Since I have spent the summer studying mathematics at Harvard University with Jameel Al-Aidroos (Ph.D Berkeley), expect that my next few posts, or at least some of them, will be on topics related to mathematics. I want to take some time, in this blog post, to look at where mathematical thought fits into some of my understandings of I have gleaned from studying the history of science. The upshot of the historical, philosophical, and mathematical content and musings will be pedagogical, just to give the reader some idea of where I am going. An important thing to understand, before reading this post, is the distinction between pure and applied mathematics. “Pure mathematics,” as opposed to “applied mathematics,” is, in its essence, math for its own sake, entirely apart from possible applications. In many cases, pure mathematics initially has no known application. Additionally, pure mathematics deals with abstract entities that have been detached from particular entities —and this will prove to be important to what I will say later.