Abstract

The early twentieth century was a lively time for the foundations of mathematics. This ensuing debates were, in large part, a reaction to the settheoretic and nonconstructive methods that had begun making their way into mathematical practice around the turn of the twentieth century. The controversy was exacerbated by the discovery that overly na¨ıve formulations of the fundamental principles governing the use of sets could result in contradictions. Many of the leading mathematicians of the day, including Hilbert, Henri Poincar´e, ´.