Overview

Over the course of the nineteenth century, mathematicians and philosophers were forced to change their view of the subject matter of mathematics. At the start of the century many scholars considered it to be a collection of self-evident truths about nature. By 1900 many were convinced that mathematics was principally a creation of the human imagination and as such subject to error. This shift in view resulted from the discovery of new geometries and number systems calling into question whether the traditional mathematical description of nature using Euclidean geometry and real numbers was necessarily correct and free of potential contradictions. The principle of induction was formalized during this period in an attempt to put arithmetic on a firm logical foundation.

Background

The principle of induction is simply stated: If P(n) denotes...