More history facts

I subbed for a colleague's multivariable calculus class today, and looked up Taylor series on (gasp!) Wikipedia. Why would I do something so crass? Well, Wikipedia is actually pretty good for math -- I can evaluate what is true and what is false on a mathematical level, and the Wikipedia article has some history and links to other topics that I would not necessarily come up with on my own. In particular, some of the Wikipedia articles on math have some historical background included. The Taylor series article of course mentions Zeno, who comes up in my single-variable calculus class as well for his work on limits, and Taylor and Maclaurin, for whom Taylor and Maclaurin series are fairly or unfairly named. But I didn't know about Liu Hui's work on approximating pi (or work in applications of geometry), or Madhava of Sangamagrama's pioneering work on the infinite series for trigonometric functions. It sounds like Madhava in particular understood limits (and error terms and convergence of series) far before mathematicians in Europe, for instance. There's a rumor that Jesuit priests visiting India brought some of his ideas back to Europe.

In my historical explorations, I also found out that Cornell (my current institution) can boast of graduating the first black PhD mathematician in the world! Elbert Cox earned his PhD here in 1925, a year in which there were only 28 PhDs in mathematics given in the entire country. American mathematics was still very young. His advisor was William Lloyd Garrison Williams, a Quaker named after the abolitionist. Cox's thesis was on solutions to polynomial difference equations. Difference equations are a discrete analogue of differential equations, at least if the language then is the same as now. Difference equations are really cool, giving us maps like the logistic map. Chaos shows up pretty soon in this story...

A little bit more history: apparently the year that Elbert Cox was awarded the Scholarship of Mathematics at Cornell (the graduate fellowship of the time), the other awardee was Julia Dale, who had attended college in Missouri. Julia Dale also ended up in academia, in the end at Duke University. There she apparently headed the "women's division of mathematics" (!!). This contrasts with the career of Ida Metcalf, the second women in the US to get a PhD in mathematics (not necessarily coincidentally, also from Cornell) and the first American woman with a PhD in math to get recruited into finance, as a security analyst!