The Idea of Pure and Practical Mathematics

Oftentimes we as mathematicians, math teachers and anyone else who enjoys mathematics clearly see the practicality in studying such an abstract language.  I believe that many teachers use word problems in attempt to share and show students their love for mathematics, hoping they can later on transform those abstract mathematical concepts to a more practical use.  For example, rther than teaching the very dry concepts of sine, cosine and tangent, it could be more exciting to link it to the ancient Greek problem of bow hunting.  The idea of sine came from the Greek problem of a bow string at rest versus when it was stretched is interesting.  We then can connect this idea to the common representation of opposite over hypotenuse or y value over the radius. Was this invention a simple practical daily use or for the Greek to advance their pure scientific study such as astronomy?  Likewise, the ancient Babylonian mathematics which has the impression of “merely practical” at the beginning, but the structure of the unknowns is far from practical. Then how can we draw conclusion on which school does Babylonian mathematics belong to, pure or applied?  Therefore, I agree with Robson’s argument that we truly cannot separate math into a dichotomy between “pure” and “applied or practical”.