As with most nerds, I have a predisposition to being nerd sniped. Sometimes it’s a puzzle, but more often it’s simply an idea or the opportunity for a new project. After a conversation with a few coworkers, I’ve latched onto the idea of developing a summer course focused on the history of mathematics.
I’ve been fascinated by mathematics history for a number of years. I’ve slowly been going through Stillwell’s fantastic book, that takes a higher level approach and assumes a lot of prior mathematical knowledge. Because of that, it is fascinating. It provides significant historical context while tying many approaches into modern methods.
Now that I have this idea stuck in my head, I’ve also been reading a few other books of a more expository nature. Specifically, Boyer and Merzbach’s book, and I am waiting for two books that are slightly more vintage by David Smith. Not only is mathematics full of colorful characters that make for engaging stories, the actual process through which mathematics has been developed is amazing. Mathematics existed before any meaningful written languages (and perhaps spoken languages) came into use. Mathematical thinking can be considered one of the features that make us human.
I’m still reading, learning, and writing down ideas that I have. A course like this would need to be aimed at high school students who have at least algebra and some geometry experience, as all ancient mathematics amounts to arithmetic in various bases, and the development of those two disciplines. To go even further requires a bit more expertise, but I think some rough understanding can still be gained.
It’s important to put disciplines in their historical contexts. It allows students to recognize the non-linear development of a field, the evolution of ideas, and the immense amount of work that went in to the finely tuned textbooks they currently have. Some disciplines, such as genetics for example, have more recent roots that are more apparent to those who study. Mathematics is more unique because of its ancient development. Students are rarely aware of the pathways taken to bring mathematics where it is today, the huge leaps forward that were taken at a few key points in time.
I also believe that mathematical thinking is useful when reasoning about history and communicating ideas clearly. Beyond the excitement and amusement that studying history can gain, it is also good to show students how their skills in math can be usefully applied to other areas of academics. Reading and writing critically are excellent skills, and not every math student will want to take an advanced language arts course. Mathematics history might be able to rope them in, and trick them into learning some skills that will prove invaluable later on.
I’m not sure where this will lead, or if anyone in my company will take a chance on this idea. But it’s given me an excuse to learn more mathematics history, read some books, and brainstorm activities. That’s not a bad way to spend my time.