay.
Flexner's essay is freely available online. Here's a link to the Princeton University Press page for the new book.