Journey through Mathematics

Abstract

In the fall of 2000, I was assigned to teach history of mathematics on the retirement of the person who usually did it. And this with no more reason than the historical snippets that I had included in my previous book, Fourier Analysis and Boundary Value Problems. I was clearly fond of history. Initially, I was unhappy with this assignment because there were two ob- vious difficultie from the start: (i) how to condense about 6000 years of mathematical activity into a three-month semester? and (ii) how to quickly learn all the mathematics created during those 6000 years? These seemed clearly impossible tasks, until I remembered that Joseph LaSalle (chairman of the Division of Applied Mathematics at Brown during my last years as a doctoral student there) once said that the object of a course is not to cover the material but to uncover part of it. Then the solution to both problems was clear to me: select a fewtopics in the history of mathematics and uncover them sufficientl to make them meaningful and interesting. In the end, I loved this job and I am sorry it has come to an end. The selection of the topics was based on three criteria. First, there are always students in this course who are or are going to be high-school teachers, so my selection should be useful and interesting to them. Through the years, my original selection has varied, but eventually I applied a second criterion: that there should be a connection, a thread running through the various topics through the semester, one thing leading to another, as it were. Thiswould give the course a cohesiveness that tomewas aesthetically necessary. Finally, there is such a thing as personal taste, and I have felt free to let my own interests help in the selection.