Word Problems

  Throughout my studies in the field of Mathematics (especially in high school), word problems is used to check if we can “apply” what we learnt in a situation. The interpretation of “practical” changes as I study higher level of Mathematics. With regard to the reading, my interpretation of “practicality” is that it has to be realistic. While the “ abstract” problems are those with unrealistic measurements. An example of that would be the Babylonian grain-pile problem. Today’s definition of “applied” is no longer limited to the possibility of using it in daily life, but the possibility to use it in different fields of study to advance technology. On the other hand, “pure” Mathematics is seen as “invented” math for people who study it for the sake of studying it; which is equivalent to Hoyrup referring Babylonian’s “pure Math” as art pour l’art.

 

I believe our interpretations on the above definitions are heavily influenced by the Math we have studied since we were a child. We learn about the math and we were given word problems to demonstrates how do the math we learn is applicable. As a result we acknowledge those are applied math. While pure Math are things that come out of “nowhere”. However, now it invites the question “ what if the reason we called those math “pure math” is simply because human science has not caught up with the hypothetical math?”. If one day some scientists discover a way to use non-Euclidean geometry does it now make it “applied math”? On the other hand, we can also argue algebra is “invented” to model the world. For example, kinematics equations still work the way they do without actually mapping to a real situation. My point is, if we look at all types of math in a vacuum, are they all abstract? I know I am a bit all over the place here with questions I don’t have answers to, but this is how this article led me to think about the idea of “pure math” V.S. “applied math”.

Okay, time to gather my thought here on Babylonian word problems. In general, I thinking my idea of abstract Mathematics is very different than how it is interpreted in the Babylonian word problems. In order for a Babylonian word problems to be practical, not only the situation has to be “real life” but the quantity involved also has to be realistic. I do not have this perception because throughout my studies in mathematics, the measurements or numbers given doesn’t have to be as long as the situation itself is relatable. Refer back to the reading “Old Babylonian mathematics is ‘pure’ in substance, it remains applied in form”, however for us today, the substance doesn’t affect the idea of “pure” or “applied”.