Arithmetic of the Medieval Universities

"The very word "liberal" implies that these arts be longed to the education free men not to the technological training of slaves." (pp. 264)

    This quote really helped frame the purpose of Greek education. I never knew this before reading it now, but it makes a lot of sense. Many topics in the liberal arts are those that have little practical usage, and that you don't people who are struggling to make ends meet to study. I think it's interesting that the ancient Greeks explored so many proofs in mathematics as you don't need to prove something works in math if you know how to use it. From the quote, I now know that the people studying these topics were probably very well off and could afford to spend time to think about subjects like this. I sound very critical, but I think these contributions that the Greeks made to mathematical concepts were really important. However, they also sound a little snobbish when they reject subjects such as medicine to be considered a free man's subject because it's something someone would learn out of necessity rather than for the sake of thinking.

"Much of this intellectual activity was centered in the Islamic universities of Spain, and from there learning spread throughout Europe." (pp. 267)

    This quote was said in context of the intellectual revolution in Europe near the end of the Middle Ages. This was around the time the Hindu-Arabic number system was introduced and many texts from the times of the Ancient Greek were translated into Latin from Arabic and Syriac. I thought this quote was interesting because it demonstrates that during the Middle Ages or the Dark Ages, other parts of the world were still making mathematical discoveries. Based off the information I learned in school, I never knew that this was how math was 'reintroduced' in Europe. The entire article that this quote originates from is super interesting to me because usually when talking about the history of mathematics from an Eurocentric perspective, this part of history is glossed over because not many discoveries were made during this time. However, now we get insight into how schooling was conducted during the Middle Ages and how all this attributes to the gap of mathematical discovery, and how math was revitalized during the intellectual revolution.

"Arithmetic was a study of the universities; logistic was not." (pp.266)

    This is similar to the first quote, but I never thought too deeply into what constitutes as arithmetic in the liberal arts. When I hear arithmetic, I think of what is defined in the book as logistic. I think of computations and the mechanical part of math. I thought that was what Greek mathematicians such as Euclid was doing. However, they seemed to have defined arithmetic as the thinking of numbers in the abstract and logistic as the doing with numbers in a more concrete sense. I think this distinction between arithmetic and logistic was important to how we view mathematics now because we almost do a similar thing. In elementary and secondary school, we do computational things with numbers, and in postsecondary if we choose to purse math, we deal with arithmetic, or proofs of mathematical concepts.