Numbers: Histories, Mysteries, Theories

This short book is an attempt to answer an obvious, yet very deep and important question. “What exactly is a number?” Intuitively, this is a question that humans and some animals can give a partial answer to. A number is a mechanism used for counting. However, that answer is extremely limited in effectiveness. For as societies became more advanced with dramatic increases in the size and complexity of commerce, other uses and types of numbers were developed. For example, negative numbers are an essential feature of accounting. 

The answer is developed by the presentation of a history of the creation and need for more advanced forms of numbers. Fractions, negative numbers and then the use of complex numbers are explained within the historical context of the need for them to be developed. It is an everlasting tribute to the ingenuity and imagination of mathematicians that when a new class of numbers was needed, they were created and used. Even though at times the existence was counterintuitive. All of the new classes of numbers were created while maintaining the properties of pre-existing classes. For example, the commutative laws that hold for integers also hold for complex numbers.

This book can serve as a primer or refresher of the history of the development of new number classes, making it ideal as a supplement for classes in the history of mathematics. The timeline of the development of new number classes coincides very well with the growth in the complexity of commerce as well as the increasing power of science in explaining the universe.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, and teaching college classes. In his spare time, he reads about these things and helps his daughter in her lawn care business.