Introduction to the Book

BRANCHES AND ROOTS OF THE TREE MATHEMATICA

 

by

 

Leo Lusk

 

 

“But the Oak-tree understood, and felt sad, for he was very fond of the little Nightingale who had built her nest in his branches.  ‘Sing me one last song, ‘ he whispered; ‘For I shall feel very lonely when you are gone.’”

 

From The Nightingale and the Rose, by Oscar Wilde

 

 

This text is being written for use in a college level mathematics course such as Liberal Arts Mathematics. It can also be used for education majors who will be teaching mathematics at any level. It is not intended to be a History of Mathematics text, since there are sufficiently many fine books on the market today, most notably Victor Katz’s A History of Mathematics, David Burton’s The History of Mathematics, and Howard Eve’s popular An Introduction to the History of Mathematics. Instead, this author is intending to create a text that gives all who choose to study it the opportunity to deepen and expand their knowledge and appreciation of mathematics and the men and women whose lives were dedicated to its growth. For those who are education majors it is this authors purpose to give some direction to studying and applying mathematical history to you, our future educators. 

 

The analogy of comparing mathematics to a tree is intentional. For if mathematics were a tree it would best be represented by the great and majestic oak. Its strength and towering beauty would serve as evidence to the casual observer of the vastness of the discipline it represents. Its expansive and powerful branches reaching out in all directions would serve notice of the many facets this discipline possesses, and how they come together to form one enormous, yet elegant and beautiful, tree which stands center stage in a field in the Land of Academia. Lying silently hidden beneath the ground is its roots. This underground plant growth is the foundation from which mathematics was raised and from which stability and supplemental nourishment is obtained. The roots are strong and deeply grounded within the earth and their importance cannot be overstated. 

 

It is, therefore, the intent of this book to keep us from being only distant casual observers of the tree Mathematica. Instead, after allowing us to gaze admiringly at its stately beauty, we shall be encouraged to put an ear to the ground where we may hear it whisper some of its own history to us. As we rise and begin to approach the tree its strength becomes more evident for touching its thick trunk may cause one to feel intellectually pauperized since this stock supports such an enormous weight of intelligent thought and reason. We will then begin our ascent into the limbs of the tree.  But our climb is not meant to be too difficult, nor is it meant to be so high that we pass our own limitations of understanding. Our climb into the branches of Mathematica is meant to be an enjoyable one, and after a sufficient but short amount of time it should have elevated us to a lofty new position from which an admirable view is afforded.  

 

When dealing with historical content in a mathematics text one must first ask, “What is the history of mathematics?” and then, secondly, “What is important within the scope of history and what is not?” To answer the first question would be a voluminous undertaking indeed for the breadth of historical knowledge and scholarship of mathematics is quite lengthy.  Any attempt to cover the vast span of mathematical history would become encyclopedic in a very short amount of time. The second question, at this writing, must be left to this author’s judgment which will be based upon the limitations of time and space. The material selected for coverage reflects personal interests and objectives, therefore, it stands to reason, that not everyone will be satisfied with the first offering of this work. The omission of topics and individuals herein is currently dictated by personal sway and there is no intention to slight the contributions of the many great mathematicians who have lived, struggled, loved, and gained the acceptance of their peers as they passed through the boundless sweep of time.

 

I am indebted to those who are supporting this project from its infant stages and to those many scholars who, through their writings and teachings, have captivated and cultivated my interest in mathematics and mathematical history. It is their labor that has laid the groundwork for me to follow.  Like Newton, I, too, stand on the shoulders of giants.