Arguably the first significant innovation in the undergraduate mathematics curriculum of the second half of the twentieth century was the finite mathematics course. The origins of this course lie in the excitement that arose, in the period around World War II, about applying mathematics to the social sciences. In this article we tell some of that story, a tale that shifts back and forth between intellectual and organizational factors and that resulted in the appearance in 1957 of the book that created the finite mathematics course, Introduction to Finite Mathematics, by John Kemeny, Laurie Snell, and Gerald L. Thompson.