1.4 - The Role of the History of Mathematics in Courses Beyond Calculus

Summary

I am sure that no subject loses more than mathematics by any attempt to disassociate it from its history.

– James Glaishier (1848–1928)

Introduction

Glaishier's comment is especially true in mathematics courses beyond calculus. A mathematics course that fails to integrate the history of the subject matter presents the mathematics in skeletal form. While the skeletal structure might be instructive, the real meat and heart of the subject are missing. This paper discusses the role that the history of mathematics can play in courses beyond calculus. It will not discuss a history of mathematics course but rather the integration of historical topics into other mathematics courses.

The first question that one asks is “Why include the history?” We could answer (sarcastically) “Why not?” but that is not an adequate answer. As mentioned above, by seeing the mathematical content without its history students see only a skeletal foundation for the subject. They fail to see some of the motivation for the subject and fail to appreciate the human effort involved. They also do not gain a proper appreciation for the process of mathematical development that has occurred. We all know that most mathematics that we study today went through a metamorphosis over the years. A student seeing this development will gain a greater appreciation for how far the subject has come since its beginnings.