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...