Pure Mathematics

Pure mathematics is, in its way, the poetry of logical ideas.  One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships.  In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.