TL;DR: In this article, Courant and Robbins present What is Mathematics? An Elementary Approach to Ideas and Methods, which is a good book which deserves to run through many editions and is not a book on mathematical logic or philosophy: it deals not with the nature of mathematics but with its content.
Abstract: THIS is a thoroughly good book which deserves to run through many editions. It is not (as its title might suggest) a book on mathematical logic or philosophy: it deals not with the nature of mathematics but with its content. Its purpose is to show, not by general disquisitions but by concrete examples, drawn from almost every branch of pure mathematics, how mathematicians think and what they do. What is Mathematics? An Elementary Approach to Ideas and Methods. By Richard Courant and Herbert Robbins. Pp. xix + 521. (London, New York and Toronto: Oxford University Press, 1941.) 25s. net.