A History of Mathematics Blog by Tim

  " The Greeks were concerned with the  education of free men as future citizens." This quote is interesting in the way that it shows the way Greece valued education, but also how it was only available to men and to citizens. Because ancient Greece has been so influential in western culture, those inequities continued to perpetuated even in recent times and still continue to today. We need to be asking ourselves how we can decouple our education system from socio-economic statuses.  " Towards the end of this period, the  Hindu-Arabic number system was be  ginning to be known in Europe." This quote reminds me of how much math migrated into Europe from places other than Ancient Greece. Because I was taught such a Eurocentric and Greekcentric mathematics history, I never learned how so many ideas from India, China and the Arabic world flowed into Europe and lead to so many European mathematics ideas. "Th e student  had simply to swear ...

  In the poem Euclid Alone has Looked on Beauty Bare by Edna St. Vincent Millay, she is arguably defining beauty as geometric proofs. Euclid certainly defined his geometry with precision, clarity and simplicity that is regarded by many (including myself) as beautiful. However, I do not agree that Euclid was alone in seeing this beauty as he based his work on those who came before him (especially Eudoxus), and many have came after him who have even expanded upon his work.  Moving past the idea that geometrical proofs are the purest form of beauty which is certainly debatable, the poem in general seems to fall into the "great man fallacy". This is the idea that history is defined by specific great people (usually men) who alone contribute to the advancement of ideas, science and societies. While many specific individuals have contributed important and influential ideas, the fallacy often ignores the other factors that lead to those ideas. Even the greatest mathematicians a...

Both the video and the paper on "Dancing Euclidean Proofs" brought several interesting ideas to light. The notion of embodying mathematics is not one that I have encountered before, and it certainly provides new ways to engage with math. In particular, I found their discussion about the differences and similarities between constructing proofs with pencil and paper compared with using bodies. While I immediately recognized the imagination and simplification that is required when embodying the proofs, it was helpful to be shown how those same elements apply to a proof drawn on paper. The points we draw aren't infinitely small, the lines we draw don't extend infinitely, and the circles we draw definitely aren't perfect circles! In both cases of embodiment and 'empaperment' (is that a word?), we are simply representing abstract ideas in a concrete way. This limits how "exactly" we can show these abstract ideas, but both methods encapsulate the concep...

  This article brings up several interesting ideas and expands the history of math significantly from what most of us have grown up with. As we as are culture slowly starting to recognize the importance of representation in the media we consume, but the conversation around representation in our education system seems to be still developing. In math classes, we have the opportunity to vastly expand the scope of our students' mathematical role models and historical figures beyond the 'traditional' Greek and European people.  Many theories are named after the Greek or European thinkers who popularized them in that particular area of the world. I think it's still important to teach students those names for the theories so that they can understand, and communicate well with, mathematicians throughout the world. However, finding other thinkers from other ancient cultures and associating their names with those theories as well broadens students' learning and possibly allow...

Perhaps the most straightforward answer to whether the Eye of Horus is mathematical, mystical or medical is yes... all of the above, but diving into the interesting relationships between the three leads to some fascinating discussions around this ancient civilization.  The symbol gets its name from a mythical figure: the god Horus, son of Osiris and Isis, so it ties in to the mythological culture central to ancient Egypt. It also has been linked to several unit fractions with denominators that are powers of 2; this links it as well to the mathematical ideas originating out of this area of the world at that time. Finally, it is also thought to represent the senses as they were know to the ancient Egyptians (smell, sight, thought, hearing, taste, and touch) and mysteriously matches quite well with modern anatomy's understanding of the structure of the human brain, linking it to the ancient culture's understanding of medicine and anatomy.  The different parts of the symbol are th...

While much of this class has been spent looking at very different ways of writing and solving math problems, researching and working through the problems related to the volume of a pyramid opened my eyes to some of the similarities between ancient and modern ways of conceptualizing mathematical problems. One similarity that fascinated me was the cross-cultural relevance of geometric reasoning. Though it was often difficult in past lessons to wrap my head around the Babylonian sexagesimal system, the geometric reasoning from Lui Hui (the mathematician from ancient China) was reasonably straight forward to understand.  For me, this reinforces the importance of trying to find simple geometric ways to demonstrate solutions for future students instead of relying only on algebraic solutions. As math teachers we will be teaching students the 'language' of math, which certainly includes algebra, however understanding that many of our students not be 'fluent' yet, we need to loo...