Response: More on Babylonian Word Problems

 I enjoyed Susan's perspective on Babylonian word problems being more about exercising methods that the Babylonians had developed rather than for practical problem solving purposes. It gives me a sense that some Babylonians were simply very excited to share what they'd learned! I agree that the presence of infeasible numbers in some of the real-world examples seems to imply that the word problems were more about doing the math and thinking through the process rather than obtaining a solution and using it to do something useful in the physical world. Thinking about the overlap between pure and applied mathematics made me consider the occasional times where I've applied some of my math knowledge outside of the classroom. Whenever this happens, it's often because I see something with potentially interesting combinatorial structure and ponder what questions I could ask about it. Then, I try to see how I can use the methods I've learned to answer these questions, usually about how many different ways there are to arrange some group of things. For examples like these, I'm doing the same process of seeing places where I can do math for the sake of doing math rather than truly needing the answer to some question for a practical reason and then using math to give me the solution.

I was also fascinated by Høyrup's suggestion that Babylonians did lots of word problems because they didn't really have any other "non-applied" ways to exercise these methods, since no formal system of algebra was around yet. I'm reminded of the questions we've seen about solving for the side length of a square where you are given a sum in terms of its side length and area (which are really just about solving quadratic equations.) I think it's interesting that what would normally be expressed as simply an algebraic equation nowadays had a much more geometric interpretation back in Babylonian times through these word problems. While they may not all be extremely practical, I still think that word problems are quite useful in getting students to be problem-solvers and think about ways in which they might be able to apply what they've learned in different areas.