Mathematics in Fun and in Earnest

A world-renowned mathematician takes a lighthearted look at the philosophy, form, and recreations of mathematics in this fascinating book. In lucid and witty language, he discusses and illustrates the charm of mathematics as well as the science's vast practical utility and its vital significance to our cultural history. 1958 edition.

In this book, Court examines a great deal of the philosophical underpinnings of mathematics. While on this journey, he is both profound and humorous, occasionally at the same time. My favorite is the section with the title, "Running around in circles", where he gives mathematical explanations as to why humans lost in the desert or snows and chickens with their heads cut off almost always travel in circles. 
He also takes a long, hard and occasional light-hearted look at reasoning, which is the fundamental bedrock of mathematics. Intuition is part of the beginning of any system of mathematics, in the sense that it is often the justification of the postulates. For example, Euclid's first four postulates: 

1. A straight line segment can be drawn joining any two points. 
2. Any straight line segment can be extended indefinitely in a straight line. 
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. 
4. All right angles are congruent. 

Are all based on intuitive notions that appear obvious. Although mathematicians try to limit the amount of justification by intuition that appears in their structures, one cannot avoid relying on it at some point. Court uses several pages to explain the development of Non-Euclidean geometry and how it is fundamentally counterintuitive. The book closes with a series of basic problems in applied mathematics, including the classic Wolf-Goat-Cabbage and the problem where each of three people take what they believe to be their share although each does it sequentially and without any knowledge of the actions of the others. 
There are no great mathematical results in this book; that is in no way the author's intent. His goal was to put forward an explanation of the principles of mathematics that could be understood by anyone with a desire to know mathematics. In that way, the book is a significant success. 

Published in Journal of Recreational Mathematics, reprinted with permission