At some point in history, abstract mathematics appeared. Sketchy histories tend to emphasize the role of the Greeks, which was substantial, but their ideas did not sprout from the mathematical equivalent of nothingness. Before there was Greek mathematics, the Babylonians and Egyptians were doing a good deal of mathematics. For this reason, I was pleased to see that the first few papers in this collection deal with Babylonian mathematics, and the title of the book is taken from the title of the first one. The book is divided into four sections: ancient mathematics, medieval and renaissance mathematics, the seventeenth century and the eighteenth century. Most of the papers examine a specific concept of mathematics as well as the people who developed it. The papers first appeared in mathematics journals such as "College Mathematics Journal" and "American Mathematical Monthly", over the last century. One paper by Florian Cajori appeared in 1917 and one by Eleanor Robson was published in 2002. A wide range of topics are covered in the papers of this collection and some early papers examine the development of mathematics in non-western cultures such as China, the number systems of North American Indians, the Mayas and the Incas. Some of the papers take an approach that raises possibilities that are outside the coverage found in most books on mathematical history. The paper, "Was Calculus Invented in India?" is overstated, but not by as much as we are often led to believe. Most books tend to state that calculus was simultaneously invented by Newton and Leibniz and largely ignore the shoulders upon which they stood when they made calculus. Two hundred years before Newton, Indian mathematicians were capable of deriving the infinite series expansions for the sine, cosine and arctangent functions. I was also amazed to learn that the first mathematical work published in the New World predates the voyage of Henry Hudson up the Hudson River by fifty years. I have never taught a course in the history of mathematics. However, if I ever do teach mathematical history, this will be a book that I will use. By presenting areas of mathematics developed in non-western cultures and outside what can be considered the historical mainstream, this book shows us that mathematics is truly a human endeavor.
Published in the recreational mathematics e-mail newsletter, reprinted with permission.