This ‘key-value’ thing is so true in my experience — speaking with anyone who has no mathematics education beyond the mandatory years, it’s clear that almost everyone thinks of it being a subject of classification and naming rather than understanding and exploring. The standard example of ‘the sort of thing mathematicians do’ probably begins with a recital of the quadratic formula or Pythagoras’ theorem (invariably stated simply as ‘a^2 + b^2 = c^2’, as if each of these symbols has specific mathematical meaning on their own), or perhaps a statement about which triangles are considered ‘isosceles’ or ‘scalene’.
The most common view of mathematicians seems to be that of a slightly more general stamp collector who likes collecting and giving needlessly complicated-sounding names to things.
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This ‘key-value’ thing is so true in my experience — speaking with anyone who has no mathematics education beyond the mandatory years, it’s clear that almost everyone thinks of it being a subject of classification and naming rather than understanding and exploring. The standard example of ‘the sort of thing mathematicians do’ probably begins with a recital of the quadratic formula or Pythagoras’ theorem (invariably stated simply as ‘a^2 + b^2 = c^2’, as if each of these symbols has specific mathematical meaning on their own), or perhaps a statement about which triangles are considered ‘isosceles’ or ‘scalene’.
The most common view of mathematicians seems to be that of a slightly more general stamp collector who likes collecting and giving needlessly complicated-sounding names to things.