Practicality vs. Abstraction

The big picture of pure mathematics has emerged in my mind since I started pursuing my master's degree in mathematics. It was the first time that I encountered the world of “symbol” in abstract algebra, mathematical analysis, and especially classic geometry which is totally different from the geometry I knew in my secondary school. After that period of time, the boundary between pure mathematics that I learned in graduate program and applied mathematics that I learned in undergraduate program became clear. However, the history of Babylonian word problems brings me a brand-new perspective on the idea of pure and applied mathematics, illuminating the era before the bloom of modern symbolic algebra and re-establishing an ambiguous connection between “pure” and “applied” instead of drawing a dichotomy between two realms.

According to Jens Hoyrup’s distinction between Babylonian scribal school mathematics and Greek mathematics, we can visualize the trajectory of transformation of mathematics from the applications to the intellectual challenges. Interestingly enough, many second-degree problems in Babylonian problem texts appear to be sublimated from the real-world problems. Therefore, Assyriologists like Eleanor Robson and Jens Hoyrup keep implying the significance of the deliberately ambiguous view of ancient mathematics. 

Back to our teaching practices, we can use the history of Babylonian word problems to reflect on our use of word problems in mathematics. By educating our students with word problems originating in real-world concerns, students are equipped with methods. Meanwhile, we should also provide an understanding of those methods by extending word problems.