Trivium and Quadrivium

"The Arithmetic of the Medieval Universities" by Dorothy Schrader was enlightening. Here are 3 points that stood out to me:

“Arithmetic was a study of the universities; logistic was not.” (266) The difference between arithmetic, as number philosophy, and logistics, as sensible numeration, was surprising. I wasn’t expecting that contrast between the two topics, especially in consideration of their present day unity. In terms of the evolution of mathematics, this is quite interesting because while the operations, theorems, and proofs withstand the test of time, certain vocabulary/notation, branch classification, and societal significance have changed quite a bit. 

“Jordan[us Nemorarius] treats of nine operations: numeration, addition, subtraction, duplation, multiplication, mediation (finding the mean), division, progression, and extraction of roots. About two-fifths of the work is devoted to fractions.” (271) I was immediately taken aback seeing mediation as one of the nine mathematical operations; mediation involves both addition and division, so I’m not sure how or why it counted as an operation, as yet. That said, I thought it was interesting to see that duplation, progression, and extraction of roots were involved in this list as well. Duplation stood out because it’s an operation I truly would have expected in computer science, rather than math. But, after working with the Egyptian method for multiplying by doubling and halving, I can see why this would have an appearance. And, just as a side point, I found the author’s note that “[a]bout two-fifths of the work is devoted to fractions” highly amusing. 

Lastly, this excerpt (on page 273) was absolutely fascinating! I totally took that multiplication symbol for granted, never questioning why, how, or when it came to be. That humble symbol’s constant presence doesn’t even allude to its history and its foundational purpose, nor how transformational it has been throughout math. Since the article wasn’t definite on the actual origin, I took a small tangent to do some deeper-digging on Robert Recorde, and turns out he had (also?) invented the = sign *mind blown*. A few clicks later, and I was scouring the internet for the history of mathematical notation- though this wasn’t directly in the article, that point stopped me in the middle of reading to find out more. (During this search, I stumbled on the Egyptian notation for addition and subtraction as a pair of legs walking, and I think this would be really nice to introduce to young students that are starting to learn about the number line and integer operations.)