A comment on an answer I posted asserted that "Mathematics is NOT always about counting".
My thoughts were that if there's a unit (inches / milligrams / light years etc), then someting is being counted.
An exception would be if you're describing something within maths/arthimetec itself like the concept of 2+2=4. That defines itself without needing units, but only makes a statement about itself.
So my question is: When is mathematics NOT about counting something ?
EDIT: Just to be clear, We have discrete data like the number of people in a room, or continuous data like number of miles to the nearest curry house (a measurement, ideally very small in this case).
My intention with the question is that both are "counting" - discrete data is hopefully obvious and continuous data is, I would say, still "counting" in that your'e couting a number of miles (etc).
So i'm not talking about the difference between discrete data and continuous. I'm asking more whether/when mathematics does not refer to something in the (or a) 'real' world. Having thought further about it, I think I mean "when are there no units?"
E=mC^2 has units, or a type of unit:
E=Energy = watts/calories/whatever
m=Mass = kg / lbs etc
C = speed of light (mph etc)
So to arrive at that through some presumably tricky maths, was there ever a point where a formula didn't have a unit of some sort ?