Ben G's Math History Blog

From my reading, Edna St. Vincent Millay seems to be endorsing a Platonic view of beauty; that is, she seems to be endorsing beauty as an unchanging, timeless abstract ideal which real, concrete things can approximate but never fully attain. The fact that she capitalizes Beauty is one suggesting that she views it as a Platonic Form, but for me the stronger evidence comes from her use of the metaphor of light and luminosity. In Plato’s Allegory of the Cave, the sun represents the truest things, namely the Forms. St. Vincent Millay speaks of “light anatomized”, which here I interpret to mean that Euclid has perceived the true Form of Beauty, and ‘anatomized’ it by producing his Elements and the definitions, proofs, and propositions contained therein. St. Vincent Millay also speaks of how “heroes seek release From dusty bondage into luminous air”, which again can be interpreted as a reference to those people who are chained in Plato’s cave (and hence stuck in ignorance about the true natu...

     The first think I noticed when watching the Dancing Euclidean Proofs video and reading the paper was my resistance to the arguments made therein. As I continued to read the paper, I also tried to consider where this resistance came from, and whether and to what extent it was warranted.       I think that part of my resistance comes from my long exposure to mathematics as it is currently done, and I think this impacted my reaction towards the video and article in two ways. First, culturally, I was very accustom to mathematics done the ‘traditional way’, with written or visual, but atemporal, representations. Because I am so accustom to the traditional way of understanding and of doing mathematics, I found myself resisting the idea that ‘dancing mathematics’ could be edifying, even in the face of evidence given in the paper that multi-sensory learning helps students to better internalize and understand mathematics.       The seco...

I want to state from the outset of this post that, by necessity, I come to this question from a position of relative blindness. While I can speculate all I want about the benefits of acknowledging non-European mathematicians and mathematics, I have neither the evidence base nor the lived experience that would be required to more strongly ground my musings. What I can speak to, however, is how I have benefitted from the heavy acknowledgement given to European and Western sources of mathematics. To start with, I have never felt culturally out-of-place is a mathematics classroom or venue; while certainly a large portion of this must have to do with the current demographics and culture of mathematics, I was also brought up (as were many if not all of my peers) with the idea that mathematics was mostly the product of white Europeans. Implicit in this view is that me, and people like me, were natural inheritors of our ancestors’ mathematical legacy. At an even more fundamental level, even wh...

According to the Encyclopaedia Britannica, the Eye of Horus is a symbol of mythological significance, originating in a story in which the Egyptian gods Set and Horus clashed, and Set damaged or destroyed Horus’ eye. The eye was later restored by another of the gods (according to Wikipedia, most often Thoth, though the Encyclopaedia Britannica says Hathor); as a result, the Eye of Horus took on meanings of health and restoration. In fact, the association with health may have been so strong that the image has been passed down to the modern day: according to some sources, the ¼, 1/64, and 1/32 segments of the eye can still be seen today in the Rx symbol, used to denote a medicine prescription. Numerically, it is interesting to note that the fractions present in the eye represent the first six terms in the infinite series \sum 1/2^n. It doesn’t seem like a coincidence that this series sums to 1, given that the Eye of Horus symbolizes wholeness and restoration. This raises the question of w...

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 specif...