"This sophisticated and wide-ranging book examines mid-century American mathematics as a species of high modernism, both in its pure form and in applied mathematics. It looks at how it was supported, why it was advocated, how and why it was compared to contemporary abstract art, how the evolving ideas of abstraction played out in the Cold War, and how this even affected the writing of the history of mathematics. It is a major addition to and critique of the literature that presents modern mathematics as a species of modernism, and it should be read by every historian of modern science and indeed by anyone interested in how abstract ideas have shaped the modern world."–Jeremy Gray, author of Plato's Ghost: The Modernist Transformation of Mathematics