Calculus and History

I’ve been reading Steven Strogatz' book, Infinite Powers, How Calculus Reveals the Secrets of the Universe and I’m marveling at how exciting it is to learn about how calculus came about, from Archimedes’ brilliant methods more than two millennia ago, to Galileo’s experiments with falling objects, Fermet and Descartes introducing the x-y plane, moving the state-of-the-art out of physical objects to the abstract, and finally to Newton and his incredible ability to, as the author says, mash together geometry, algebra, decimals and power series into a brilliant discovery of the integral calculus methods.

I’ve always enjoyed reading history because it’s about real people who either did something great or terrible, overcame odds, introduced a new way of doing something, or laid a foundation for the future. But there is something really special about reading about the great thinkers like those I’ve mentioned. In some ways, reading about their methods and discoveries brings home what is so fascinating about doing interesting work in modern times, as in my own engineering career. We strive to do something properly, and we are motivated by completing something. We are also driven by the processes of discovery and of learning.

At one point in chapter seven, the author suggests we go on the web to view the digitally-scanned pages of Newton's notebooks at the University of Cambridge Digital Library. They're not easy to read, being handwriting of a 17th-century scholar. It is remarkable that we can go back in time to see how he thought through problems, although it is much more expedient to have the knowledgable and skilled writer condense the story in contemporary language, as Strogatz has done.

What is not lost on me, however, is the fact that, through the ages, we have tried to make sense of the world and struggled to model it using symbolic language like algebra, geometry, power series and calculus. As a former high-school mathematics teacher, I often think about how I could continue to share my interests in the subject. I hope to be able to introduce mathematical and abstract thinking early on to my grandchildren, interspersed with how to catch a baseball and how to build a robot. I can't wait!