Many word problems from either Babylonians, Greeks, or modern humans, all contains some degrees of practicality. This is because such problems are presented in a more dialogic form, which is closer to our daily life compared to some more abstract math languages.
The ability to make mathematical language abstract, thus saving brain space for more efficient computations, did not appear until the Greeks. As a result, the Babylonians had to use a single form of discourse to communicate mathematical ideas. The concepts of "pure" and "applied" math were not distinguished during that time.
Whether a word problem is abstract or practical does not rely on our familiarity with contemporary algebra because the purpose of such a problem is clear and self-explanatory. Jens Hoyrup has commented on Babylonian word problems: "as soon as you analyze the structure of known versus unknown quantities, the complete artificiality of the problem is revealed". Unpractical problems were designed to train students in mathematical methods, which then evolved into abstract problems with algebra.
These ideas help us to study the social and pedagogic purposes of word problems at different times, which indicates the development of math discourses.
Good work!
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