Traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. This book is suitable for mathematicians and historians. "In the course of this study Gray uncovers many new and unexpected things. . . . Gray's book offers a rich and . . . balanced account of how modernist ideas gradually gained inroads within pure mathematics."---David E. Rowe, Bulletin of the American Mathematical Society