From where I happen to stand, I see four camps or so:
I have no doubt that there are more ways to segment people in terms of how they view math, then the simple model I mentioned. That just happens to be the divide that I feel like I see most commonly and that often leads to fruitless discussions.
they replied that anybody who does mathematics is a mathematician.
The problem with that is the definition of "doing mathematics". And that's where I see the divide I mentioned above. Some people would consider "finding the derivative of f(x) = x/x^2 to be "doing math" whereas other people say that's "mere computation" and think of math only as things like "proving why the derivative of f(x)=x/x^2 is $WHATEVER".
I suppose one might say the former is "using math" where the latter is "doing math", but in popular usage it seems like people freely intermix those notions, and people who feel strongly about it one way or the other get their knickers all wadded up over it and hilarity ensues.
I have no doubt that there are more ways to segment people in terms of how they view math, then the simple model I mentioned. That just happens to be the divide that I feel like I see most commonly and that often leads to fruitless discussions.
they replied that anybody who does mathematics is a mathematician.
The problem with that is the definition of "doing mathematics". And that's where I see the divide I mentioned above. Some people would consider "finding the derivative of f(x) = x/x^2 to be "doing math" whereas other people say that's "mere computation" and think of math only as things like "proving why the derivative of f(x)=x/x^2 is $WHATEVER".
I suppose one might say the former is "using math" where the latter is "doing math", but in popular usage it seems like people freely intermix those notions, and people who feel strongly about it one way or the other get their knickers all wadded up over it and hilarity ensues.