Me and the Witch

The Google Doodle for today (the 16th of May) commemorates Maria Gaetana Agnesi, an 18th century Italian mathematician/philosopher who became a professor at the University of Bologna, studied (among other things) the curves named after her, and wrote several textbooks including, if Mathworld is correct on this point, the earliest surviving mathematical work (Instituzioni analitiche ad uso della gioventù italiana — Analytical Institutions for the Use of Italian Youth) known to be written by a woman .

I remember where I first encountered the Witch of Agnesi, though: it was in seventh grade, in the midst of my own pre-algebra textbook. The book was doing its best to describe how to plot curves, although at the seventh-grade level that’s pretty much just straight lines. It tossed off a mention, though, that there was this woman, Maria Gaetana Agnesi, and a curve named the “witch of Agnesi” because of its strange shape, and gave a formula describing the relationship of points on the curve as y = \frac{8a^3}{x^2 + 4a^2} which is correct but a struggle to parse if you’re still at the y = 4x - 2 stage of things, particularly since it didn’t include a picture of the curve and I was still at that point vague about the use of abstract coefficients like a in equations. (I’m not sure if I was just slow on the uptake or if the book hadn’t described it at that point.)

Still, I did my best working out what the curve might be (I had a fuzzy impression that it might be the shape of a witch’s hat, which, for the right parameters and if you’re willing to be loose in your interpretation, isn’t too implausible), by picking a couple easy-looking values for a and then more easy-looking values for x and trying to plot the curve, but I was never back then satisfied with the results.

I admit now I wonder if the textbook hadn’t left the plot out on purpose, since I’m sure I wouldn’t have thought so much about the curve if I could just see it. But I also have suspicions that the footnote was just there at all because it allowed a chance to legitimately mention a female mathematician in a context that would make sense for students at that level, without much thought about whether a picture would help matters any. Most of the contributions of female mathematicians prominent enough to get named for them tend to cluster around more modern times and thus around higher-level materials; there’s no explaining Sofia Kowalevski’s existence and uniqueness theorems for analytic partial differential equations to a seventh-grader.