Reflection on Assignment 1

My biggest takeaway from last week’s presentations was the potential value of using historically-inspired geometry problems in a contemporary mathematics classroom. I want to start out this blog post with a quote by the Fields Medal-winning British-Lebanese mathematician Michael Atiyah. Speaking on the topic of contemporary algebra, he claimed that



“Algebra is the offer made by the devil to the mathematician. The devils says ‘I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine.’”



While intentionally provocative, I think that Atiyah’s observation contains an important nugget of wisdom: modern algebra, while extremely powerful, is also very abstract and formulaic. I, for example, remember having to memorize the volumes of a number of 3-dimensional shapes, and besides rectangular prisms, these formulas often remained unmotivated and unexplained. 

Looking specifically at Julia, Alan, and Tim’s presentation, here is an example of how I can imagine using ancient geometric problems in a modern classroom. Instead of having students simply accept the formula V=1/3 Bh for a pyramid, I can have them explore how this formula comes about by breaking a rectangular prism into three equal pyramids. This will not only help students to remember the formula, but might also make the topic of volumes more interesting; they might begin to wonder, for example, if there are clever ways of justifying the volumes of other shapes as well!

I was totally unaware of the currently-existing resources available for teaching about ancient math problems. I’m particularly impressed by the book 5000 Years of Geometry by Christoph Scriba and Peter Schreiber, which has both excellent exposition on the history and development of geometry as well as a number of well-formulated problems. I can definitely see myself borrowing from this wealth of problems in my own classroom.


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