influenced by the academic culture of the universities of Cambridge and Oxford between World War I and World War II. Some of Hardy's examples seem unfortunate in retrospect. For example, he writes, "No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years." Since then number theory was used to crack German Enigma codes and much later, figure prominently in public-key cryptography. The applicability of a mathematical concept is not the reason that Hardy considered applied mathematics somehow inferior to pure mathematics, though; it is the simplicity and prosiness that belong to applied mathematics that led him to describe them as he did. He considers that Rolle's theorem, for example, cannot be compared to the elegance and preeminence of the mathematics produced by Évariste Galois and other pure mathematicians, although it is of some importance for calculus. Notes References Full text External links Full text of An Annotated Mathematician's Apology, an annotated edition including Hardy's essay ‘Mathematics in war-time’, with commentary on the context and legacy of the Apology. 1940 non-fiction books Biographies and autobiographies of mathematicians Apologetics Aesthetics books Cambridge University Press books Books about mathematics Books about Cambridge Books about Oxford History of the University of Cambridge History of the University of Oxford