Reading for Sep 23

 It's an interesting exercise to try to imagine how general mathematical statements could be made without the use of algebra. I suppose the Babylonians use algebra implicitly in their statements, but discuss the relationships between quantities. Moreover, it almost feels like dependencies and relationships in Babylonian mathematics are almost parametrized by a time variable, t. When we write a mathematical statement with algebra, while it still reads left to right, it its on the page as one singular statement. Babylonian statements about math tend to read more like algorithms, or a series of steps (like example 4.8 in the handout).

I think that math is about whatever you decide to make it about. Without wanting to get too philosophical about it, statements about logic "exist" in a sense, and they'll be true or false. Our use of such statements and our exploration of mathematics is really what we make of it. For the Babylonians, it seems as though it's supposed to be practical. Perhaps in due time they would have developed further tools to explore the concepts of algebra and abstraction, as there was clearly an academic inclination study such topics.

One area of mathematics I think would be interesting to discuss without the use of algebra would be graph theory. If instead of using algebra, we simply discussed the relationships that different vertices have with each other, we could perhaps open up the world of graph theory to students who have yet to develop the algebra skills necessary to study the subject. For example, as is suggested in the name, the handshaking lemma can be explained not only with a simple drawing on the board, but by telling a story about how people might shake hands at a party.