On Wednesday, October 1st, we had our field trip to the archives. There were many wonderful volumes to peruse, but the one that really caught my eye was the first edition of Newton’s Opticks. It felt surreal to hold such an old book, written by one of the most important mathematicians of all time. The wannabe-mathematician within me was stirred with feelings of excitement, knowing that the book I had in front of me was an original, and that someone had held it and read it 300 years ago, and moreover, that this person had read it as new mathematics.
As I was flipping through the pages, admiring the complex diagrams of conic sections and curves, I came upon something which I found strange. I had always thought that Newton used a “prime” notation to denote the derivative, something similar to our modern f ‘ (x) that every calculus student is familiar with. But, at the very back of Opticks Newton had used the dz notation on a few of the final pages of the section “Tractatus De Quadratura Curvarum.” But this notation is Leibniz notation! This seemed highly irregular, since Leibniz (as every calculus student knows) was, along with Newton, the “creator” of calculus, and also had the distinction (as did many) of being Newton’s rival. Thus, I could not understand why Newton, known for his arrogance and pride, would choose to use his adversary’s notation.
The offending notation!
It was then that I came up with a vague notion of what my Newton assignment would consider: Newton’s notation. I have never lost the somewhat childish excitement that comes with learning new notation. It is like learning a new language, but a language endowed with a kind of “magic” that allows you to consider ideas which you could never have dreamed of without these new symbols. And, with my little “discovery,” I realized that this topic fit in well with the question “What is new/not new with Newton?” Was Newton using some unoriginal (i.e., “old”) notation? What were some of his contributions to mathematical notation? Had someone else noticed what I noticed in “Quadratura” (i.e., was what I saw in itself new?). These are the questions that I intend to investigate!
